Roulette Probability Made Easier
By Kon-Fu-Sed
For the VLS forum members
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
Table of contents:
* Preface
* Uncertainty ... or?
* Probability
* Independent spins
* Three results events - Intro
* All three-results events - Part 1
* All three-results events - Part 2
* Rare events
* Hitting the second or third trial
* Missing the first trial
* Increasing the probability
* Calculate a chain of trials
* More on chains
* Mixed chains
* Deviation from the average
* The standard deviation - Part 1
* The standard deviation - Part 2
* Recorded results
* Fair empirical studies
* Math vs. reality
* Checking my claims
* Favorable situations - Part 1
* Favorable situations - Part 2
* ... where are they?
* It will even out in the long run
* The wake-up
* Misdirected intuition
* The end
* PS - Hit or win
* PPS - Misdirected intuition; a classic
* Appendix - The files
* Appendix - Table #1
* Appendix - Table #2
* Appendix - Table #3
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
Preface
Before you start reading, I'd like to point a few things out...
* On a personal level:- English is not my first language. I have spell-checked the text but those programs don't know that I mis-spelled "whole" as "whale", for example. Also they can't tell if I have chosen or inflected words correctly. Point me at any peculiarity and I'll correct it. Thanks.
- I'm not a teacher. I have never been. In this article I have tried to be as clear as I possibly can be, starting with the very, very basics and advancing from there in a slow, slow manner so everyone can follow - the advanced math in these cases are not really advanced at all. And as I REASON you through most of it instead of handling complicated formulas, I really hope I have explained everything in a clear and concise way.
* On a contents level:The text doesn't express my personal
OPINION or something.
Everything I write is the accepted way to calculate general probabilities and roulette probabilities in particular.
Although many have tried to prove this way wrong during the centuries roulette has existed, no one has so far been able to do it. Not one single person!
Not logically. Not mathematically. And not empirically given a sample-size of significance.
Not anyone.
Not ever.
(
That I know of.)
The below is not what
I THINK is correct; it is not an
OPINION.
It is the consensus and -
so far - it's accepted as correct among mathematicians and other serious researches in gambling and probability theories. But it's still
theories - not laws.
It is however theories that are proven by empirical studies of the real world.If anyone throughout the centuries had really proven the math, the logic and/or the results of empirical studies to be wrong, the math-world (and in reality our whole world) wouldn't be what we today experience. And if someone in the future proves it, they are in for a Nobel Math Prize - at the very, very least.
So if you think I'm wrong I am willing to discuss it - if you FIRST prove your claims. And I mean prove - not the usual "I have seen..." or "I know..." thing.
A proof is
not a few visits to the casino where you've seen some phenomenon. A proof is something
anyone is able to replicate
anytime on
any random sample of
at least the same size as yours, and have approximately the same results as you have. Every time. Any time.
If you think I'm wrong; please remember: You are not only suggesting that I'm wrong; you're suggesting that fundamental probability math and the mathematical society as a whole is wrong.
So show your proof before you start a debate, please.
(I show you mine...)* On a reader's level: You will need a few things before you start...
+ A calculator for the four rules of arithmetic and also for Square Roots.
+ Basic math knowledge to the level that you understand and are able to handle and solve fractions like: (4/37)+(12/37)x(18/37)+(7/37)/(12/37), at least on your calculator.
+ Basic knowledge of the square-root is also recommended when we do a bit more advanced calculations. (It's necessary that you at least can handle the Square Root
key on your calculator...)
+ A little more than half a brain as A LOT (all of it, in fact) is based on very basic logics... logics that will seldom be spelled out but is there all the time, in the background. All the time...
+ An attention-span that lasts for a bit more than just a few paragraphs. However this post is one of the longest ones...
* And on the wheel-level:Everything in this text is for single-zero wheels.There are
37 numbers. For
double-zero wheels you have to remember that there are
38 numbers and thus change all "37" to "38" when you calculate and take
ZeroZero into account at all times. Otherwise the results will be skewed beyond recognition and the total will not be 100%. Not only does it give you trouble math-wise: Because there's ZeroZero there are
lower probabilities for everything - it is "
1 / 38" instead of "
1 / 37"...
Avoid such wheels if you can.I hope you will enjoy the reading.In the title I stress "easi
er" because it is not easy to understand - but not THAT hard...
And learn at least something new.
If you do; I'm satisfied.
I am aware that it's a looong text with lots of (
simple) math involved - and you should be aware of that fact too. But I have been trying to write in a light way and in very small doses so I hope I can keep your interest to the end.
The best for you, I think, is to read this in the small portions I post it and
digest and recapitulate each part before you go on.
What you actually learn is worth a lot more than the quantity of words you just read...
And what you learn here can be worth money - saved money.
/KFS
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
1. UNCERTAINTY ... or?
... Hmmm ...
...
No...
Probably I shouldn't begin with
probability at all, but with
CERTAINTY.
Roulette certainty.Yes.
So I ask you this question:
Can you tell me if there is
any event in the game of roulette that is
a certainty and that also can be shown to be,
without a doubt, a certainty?
Preferably mathematically.
.
.
.
There are TWO (or, rather three):
The FIRST is if you don't make any bet at all...
- Ridiculous!
- No, not at all: It is a certainty that you cannot hit any number at all. Absolutely certain. Isn't it?
- Well, yes. But how, then, is that certainty shown mathematically?
Look at it this way: There are 37 numbers and you bet 0 numbers. You bet, or "cover", 0 numbers of 37.
0 / 37Enter that into your calculator and what's the result?
0 Zero
Meaning: No, Zero, 0% chance to hit ANY number. That is certainly a certainty.
(Show me the casino that will give you chips when you bet nothing...)To hit a number when you bet nothing is a 0% chance and a certainty that you don't.
Is there anything that can make you win...? No. It is absolutely a certainty.
And the calculator showed you the probability for you to hit a selected number: 0.
A probability of 0 is the same as certainty that something will NOT happen.The SECOND event is when you cover all 37 numbers.
Then it is, of course, a certainty that the winning number will be one that you cover.
And you can look at it this way: You cover 37 of the 37 numbers of the wheel.
37 / 37Enter that into your calculator and what's the result?
1This "1" says that you have 100% chance to hit the winning number. And you will of course, if you're betting every number there is, 37 of 37 possible.
(We usually multiply the result of a division by 100 and talk about per cent, so the "1" in this case becomes "100%" just as 0.25 becomes 25%)To hit a number when you cover every one is a 100% chance and ALSO a certainty.
Is there anything that can make you miss...? No. It is absolutely a certainty.
A probability of 1 is the same as certainty that something WILL happen.Now to the THIRD event and that's a little special because it's the event that has ALREADY happened:
Past results.Statistics, actually. But often involved when discussing roulette math. (More on that later)
You look at the marquee or your collection of spins and you see a "
25" there.
That "
25" was the result of that spin at that time at that table. Is there any doubt about that result? Could it be something else?
No, of course not (
logics!).
So that is one result, "
25", and there can only be one result - it cannot be "4" in some other situation, can it?
The PAST result "25" is 1 result out of 1 possible.
1 / 1Enter that into your calculator and what's the result?
1This "1" says that it is a 100% chance that the "25" WAS the hitting number at that spin. And of course it was.
Past results most certainly are certainties.
Is there anything that can make it change...? No. It is absolutely a certainty.
A probability of 1 is the same as certainty that something HAS happened.Or, as we saw before, WILL happen,
whichever happens first...So now we know this about
CERTAINTY:
It can be
0 or it can be
1 in figures, on the calculator. Or
0% or
100% in words.
And nothing in-between.Usually, when we talk about past spins we talk about
STATISTICS.
Statistics are certainties because it reflects events that
have already happened and thus cannot be changed.
It is a certainty that it HAS happened.
But...
Will it happen again?? Do we know??
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
2. PROBABILITY
SO ... let's talk about ... <drum-roll here> ... UN-certainty!
Uncertainty. It may happen or it may not happen. Maybe it will happen... It will probably happen... Or not.
Probability.Now, we do play the roulette, so why don't we place a chip somewhere?
So you place it on a single number - the "13".
What's your chance that the result will be exactly that number? That you hit?
There are 37 numbers and you cover one. No more and no less. 1 number of 37.
1 / 37If you enter that into your calculator you get the result
0.027027027027Multiply by 100 and you get 2.7027027 which is the percentage.
2.7%Likewise, if you place your chip on - for example - the double street 1-6, you cover six numbers. No more and no less.
The chance that you will cover the the result will be 6 / 37 because you cover six numbers. Out of the 37 possible.
And
6 / 37 is 0.162162162 or in other words
16.2%Last let's look at the RED (or Black, Low, High, Even, Odd) numbers.
If you count them you'll find there are 18 in total and therefore, if you place your chip on Red, you cover 18 of the 37 possible numbers.
18 / 37 is 0.486486486 or
48.6%The chance that the result will be your selected number(s) is obviously increasing by the increasing number of numbers you cover.
And of course it is - the more numbers you cover the closer you come to certainty that is 37 covered numbers (or 37 / 37 or 100%).
36 numbers are as close as you can get, without betting all, and it is 36 / 37 or 97.3%.
- Hey! There is, then, a risk of missing the number!
- So...We are UN-certain now, are we? We are not 100% sure we will hit with our 36 numbers.
And that UN-certainty is
1 / 37 or 2.7%.
The chance for 36 numbers to hit is
36 / 37 (97.3%) and to miss is
1 / 37 (2.7%) because there is only one number we haven't covered.
We cover 36 numbers with a 36/37 chance to hit and a 1/37 chance to miss.
We cover 36 numbers with a 97.3% chance to hit and a 2.7% chance to miss.
Add them together and you get
37/37 or 100% -
certainty.
And that's correct: You know for certain that you will either hit or miss your numbers
(that's logics!). Or? Can there be anything else? No. Of course not.
Once again we have seen that 37/37 or 1/1 or 100% means certainty.And this is what we do when we deal with chances and probabilities:
We do "
Reality Checks" to see that all chances to hit and all chances to miss added together equals 100%, is a certainty.
If it's not 100% there is something wrong in our calculation, because we cannot hit AND miss in neither less nor more than the bets we actually do. Of course.
If we hit in 60% and miss in 30% -
what will happen in the other 10%?
Or if we hit 60% and miss 50% -
where did the extra 10% come from?
Reality Check = 100%.Always. That's for certain.
Now you know how to calculate the chance (probability) of a hit on the next spin.
And I have already given you a clue on how to calculate the chance of a miss...
As the chance to a hit, covering 36 numbers, is
36 / 37 the chance of a miss must be
1 / 37 as the sum can only be
37 / 37 = 100%So the chance of a 6-number bet to miss has to be
(37 - 6) / 37...
The parenthesis show you the trick: Subtract the
known figure (the numbers you cover, in this case) from the total (37) and you get the chance of the other (the uncovered numbers, in this case):
31 / 37 or 83.8%And the same for Red:
(37 - 18) / 37 = 19 / 37 = 51.4%To prove that it is mathematically correct we do our "
Reality Check" and add the hit-% to the miss-% and we should end at 100%.
Do we, in these examples?
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
3. INDEPENDENT SPINS
And so you know how to calculate everything regarding ONE bet,
but only one...
This is valid no matter what, really.
As long as the wheel and ball are fair and the dealer doesn't aim for certain parts of the wheel (
with more success than random) it is valid.
Because the wheel
cannot remember any past results and
cannot influence any future ones and - most important -
all 37 numbers are there each and every time so the chance is equal for all numbers in all spins. Always.
We talk about "
Independent trials" - each trial has the same probability every time and is, in reality, not dependent on any past results.
Some people claim that because their selected bet hasn't turned up for so-or-so long time, it is "
due". But think about it
(logics now):
How can the ball or wheel have any influence whatsoever on the result?Do they discuss the matter:
"Red hasn't come for 20 spins so now we have to make it hit!"
"No, the number 24 hasn't hit since we opened - it is really
due to come now."
?If this was the case, empirical studies over significant sample-sizes would have shown that, many, many moons ago.
A lot of people,
myself included, have tried endlessly to find proof by studying recorded roulette-spins.
None have so far, to my knowledge, found any evidence. Unfortunately.
(But a lot more on empirical studies later)
So the theory of "
Independent trials" is here to stay - at least for a while longer. (Quite a while, I'd think but it IS a theory...)
And this is important, as the rest of this article is based on that phenomenon -
that the wheel and ball can NOT influence future results by themselves.
If you think they can, you shall know that I can see your point if you say that mathematics is BS in roulette (you can't think both are correct):
If the wheel has decided to select a certain number to hit,
no math, as we know it, can be used. We have to have a way to quantify or "parameterize" the
mood of the wheel. And we haven't...
I mean... What if the wheel all of a sudden doesn't care? Or is absent-minded and forgets which number was due? Will the ball be in charge???
As long as there are no formulas including such, we have to cope with the math as it is.
And as I said:
No empirical studies, over significant sample-sizes, has ever shown the probability theories or the math wrong. Ever.But please; read on even if you think future results are influenced in any way by the past - maybe you will learn something you have use for, in the future...?
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
4. THREE-RESULTS EVENTS - Intro
Now, I will use a lot of fraction-math here.
The reasons are that fractions are EXACT and clearly show relations. In only a few cases a decimal-number is not needed to be rounded when divided by 37.
To show the hit-probability for a 6-number bet we can use two ways:
p = 6 / 37 (this is exact)
or
p = 0.162162162 (this is rounded) or 16.2% (this is even more rounded)
The first example entered into a calculator gives the second as the result.
The first example also tells us the EXACT RELATION: It is 6 (somethings) of 37 (somethings).
The second example lacks that exact information. It could as well be 16,216,216,211,199,999 of 100,000,000,000,000,000 because it's rounded.
And rounding is bad especially if we start getting really small figures - the rounding errors will cause us trouble in the long term.
I will use the fraction notation a lot, not so much the decimals.
Now let's focus on THREE RESULTS...How many combinations are possible?First you have to take every number 0 - 36 and combine them each with every number 0 - 36 and so you have (
37 x 37) 1,369 combinations. This is for two results.
Now combine each and every one of those results with all numbers 0 - 36 and you end up with (1369 x 37 or
37 x 37 x 37) 50,653 three-numbers sequences.
(Did you really do it?)For three results we have
50,653 combinations and there are no more possible to find. And there can't be less, either, if we want them all. 50,653... This is
100% of all there are.
But we cannot use 50,653 series to show math and probability in a clear way. That's impossible. So first of all we will call those combinations the "
Low-Level" combinations. They really are on the lowest level - single numbers.
LL combinations.
50,653 of them...
I could, of course, use only Red and Black for example - excluding the Zero - but that wouldn't be
fair. The calculated probabilities wouldn't be true, because it's a simplification.
And it wouldn't be roulette - more like coin-tossing.
And this is about
roulette probability.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
5. ALL THREE-RESULTS EVENTS - Part 1
So we have to use a middle-way - please take a deep breath and hold on to your hat.
Here we go:We will use "
High-Level" (
HL) combinations: the "even" bets
Red and
Black, that each have a 18 / 37 probability to hit PLUS the
Zero that has a probability of
1/37 to hit.
We will use combinations like "
R-B-B" or "
R-0-0" or "
0-B-R" or... you understand, I guess.
Red + Black + Zero =
(18/37) + (18/37) + (1/37) = 37/37 = 100% = Nothing missing.
This will bring down the amount of combinations considerably; from 50,653 "LL" to
27 "HL".
That is because every
HL combination in reality contains more than only one of the
LL-combinations.
Let's find out how many.
And don't even think about skipping this section - it is VITAL that you KNOW this later!We can check this one for example: "
R-R-R".
In this group you will find...
1 1 1 1 1 1 ... 16 16 16 18 18 18 ... 36 36 36 36 36 36 <--- All the 18 red numbers combined with...
1 1 1 1 1 1 ... 36 36 36 1 1 1 ... 36 36 36 36 36 36 <--- ... all the 18 red numbers combined with...
1 3 5 7 9 12 ... 32 34 36 1 3 5 ... 25 27 30 32 34 36 <--- ... all the 18 red numbers
Each "R" is in reality 18 numbers so what you have to do, to find the number of possible combinations, is to multiply 18 by itself three times (
18 x 18 x 18) = 5,832.
This is the same calculation you did to find how many possible combinations there were using ALL numbers - you multiplied 37 by itself three times.
That was three groups of 37 numbers, now you have three groups of 18 numbers.
18 x 18 x 18. OK?
This particular
HL combination contains
5,832 LL combinations of the possible
50,653.
Another group is "
B-R-B" in which you will find...
2 2 2 2 2 2 ... 17 17 17 20 20 20 ... 35 35 35 35 35 35 <--- All the 18 black numbers combined with...
1 1 1 1 1 1 ... 36 36 36 1 1 1 ... 36 36 36 36 36 36 <--- ... all the 18 red numbers combined with...
2 4 6 8 10 11 ... 31 33 35 2 4 6 ... 26 28 29 31 33 35 <--- ... all the 18 black numbers
Is there a difference in numbers if the three are "
B-R-B", compared to "
R-R-R"?
No, each group have the same
18/37 chance each to hit so this
HL combination also contains
5,832 LL of the 50,653.
In fact:
ALL HL combinations that contains only
R and/or
B is the same. Here they are:
R-R-R (18 x 18 x 18 = 5,832)
R-R-B
R-B-R
R-B-B
B-R-R
B-R-B
B-B-R
B-B-BThere are 8 of them so they together contain 8 x 5832
= 46,656 LL combinations.
Reality Check: 50,653 - 46,656 = 3,997We are
missing 3,997 combinations!
Where are they?
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
6. ALL THREE-RESULTS EVENTS - Part 2
This is roulette. There is a
ZERO also!
"
R-R-0" - there is a
HL with a
Zero. In this group you will find:
1 1 1 1 1 1 ... 16 16 16 18 18 18 ... 36 36 36 36 36 36 <--- All the 18 red numbers combined with...
1 3 5 7 9 12 ... 32 34 36 1 3 5 ... 25 27 30 32 34 36 <--- ... all the 18 red numbers combined with...
0 0 0 0 0 0 ... 0 0 0 0 0 0 ... 0 0 0 0 0 0 <--- ... the Zero
How many
LL combinations does it contain?
Red (and Black) is 18 numbers and Zero is... well, only
1 number of the 37.
So the calculation is:
18 x 18 x 1 = 324. Each one of those
HL that contains one (
and only one) Zero contains
324 LL of the 50,653 possible combinations.
Another group is "
B-0-R" and there you will find:
2 2 2 2 2 2 ... 17 17 17 20 20 20 ... 35 35 35 35 35 35 <--- All the 18 black numbers combined with...
0 0 0 0 0 0 ... 0 0 0 0 0 0 ... 0 0 0 0 0 0 <--- ... the Zero that is combined with...
1 3 5 7 9 12 ... 32 34 36 1 3 5 ... 25 27 30 32 34 36 <--- ... all the 18 red numbers
And all those "
one-zero" groups are:
R-R-0 (18 x 18 x 1 = 324)
R-B-0
B-R-0
B-B-0
R-0-R
R-0-B
B-0-R
B-0-B
0-R-R
0-R-B
0-B-R
0-B-BThere are 12 of these so they altogether contain 12 x 324 =
3,888 LL of the original 50,653.
Reality Check: 46,656 + 3,888 = 50,544 - still not 50,653
Still missing some...
There are also HL combinations with
two Zeros like "
0-B-0" in which you will find:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 <--- The Zero that is combined with...
2 4 6 8 10 11 13 15 17 20 22 24 26 28 29 31 33 35 <--- ... all the black numbers combined with...
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 <--- ... the Zero
That's all: 18 combinations in this group. It has only 1 result with 18 numbers but two with only one number (the Zeros).
Therefore the calculation is:
18 x 1 x 1 = 18 for all such groups.
And they are:
R-0-0 (18 x 1 x 1 = 18)
B-0-0
0-R-0
0-B-0
0-0-R
0-0-B
6 of them, each having 18 combinations, give 6 x 18 =
108 LL.
Reality Check: 46,565 + 3,888 + 108 = 50,652.100% = 50,653.
ONE is missing!
This one: "
0-0-0"
As it is only one number in each result the calculation is quite simple:
1 x 1 x 1 = 1
And there you are:
27 HL combinations containing each and every one of the
50,653 possible LL.
And this is the complete table, showing how many each contains and their probability to hit:
B-B-B - 5,832 p = 5832/50653 = .115136 (11.5%)
B-B-R - 5,832
B-B-0 - 324 p = 324/50653 = .006396 (0.64%)
B-R-B - 5,832
B-R-R - 5,832
B-R-0 - 324
B-0-B - 324
B-0-R - 324
B-0-0 - 18 p = 18/50653 = .000355 (0.036%)
R-B-B - 5,832
R-B-R - 5,832
R-B-0 - 324
R-R-B - 5,832
R-R-R - 5,832
R-R-0 - 324
R-0-B - 324
R-0-R - 324
R-0-0 - 18
0-B-B - 324
0-B-R - 324
0-B-0 - 18
0-R-B - 324
0-R-R - 324
0-R-0 - 18
0-0-B - 18
0-0-R - 18
0-0-0 - 1 p = 1/50653 = .00002 (0.002%)
---------------
Sum: 50,653 = (
37 x 37 x 37) = Correct
I will refer to this table
a lot later and therefore it is VITAL that you understand what each group contains.
Please recapitulate if you are uncertain of anything...
(there is a high probability that you are)
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
7. RARE EVENTS
As each combination in the above table is
three results, the total of results are 3 x 50,653 =
151,959!
- Hey! Why bother to have that
0-0-0? It happens only
once in 152K spins? That's a
rare event if I've ever heard of one! I will never bet 152 thousand times in my life!
- First of all it HAS to be there - without it the table would be incomplete and not be covering 100% of all possible combinations.
Second: That particular combination has
the exact same probability to hit as the combination
25-3-31. You wouldn't exclude that one, would you?
Or any other three-numbers combination? They are all
1/50653 chances.
1-2-3 or
7-34-22 or
36-36-36... All of them are equal - the
0-0-0 is no exception in that context. It's just
painted green on the wheel.
The ONLY reason
0-0-0 is distinguished in the TABLE, is because
25-3-31 is contained
inside the
R-R-B combination and the other examples
inside their respective groups.
0-0-0 doesn't fit anywhere
(it's bullied because it's green!) but it has
exactly the same probability as any other combination.
Why should we exclude it?
Why should we bully any...one?
As a side-note: The
0-0-0 combination doesn't come once in 152K spins, it comes in
1/50653 combinations of three spins, and that's quite a difference. Suppose this sequence of spins:
R-B-
0-0-0-R-B-B-R
There is a
0-0-0 combination, obviously. But then you split the sequence into 3-results events:
R-B-
00-0-R
B-B-R
None of these is a
0-0-0 combination... So the probability to find a
0-0-0 combination in a three-results event is a lot lower (1/3, actually) than simply find it anywhere.
In three-results combinations:
1 in 50,653 COMBINATIONS (times 3 = 151,959 results in total)
Anywhere:
1 in 50,653 SINGLE RESULTS when we treat the results as one looong continual chain.
(Isn't math beautiful?)Also;
0-0-0 has a probability (mathematical average) to happen like 2.16 times a year at a 300 spins/day table.
Maybe,
just maybe, you happen to be there at the time that happens - why not, really?
And you know what they say:
If s**t can happen, s**t will happen.
- But when it hits the fan, probability theory is like having an umbrella.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
8. HITTING THE SECOND OR THIRD TRIAL
OK now. Order in class!
Let's go back to the table.
We saw before that the probability to hit at THE NEXT trial, if we cover 18 numbers, is always
18/37. Now; how about the trial after that? The
second trial? Is it the same probability?
We can use the table for that but first we have to decide where to bet. Let's say we are going to bet
Red.
We also HAVE to check that the
18/37 for the FIRST Red-bet trial is correct:
To do that, you look for all combinations that contains a "
R" in the
first position. Note the number of
LL combinations and add them together:
R-B-B - 5,832
R-B-R - 5,832
R-B-0 - 324
R-R-B - 5,832
R-R-R - 5,832
R-R-0 - 324
R-0-B - 324
R-0-R - 324
R-0-0 - 18
---------------
Sum: 24,642 / 50,653 possible.
24642 / 50653 = 18 / 37. We were correct.
- OK that's fine but what about the second?
- Do the same thing: Collect all combinations where "R" is in the second position.
B-R-B - 5,832
B-R-R - 5,832
B-R-0 - 324
R-R-B - 5,832
R-R-R - 5,832
R-R-0 - 324
0-R-B - 324
0-R-R - 324
0-R-0 - 18
---------------
Sum: 24,642 / 50,653 possible.
24642 / 50653 = 18 / 37. Correct?
And for the third position:
B-B-R - 5,832
B-R-R - 5,832
B-0-R - 324
R-B-R - 5,832
R-R-R - 5,832
R-0-R - 324
0-B-R - 324
0-R-R - 324
0-0-R - 18
---------------
Sum: 24,642 / 50,653 possible.
24642 / 50653 = 18 / 37. Correct?
Yes, it's correct. What we've seen here is that
it doesn't matter if you bet at the first, second or third attempt of three: The probability to hit is
always 18 / 37.
But that's on one IMPORTANT condition: That we have
THREE TRIALS LEFT.
Remember this!
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
9. MISSING THE FIRST TRIAL
- So if we DON'T have all three left... Like, what if I miss the first bet - it's Black or Zero? Then for sure Red will have at least a
little higher probability to hit.
- That's a good question. We will check that.
What combinations can possibly end our three-trials combination AFTER the first trial?
These ones:
B-B
B-R
B-0
R-B
R-R
R-0
0-B
0-R
0-0
That's all there are!
- But what about the first, lost, trial? It isn't there!
- That's OK, I can put it there. It was a non-Red, right?
- Yes.
24.
- OK, here's the table including the number of
LL combinations within each
HL:
24-B-B - 324 (1 x 18 x 18 = 324)
24-B-R - 324
24-B-0 - 18 (1 x 18 x 1 = 18)
24-R-B - 324
24-R-R - 324
24-R-0 - 18
24-0-B - 18
24-0-R - 18
24-0-0 - 1 (1 x 1 x 1 = 1)
--------------
Sum: 1,369 / 1369 possible LL combinations = 100%. Correct.
- How can that be correct? It's not 50,653 as it was above!
- First of all: The
24 is a past spin and is KNOWN. If you remember the beginning of this article; a known result is a
CERTAINTY.
Because it cannot be anything else.
So it cannot possibly be ANY Black or the Zero as it WAS, you said it yourself, number
24...
It was number
24 and it is one number of one possible.
1 / 1. The probability is 100% or
p = 1.
And so, the calculation for the number of
LL in
24-B-B is:
1 x 18 x 18 = 324.
The
Zero is one number out of 37 so for the combination
24-B-0 the calculation is:
1 x 18 x 1 = 18.
Now, this is important that you understand: A
known result is a
certainty and therefore it cannot have any other probability but
p = 1.
The probability to hit cannot be 1/2 or something else. Right? It really
did hit.
I mean; can it be possible that all of a sudden it DIDN'T hit and what will happen then? It was just last spin and it WAS number 24... And now it's ...
No, it can not be anything else but the 24 we saw hit.
A certainty is a certainty and it's 100% sure - no more and no less - so
p = 1.
So, Because we have only
TWO FUTURE events, the total of POSSIBLE combinations is calculated as:
1 x 37 x 37 = 1369.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
10. INCREASING THE PROBABILITY
And your question was...?
Aaah - will the chance to hit Red
increase (
at least a little bit) at the second attempt if the first was missed?
Just look at the table for
[two trials (remember there are only two left in our three-trials series - one, number 24,
is gone and is not in the future) and count the number of
LL in each
HL combination where "
R" is in the
second position.
24-R-B - 324
24-R-R - 324
24-R-0 - 18
--------------
Sum: 666 / 1369 =
18 / 37It's the same old
18 / 37 chance, I'm afraid. And it doesn't matter if you bet Black instead - check the table.
(Of course it is another thing if you bet Zero because it's one single number instead of 18. Can you do the calculation for a 0-hit instead of this Red-hit?)Now, I hope you understand why we have to put "
24" in the beginning of our three-trials combinations.
The "
24" isn't part of "
R-R-B", for example. It IS part of "
B-R-B" (and some others) and if we use them (still calculating the chance for
Red to hit in the
second trial) we would use
B-R-B - 5,832
B-R-R - 5,832
B-R-0 - 324But that would be very wrong as "
B-R-B" also includes
2, 4, 6, 8, 10, 11... - not only
24 - as a start in all its
5,832 LL combinations. And we know that
24 hit - not 11 or 4.
So we have to
eliminate all combinations with another number but
24 in the
first position, to have the correct number of possible combinations in the
TWO REMAINING trials:
1 x 37 x 37 = 1,369.
For the third trial, it's exactly the same: If the second result was also a non-Red,
33 for example, the only combinations that can finish our three-trials series are:
24-33-B - 18
24-33-R - 18
24-33-0 - 1
--------------
Sum: 37 / 37 possible numbers to finish the series.
So for
both Red and Black it is a
18 / 37 chance to hit that last, third, trial after the two first have been seen.
I mean; the end-result cannot possibly be
12-33-1 or
24-12-2 or
11-15-3, can it?
No, of course the end-result must start with
24-33 and nothing else, regardless the last result.
SO, the answer to your question is:
No, the probability does NOT increase if you miss one or more bets.Have you noticed something? Until now, I've only talked about the
NEXT trial.
First, before anything happened, I showed that there is a
18/37 probability for Red to hit at the first trial - the "
next" trial in that context.
Then I showed you that the probability to hit the second trial (the now "
next") is also
18/37 and that is
REGARDLESS if you saw the "
24" or not.
And the same goes for the third trial when it is the "
next": The probability to hit is
18/37. And it doesn't matter if you missed the two first trials or not.
The fact is, that you can
expand this for as long as you like and to any roulette bets you like; the probability to hit at the next trial is always the same:
"
The number of covered single numbers divided by 37".
It's never anything else.
And the risk to miss is always "
(37 minus the number of covered single numbers) divided by 37".
If your calculations are correct, the two results added together equals
37/37 or
1.0 or
100%.
Always.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
11. CALCULATE A CHAIN OF TRIALS
Before, you have learned to how to calculate the probability for ONE trial - now we will calculate the probabilities for a CHAIN of trials.
- Yes! What's the chance to hit three Reds in three trials?
You just have to look in the
three-trials table and see how many
LL there are in the "
R-R-R"
HL. No other
HL group gives you three Red numbers in a row, right?
5,832 LL combinations of the possible 50,653. So the chance to hit ALL THREE is
5832 / 50653 = .115136 or 11.5%
We already did the calculation when we calculated the number of
LL:
18 x 18 x 18 = 5832. Remember?
It's the same for all combinations of only Rs and Bs, for example "
R-B-R" or "
B-B-R" or any other, as long as they don't include any
Zeros.
- So what's the probability to have
one hit in the three trials if we exit right after the hit?
We can do this in two ways:
* The long and tiresome way, or
* The short and quick one
The former includes lots of adding while the latter includes some, but not a lot, of logic and multiplication. And one subtraction.
Your choice...
Joke; I'll do them both.
The logic way: If you don't care
when you hit, during the three trials, and you will be satisfied by the
first hit...
In that case, there is only
one occasion we need to calculate: When you
miss all three attempts.
Think about it: If you don't miss
ALL, obviously you
MUST have hit once...
(logic!)Right?
The probability to miss one trial is
19/37 so for three trials the calculation is:
(19/37) x (19/37) x (19/37) = 6859 / 50653
You have 6,859 chances to miss all three events, so you have (50,653 - 6,859 =)
43,794 / 50,653 chances to hit. (Like 86.5%)
The long way: Check the
three-results table and add the
LL values from all
HL combinations that include one or more "
R":
(The "X" shows the eXit-point)
B-B-R X - 5,832 (3 bets to eXit)
B-R X B - 5,832 (2 bets to eXit)
B-R X R - 5,832 (2 bets)
B-R X 0 - 324 (2 bets)
B-0-R X - 324 (3)
R X B-B - 5,832 (1)
R X B-R - 5,832 (1)
R X B-0 - 324 (1)
R X R-B - 5,832 (1)
R X R-R - 5,832 (1)
R X R-0 - 324 (1)
R X 0-B - 324 (1)
R X 0-R - 324 (1)
R X 0-0 - 18 (1)
0-B-R X - 324 (3)
0-R X B - 324 (2)
0-R X R - 324 (2)
0-R X 0 - 18 (2)
0-0-R X - 18 (3)
-----------------
Sum: 43,794 / 50,653 (Exactly the same as the above result)
Some simple logic can help a lot, sometimes ;)
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
12. MORE ON CHAINS
Also: If you want to know the probability for you to hit
IF you miss the first time (
but you are not SURE to miss as the first result has NOT come yet)... how's that calculated?
Remember in this calculation, the first trial of the three has no result
YET - we are
BEFORE the first spin. (Otherwise it's of course the same conditions and result as above, when
24 hit the first trial)
Let's do it the long way first: We have the following
HL combinations
WITHOUT a "
R" in the first position but
WITH a "
R" at the second or third (or both).
B-B-R X - 5,832 (3 bets to eXit)
B-R X B - 5,832 (2 bets)
B-R X R - 5,832 (2)
B-R X 0 - 324 (2)
B-0-R X - 324 (3)
0-B-R X - 324 (3)
0-R X B - 324 (2)
0-R X R - 324 (2)
0-R X 0 - 18 (2)
0-0-R X - 18 (3)
-----------------
Sum: 19,152 / 50,653 (Some 37.8%)
That's the probability for you to miss at the first trial
AND THEN hit (at least) one of the two remaining.
IF you STILL have ALL THREE trials WAITING for you!- Can this be solved by some logic, then?
- Well, look at it this way: You
ALWAYS have a
18/37 probability to hit the
next - in this case the
first - trial. That is equal to
24,642 of the 50,653 possible combinations. (This was calculated above)
We also calculated the probability to hit
ANYTIME during the three trials and that was
43,794 / 50,653.
So if we exclude all those first-trial hits,
because we calculate to miss that one, we get 43,794 - 24,642 = 19,152...
19,152 / 50,653.
The same as above...
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
13. MIXED CHAINS
Now, with a little bit of logic thinking and a calculator, you can use what you have learned above to make all those calculations for all the roulette-bets there are.
Instead of using the
18/37 fraction, you change the "
18" to the "
number of covered single numbers" in your bet.
Each trial can have their own bets:
Trial 1: Bet a
Dozen (
12/37)
Trial 2: Bet a
6-Street (
6/37)
Trial 3: Bet
Low (
18/37)
Trial 4: Bet a
Split (
2/37)
What's the probability to hit
ALL four?
Solution:
(12/37) x (6/37) x (18/37) x (2/37) = 2,592 / 1,874,161 (Some 0.14%)
What's the probability to hit
AT LEAST once?
First trial:
12/37 +
Second trial:
(25/37) x (6/37) +
Third trial:
(25/37) x (31/37) x (18/37) +
Fourth trial:
(25/37) x (31/37) x (19/37) x (2/37) =
That is: (12/37) + ((25x6) / 37x37)) + ((25x31x18) / (37x37x37)) + ((25x31x19x2) / (37x37x37x37))
=
1,358,786 / 1,874,161 to be exact.
:)
Or 72.5% rounded.
- Can you PLEASE explain?
Of course...
The first trial: The bet is a Dozen so you have a probability of
12/37 to hit. And a
25/37 probability to miss. Nothing special.
The second trial: First of all you lost the first trial; that's a
25/37 probability (see above). Then you have a
6/37 to hit the second trial.
*** The probability to
hit at this trial is:
The probability to MISS the previous trial times the probability to HIT this trial.So the probability to hit at this trial is
(25/37) x (6/37) = 150 / 1369.
*** The probability to
miss at this trial is:
The probability to MISS the previous trial times the probability to MISS this trial.So the probability to miss at this trial is
(25/37) x (31/37)Do you understand the "25 / 37" - why is it there?It's because you had lo
lose the first trial to come to this,
the second, trial. That was a
25/37 probability and therefore it has to be included.
It's the
25/37 results in the first trial
that didn't hit.
A loss here therefore happens in
(25/37) x (31/37) as that many results didn't hit here.
The
25/37 left from the first trial and now
31/37 left from here.
As they are combined,
you have to multiply them.
REMEMBER:The probability to
hit at this trial is:
The probability to MISS the previous trial times the probability to HIT this trial.The probability to
miss at this trial is:
The probability to MISS the previous trial times the probability to MISS this trial.The third trial: First of all you lost the second trial and the probability to do that was
(25/37) x (31/37). See above.
Now you bet
Low, that has a
18/37 probability to hit and therefore the calculation is:
To hit:
(25/37) x (31/37) x (18/37)To miss: (25/37) x (31/37) x (19/37)The fourth trial: Now you missed at the third trial as well and that was, as we saw above, a probability of
(25/37) x (31/37) x (19/37).
And now you bet a 2-numbers split that has a
2/37 chance to hit. Calculations:
To hit:
(25/37) x (31/37) x (19/37) x (2/37)That is how the probability of
1,358,786 / 1,874,161 was calculated.
And if we have
1,358,786 chances to hit, there has to be
515,375 chances to miss (as 1,874,161 - 1,358,786 = 515,375)
The quicker (logic) way:If you quit at
any time you hit, you only have to calculate by the probability of a
miss on ALL the four trials - if you don't miss all four, you obviously must have hit... right? So, for this four-misses event the calculation is:
(25/37) x (31/37) x (19/37) x (35/37) = 515,375 / 1,874,161.
And therefore the chance to hit is (1,874,161 - 515,375 =)
1,358,786 / 1,874,161The same exactly.
Probably correct...----------------------------------
As a complement to this document I have written a small
probability calculator in
JavaScript.
It is a
HTML-page so it is easy to open it in your web-browser.
Download it from the members download area here:
nolinks://vlsroulette.com/downloads/?sa=view;id=167 (nolinks://vlsroulette.com/downloads/?sa=view;id=167)
You can calculate the probabilities to...
* Hit "this" trial
* Miss "this" trial
* Hit at least one trial
* Miss all trials
in as long a chain of trials you like with different bets for each.
Bet from one number to all -
both 0- and 00-wheel.
Save the output by a simple copy-and-paste.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
14. DEVIATION FROM THE AVERAGE
-
YEAH YEAH YEAH! 18/37 is a theoretical thing! If I bet Red 37 times, will I hit 18 times? No! So what's good with all this???
The
BAD thing is, what you correctly point out, that it's pure theoretical. It's the
MATHEMATICAL AVERAGE for a
large sample of results.
The
GOOD with all the above is that you've learn the basics of
how to calculate your true odds for every single bet in every possible situation.
And from
here, we can dig a bit deeper into probability theory; you
NEED to know that basic stuff before we can go on.
And yes; you suppose a sample of
37 results and you don't think there is exactly
18 Reds,
18 Blacks and
one Zero there, like math says it should be.
And
of course there aren't
(probably). One or the other will probably be
dominant. And if you check a lot of 37-spins samples you will find that sometimes Red is dominant and sometimes Black (probably not the Zero, though).
18 / 37 is just a mathematical
average. It's the kind of figure you will have from examining a lot of 37-results samples.
But it's an average and can as such be used to measure the
deviation from it.
The DEVIATION from the average.If there are
22 Reds in that sample, the
deviation for Red is
+4 hits.
If there are only
12 Blacks the
deviation for Black is
-6 hits.
(And if both are true, the
deviation for the
Zero is
+2 hits).
Red has +4 because 18 was
expected but there were 22 hits.
Black has -6 because 18 was
expected but there were only 12 hits.
Zero has +2 because only one was
expected but there were 3 hits.
Now, mathematicians have invented something they call
STANDARD DEVIATION (
SD for short) that can be used for measuring the
deviation in order to see if it is
RANDOM or not.
Through count-less (
literally) empirical studies and other means they have found it to be reliable and it is
in fact the norm.
(Maybe a subjective one...)One
SD is a certain part of the whole. To show what I mean as an
ILLUSTRATION (not a true example):
Suppose coin-tossing 100 times while recording the results. Now suppose doing that 1000 times. You have a sample of 1000
100-trials events.
Now, when you check those results (that all should be 50 heads and 50 tails
according to math) you find that the vast majority has
47 to 53 heads. The
deviation is
+-3 hits for the majority.
You could very well call this "
My Deviation" (
MD for short) and now you can categorize all 1000 samples by their
MD - your own "ruler" for success... or failure.
One
MD is equal to
three hits...
Some have
51 Heads and that's
0 MD as it didn't break the "barrier" of 53 hits.
Some have
54 Heads and that's
+1 MD as it's more than 53 hits but not more than 56.
56 hits is the next level, the
+2 MD barrier, so having
56 heads is still
+1 MD while
57 is
+2 MD.And so on. And of course also the negative way for
negative MD.
Now, that was "My Deviation"...
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
15. THE STANDARD DEVIATION - Part 1
What mathematicians have found and agreed upon, is a formula to calculate their "
Standard Deviation" (
SD for short).
And that
wouldn't be worth a rat's a*s if it wasn't for the fact that their
SD have some
very interesting characteristics...
As I said; count-less
(No! More!) of empirical studies have been done and they show this, and it can be
replicated at any time by anyone (given there is a
significant size of sample available) - and not just on roulette;
anything measurable!
And with those characteristics as a basis...
This is the consensus:Breaking the
1 SD barrier is said to be equal to a
16% probability that the result is
randomBreaking the
2 SD barrier is said to be equal to a
5% probability that the result is
randomBreaking the
3 SD barrier is said to be equal to a
1% probability that the result is
randomBreaking the
4 SD barrier and beyond is said to be a
very small probability that the result is
randomI bold "
random" as that is what the
SD is measuring: If the results are random (
within normal fluctuation) or if they are "static" (have the ability to
consistently stay positive or negative).
Now, here's where those
characteristics I talked about come into play:
When an operation (a betting- or selection-method or any other thing that gives a measurable result on a
random set of results) is at a positive
SD and manages to
STAY there, in many smaller samples, it may very well start to
CLIMB towards
+3 SD AND BEYOND given larger and larger samples.
For example:
You have a lot of
100-results samples for an "even" chance and you find yourself consistently being at
50 hits. Every 100-spins sample. If you check, you will find it is a positive
SD of
+0.27 in a 100-spins sample.
Now, if you take 10 such samples you get
500 hits in a
1000-results sample. That
SD is at
+0.85 - it is growing!
Ten 1000-spins samples having 500 hits each is
5,000 hits in
10,000 results. That is a nice
+2.7 SD. Closing in at +3 SD...
And ten SUCH samples, each having 5,000 hits, is
50,000 hits in
100,000 results and THAT, my friend, is
+8.55 SD! It grows a lot!
"
Breaking the 4 SD barrier and beyond is said to be a very small probability that the result is random"
Think about that.
Now, to break the
+3 SD barrier in no way means that your "operations" are
MONETARY profitable... You saw it above as the "even" bet had a
0 profit in all samples but was at
+8.55 SD.
(This is probability theory - not economics...)
The break-even,
money-wise, for a single "even" bet at
+3 SD goes at approximately
12,350 bets and
6,175 hits. (The "e
n prison" or "l
e Partage" rules are not considered)
For a single dozen or column bet, the figures are around
24,420 bets giving
8,140 hits.
A 6-number street bet breaks even at
+3 SD just around
60,600 bets giving
10,100 hits.
Etc.
So just because you break the
+3 SD barrier doesn't mean that your method is monetary a sound method. You have to break it
quite quickly if you want to be profitable...
(So THAT is what we all are looking for: A method for roulette that consistently gives us so many hits that it quickly break the +3 SD barrier and goes beyond.)
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
16. THE STANDARD DEVIATION - Part 2
But that was money-talk; we're talking
probability theory and they are very separate subjects...
Now, we were talking about the
SPREAD of results, the
deviation from the average.
A random deviation is agreed to never break the
+-3 SD barrier and so the mathematical "prediction" for the results in a sample, is the expected
mathematical average of the sample
+-3 SD. Not an exact number any more, but a
spread.
And here's how the
SD is calculated:
SD = SQR(n * p * (1 - p))Yeah, I know; it's a formula. But it's not really complicated - let me explain...
We have some letters there:
n =
number of
bets or predictions - we do
NOT measure results for something not giving us
results, like skipped spins.
p = the
probability to
hit - 18/37 or 1/37 or quite anything, really.
And then there is the "
SQR", meaning the
SQuare
Root - check your calculator for the
Square Root key - it's necessary if you want to do these calculations...
First look at the end: "
(1 - p)".
1 minus the
probability to hit. Do you
remember? This is the way to calculate the probability for a
miss.
In other words: the Standard Deviation is equal to "
the Square Root of (number of spins times Probability to hit times Probability to miss)"
Supposing a
Red bet for
1000 times, we solve the formula this way:
For Red to hit is
p = 18/37 so the probability to miss is
(1 - 18/37) = 19/37.
So now we can insert values for "
n", "
p" and "
(1-p)"...
1000 * (18 / 37) * (19/37) = 249.82
And last you calculate the
SQuare
Root of this 249.82 =
15.8One
SD = 15.8 hits.
The mathematical average is
(18 / 37) * 1000 placed bets =
486.4 and so we add and subtract
15.8 to/from 486.4 to find the barriers:
+0 SD: 486.4 hits+1 SD: 486.4 + 15.8 = 502.2 hits which means that if you have 503 hits you've broken the +1 SD barrier and has left the 0 SD level.
+2 SD: 502.2 + 15.8 = 518.0 hits which means that if you have 519 hits you've broken the +2 SD barrier and has left the +1 SD level.
+3 SD: 518.0 + 15.8 = 533.8 hits which means that if you have 534 hits you've broken the +3 SD barrier and has left the +2 SD level.
534 or more hits in a 1000-results sample... That's great.The other way around for the negative SD:
-0 SD: 486.4 hits-1 SD: 486.4 - 15.8 = 470.6 hits which means that if you have 470 hits you've broken the -1 SD barrier and has left the 0 SD level.
-2 SD: 470.6 - 15.8 = 454.8 hits which means that if you have 454 hits you've broken the -2 SD barrier and has left the -1 SD level.
-3 SD: 454.8 - 15.8 = 439.0 hits which means that if you have 439 hits you've broken the -3 SD barrier and has left the -2 SD level.
(Don't use that method...)So for a
1000 results sample I
(math) would estimate the number of
hits being like
440 - 533, if the bet is
Red or any other "even" bet.
And all of a sudden we have a
practical way to measure results - not a theoretical fraction like
18/37 but an acceptable
spread for the results.
Because if your results, using your betting-method or selection on one 1000 results sample, are within the boundaries of
+-3 SD there is, really, no surprise. It is regarded random - could happen just anytime to anyone. But if it's
consistently in the positive you should get more and larger samples - that's my recommendation.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
17. RECORDED RESULTS
- OK OK OK! ENOUGH IS ENOUGH! You only talk math and probability and deviation and formulas and fractions that means - frankly -
ABSOLUTELY NOTHING at the casino. The spins tell the truth!
Oooh... You want to do some
REAL "reality checks" -
EMPIRICAL STUDIES!
Glad you asked.
I have downloaded
Spielbank Weisbaden results (table #3),
April - Dec 2003, complete
2004, 2005, 2006 and
2007 plus
Jan - July of 2008.
A total of
655,941 results over a period of
1,903 open days. [
See the file-index in the Appendix]
(That was the most I could download from one table without trouble...)- But no - they are
past results, they are not valid! The only
valid results are when you go to the casino and
put money on the table!
- You mean that past spins cannot be used for
empirical studies in this context?
- Yes! No! Old spins are old spins...
- So suppose I go to a casino, I bet and
at the same time I note the results, counting Red hits. I find them to be 135 and that's a
valid study in your opinion. But if I bring those results
home and count the Red hits and find them to be 135 - then it's
not valid any more??? Or do you mean that I will maybe find only 134?? Or 136???
I can see your point if I'm trying to develop a method to beat roulette. Then it would be all too easy to adopt that method to those results. That is called "
backwards engineering" and is in reality a useless way to develop systems because the next sample of results may differ a lot from the first one.
But here I'm not backwards engineering anything - I simply
count the occurrences of Red hits. Or whatever. They are the
same if I'm recording
at the casino or if I study the records
at home, aren't they?
- But you don't know if there are
errors! They may influence the end-result. You can
only trust spins that you have recorded yourself.
- If there are errors, do you think they are very common? I don't - but of course it's impossible to know for us. We weren't there.
But! If they are few, they certainly "drown" in the 655,941 results sample and thus cannot influence the end result at all because what we look for occurs maybe
thousands of times.
And should there be more than just a few you have to remember:
Errors work both ways. Meaning that probably are not
all errors noted as
black numbers but as
both red
and black. They will
probably even out at least to a degree and thus not influence the end result too much. Because what we look for occurs maybe
thousands of times.
But you are correct: Spins that are verified are better. Can you get hold of a substantial amount of such spins; please let me know and I'll use them.
- "Substantial amount" - yeah... Why do you need millions and millions of spins. Not
ONE living person will
EVER make a gazillion bets in their whole life!
- You are correct there. Absolutely. But we're not interested in how many bets you will place in your life-time.
We are interested in
FAIR studies.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
18. FAIR EMPIRICAL STUDIES
Each and every possible combination shall have the possibility to be found in the sample.
That's only fair, isn't it?
And the more possibilities (
more results) the more
secure you can be that the result is not some fluke.
If what you count occurs
only once in
one 500 results sample - what does that tell you? That it is a
1/500 (0.2%) probability to hit
always?
Maybe it was just a
fluke and in the
next 500 results it occurs
ten times. Now it's suddenly a
1/50 (a whole 2%) probability... Or? How could you
possibly tell?
Which sample contains the fluke? Maybe
both. The figures are really too small to be sure.
Now suppose you check a
5,000,000 results sample and the same combination occurs
54,869 times, you have a much better figure to work with:
54869/5000000 (1.1% rounded).
Now, if something hits like 55,000 times in a sample and you have done
nothing wrong when you count them, you can be
rather sure that the result is representative for your combination.
You can have confidence in the results as you ran a
FAIR study.
My PERSONAL opinion is that we would need absolutely
NO LESS than
(37 x 37 x 37) x
(37 x 3) for a study of
THREE-results, single-number bet, events. That's
5,622,483 events = 16,867,449 results!
Why? Because this amount gives
every 3-spins event the possibility to occur
37 x 3 (111) times in average. That isn't much in terms of statistical security
I admit that, but I wrote "
no less than" and I mean it.
111 times in average is actually not a reliable amount - something like
11,111 possibilities would be a lot better.
This shows a problem when we want to empirically study something - who's got a results-collection of a
large enough size?
My sample is, as I said,
655,941 results and gave
218,010 three-results events... Each
LL combination has the possibility to occur
4.3 times... Let's hope it's enough as we check
HL combinations.
The triple
Zero (or any other three-numbers combination) should, mathematically, occur only
4.3 times in this size and kind of a sample - do you
now realize how
small it is?
Now you know why the larger sample is preferred before the smaller. And the larger the sample, the more
realistic is the end result.
I mean; to empirically investigate the frequency of the combination "
R-B-R" you wouldn't just use three spins, would you?
If they happen to be "
B-R-B" your combination has a probability of
0 to hit at any time.
You obviously have to use a larger sample than that. Would you settle with any less than
eight as there are
eight possible combinations of R and B in three spins?
No, because if you
randomly collect
8 three-results events, you can of course not be sure that there are all the eight different R/B combinations present - and that wouldn't be
FAIR.
So you want a
larger sample.
And so on. And so on...
And the sample should be
random because we want a
FAIR study, don't we? If so, the only good thing to do is to have as large a sample as possible. The bigger is
ALWAYS the better.
(In this context...)Whatever you think about
Wiesbaden results: They give a rather significant sample size.
(And I have no other of this size - far from it)
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
19. MATH VS. REALITY
Sooo...
Do you remember the
HL-table above, for three results?
We calculated the mathematical amount of
LL in each
HL, for example that the
HL group "
B-B-B" contained
5,832 LL combinations out of the
50,653 possible combinations.
In a perfect world, if we had 50,653 three-results events, there would be exactly
5,832 "
B-B-B"s in that sample. But the world isn't perfect.
But how close to perfect is it?
In order to run the first "
Math vs Reality" check I took the spins, starting
April 1st 2003, of each day, starting at the first result and recorded them as "
B" for
Black, "
R" for
Red or "
0" for
Zero, in sequences of three.
If at the end of the day there were one or two spins left, they were
discarded. The reason being that we don't know what happens while the casino is closed.
In the end I had
218,010 such 3-results events in the 1903 day-samples. [
See the file-index in the Appendix]
As my combined (
total) sample contains
218,010 three-results events each group would occur approximately
4.3 times their total of
LL-combinations. Should. Mathematically. But do they?
I have checked.
(An empirical study!)In the below table you can, for each group, see
how many combinations they contain ("
Combs"), the
mathematical average number of occurrences there
SHOULD be in the sample ("
Math Ave") and the
Standard Deviation ("
StdDev").
You can also see the
not-breaking -3 to +3 SD span, how many occurrences that was
REALLY found in the sample ("
Real") and the
"broken" SD barrier ("
SD") - if any.
Finally I show the
difference between the
Math average and the real number of occurrances, both in
numbers ("
Diff") and in
percent ("
Diff %"), compared to the
Math average.
Group Combs Math Ave StdDev -3 SD +3 SD Real SD Diff Diff %
---------------------------------------------------------------------------------
B-B-B = 5832 25100.86 149.03 24654 - 25547 25298 +1 +197.13 +0.78
B-B-R = 5832 25100.86 149.03 24654 - 25547 25116 +0 +15.13 +0.06
B-B-0 = 324 1394.49 37.22 1283 - 1506 1421 +0 +26.50 +1.90
B-R-B = 5832 25100.86 149.03 24654 - 25547 24921 -1 -179.86 -0.71
B-R-R = 5832 25100.86 149.03 24654 - 25547 25123 +0 +22.13 +0.08
B-R-0 = 324 1394.49 37.22 1283 - 1506 1407 +0 +12.50 +0.89
B-0-B = 324 1394.49 37.22 1283 - 1506 1389 -0 -5.49 -0.39
B-0-R = 324 1394.49 37.22 1283 - 1506 1467 +1 +72.50 +5.19
B-0-0 = 18 77.47 8.80 52 - 103 65 -1 -12.47 -16.09
R-B-B = 5832 25100.86 149.03 24654 - 25547 25159 +0 +58.13 +0.23
R-B-R = 5832 25100.86 149.03 24654 - 25547 24966 -0 -134.86 -0.53
R-B-0 = 324 1394.49 37.22 1283 - 1506 1387 -0 -7.49 -0.53
R-R-B = 5832 25100.86 149.03 24654 - 25547 25021 -0 -79.86 -0.31
R-R-R = 5832 25100.86 149.03 24654 - 25547 25041 -0 -59.86 -0.23
R-R-0 = 324 1394.49 37.22 1283 - 1506 1369 -0 -25.49 -1.82
R-0-B = 324 1394.49 37.22 1283 - 1506 1381 -0 -13.49 -0.96
R-0-R = 324 1394.49 37.22 1283 - 1506 1446 +1 +51.50 +3.69
R-0-0 = 18 77.47 8.80 52 - 103 72 -0 -5.47 -7.06
0-B-B = 324 1394.49 37.22 1283 - 1506 1419 +0 +24.50 +1.75
0-B-R = 324 1394.49 37.22 1283 - 1506 1367 -0 -27.49 -1.97
0-B-0 = 18 77.47 8.80 52 - 103 88 +1 +10.52 +13.58
0-R-B = 324 1394.49 37.22 1283 - 1506 1424 +0 +29.50 +2.11
0-R-R = 324 1394.49 37.22 1283 - 1506 1428 +0 +33.50 +2.40
0-R-0 = 18 77.47 8.80 52 - 103 71 -0 -6.47 -8.35
0-0-B = 18 77.47 8.80 52 - 103 84 +0 +6.52 +8.42
0-0-R = 18 77.47 8.80 52 - 103 77 -0 -0.47 -0.60
0-0-0 = 1 4.30 2.07 0 - 10 3 -0 -1.30 -30.29
---------------------------------------------------------------------------------
50653 218010.00 (when all decimals are incl. Here: 218009.88)
I would say that the mathematical distribution is pretty close to the real. Wouldn't you agree?
I also gave examples of combinations that have the same probability as "
0-0-0" and therefore should appear
approximately the same number of times:
Group Combs Math Ave StdDev -3 SD +3 SD Real SD Diff Diff %
------------------------------------------------------------------------------------
0- 0- 0 = 1 4.30 2.07 0 - 10 3 -0 -1.30 -30.29
1- 2- 3 = 1 4.30 2.07 0 - 10 9 +2 +4.70 +109.30
7-34-22 = 1 4.30 2.07 0 - 10 0 -2 -4.30 -100.00
25- 3-31 = 1 4.30 2.07 0 - 10 9 +2 +4.70 +109.30
36-36-36 = 1 4.30 2.07 0 - 10 5 +0 +0.70 +16.30(Such small figures - "Real" - in only
one collection are
NOT to be taken too serious as they are not statistically sure, but they give an
indication...)
That was how many times they appeared within the 3-results sample.
How many times did they appear if we used the results as
continual sequences per day (break at the end of the day but we calculate the sample as 655,941 results):
Group Combs Math Ave StdDev -3 SD +3 SD Real SD Diff Diff %
------------------------------------------------------------------------------------
0- 0- 0 = 1 12.95 3.60 3 - 23 9 -0 -3.95 -30.50
1- 2- 3 = 1 12.95 3.60 3 - 23 13 +0 +0.05 +0.39
7-34-22 = 1 12.95 3.60 3 - 23 14 +0 +1.05 +8.11
25- 3-31 = 1 12.95 3.60 3 - 23 8 -2 -4.95 -38.22
36-36-36 = 1 12.95 3.60 3 - 23 11 -0 -1.95 -15.06(Such small figures - "Real" - in only
one collection are
NOT to be taken too serious as they are not statistically sure, but they give an
indication...)
BTW, for the reader's knowledge: I was not personally the one who did the actual job making these tables - it was a computer-freak friend of mine who did.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
20. CHECKING MY CLAIMS
For the next "
Math vs Reality" check, let's consider what I claimed in the beginning:
If you make a
18/37 bet, you will have the probability to hit in
18/37 - no matter if you bet on the first, second or third trial.
You will always hit in 18/37 - as a mathematical average.The math therefore
also says that
18/37 three-results events in a sample will have a "
R" in the
first position,
18/37 will have a "
R" at the
second position and
18/37 will have it in the
third.
As the sample-size (the three-results samples) is
218,010...
... the
18/37 Mathematical average =
106,058.92 (rounded) ...
... the
SD =
233.37 and so ...
... the
not-breaking -3 to +3 SD span is
105,359 - 106,759.
That's the
math. What about
reality?
Black in position 1: Found 106,207 +0 SD +148.08 = +0.14%
2: Found 106,221 +0 SD +162.08 = +0.15%
3: Found 106,096 +0 SD +37.08 = +0.03%
Red in position 1: Found 105,842 -0 SD -216.92 = -0.20%
2: Found 105,805 -1 SD -253.92 = -0.24%
3: Found 106,031 -0 SD -27,92 = -0.03%Quite similar, I'd say... Not a
quarter of one percent wrong either way...
More "Math vs Reality": What about
only making a new bet (second or third)
after a miss?
I claimed this to be true:
A: Making a
first 18/37 bet of three, there is a 18/37 probability to hit at the first trial.
So
18/37 of the 3-results events in the sample will do that. (As we actually just saw above)
And
19/37 of the 3-results events in the sample will miss at the first trial.
B: Making a
second 18/37 bet of three, there is a 18/37 probability to hit at the second trial,
for the 19/37 that missed the first trial.
So
(18/37) x (19/37) of the 3-results events will do that.
And
(19/37) x (19/37) of the 3-results events will miss also at the second trial.
C: Making a
third 18/37 bet of three, there is a 18/37 probability to hit at the third trial,
for the (19/37) x (19/37) that missed the first AND the second trials.
So
(18/37) x (19/37) x (19/37) of the 3-results events will do that.
And
(19/37) x (19/37) x (19/37) of the 3-results events will miss also the third trial.
These are the
Mathematical averages (in fractions). I will add and subtract
3 SD in order to make a mathematical "prediction" of the number of occurrences. And we will be able to see if math and probability differ
very much from reality.
What do you think?
I used the following sample-sizes:
1: The first 100 three-results events of the file
2: The first 500
3: The first 1,000
4: The first 5,000
5: The first 10,000
6: The first 50,000
7: The first 100,000
8: All 218,010 three-results events of the file
The below table shows the results in the same format as above, for each trial (
A - C) and the sample-sizes
1000, 10000 and
all. And for
both Black and Red...
[
For a COMPLETE table incl all sample-sizes: See the Appendix - Table #1]
Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
------------------------------------------------------------------------------------------------------------
BLACK 1000 1 486.48 15.80 440 - 533 509 +1 +22.51 +4.62 491
491 2 249.81 11.32 216 - 283 243 -0 -6.81 -2.72 248
248 3 128.28 8.11 104 - 152 116 -1 -12.28 -9.57 132
No hits 135.41 8.11 111 - 159 132 -0 -3.41 -2.51
BLACK 10000 1 4864.86 49.98 4715 - 5014 4871 +0 +6.13 +0.12 5129
5129 2 2498.17 35.81 2391 - 2605 2542 +1 +43.82 +1.75 2587
2587 3 1282.84 25.66 1206 - 1359 1264 -0 -18.84 -1.46 1323
No hits 1354.11 25.66 1277 - 1431 1323 -0 -31.11 -2.29
BLACK 218010 1 106058.91 233.37 105359 - 106759 106207 +0 +148.08 +0.13 111803
111803 2 54462.68 167.23 53961 - 54964 54386 -0 -76.68 -0.14 57417
57417 3 27967.32 119.83 27608 - 28326 27910 -0 -57.32 -0.20 29507
No hits 29521.06 119.83 29161 - 29880 29507 -0 -14.06 -0.04Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
------------------------------------------------------------------------------------------------------------
RED 1000 1 486.48 15.80 440 - 533 461 -1 -25.48 -5.23 539
539 2 249.81 11.32 216 - 283 270 +1 +20.18 +8.07 269
269 3 128.28 8.11 104 - 152 138 +1 +9.71 +7.57 131
No hits 135.41 8.11 111 - 159 131 -0 -4.41 -3.25
RED 10000 1 4864.86 49.98 4715 - 5014 4855 -0 -9.86 -0.20 5145
5145 2 2498.17 35.81 2391 - 2605 2514 +0 +15.82 +0.63 2631
2631 3 1282.84 25.66 1206 - 1359 1249 -1 -33.84 -2.63 1382
No hits 1354.11 25.66 1277 - 1431 1382 +0 +27.88 +2.05
RED 218010 1 106058.91 233.37 105359 - 106759 105842 -0 -216.91 -0.20 112168
112168 2 54462.68 167.23 53961 - 54964 54374 -0 -88.68 -0.16 57794
57794 3 27967.32 119.83 27608 - 28326 28027 +0 +59.67 +0.21 29767
No hits 29521.06 119.83 29161 - 29880 29767 +0 +245.93 +0.83This was
only ONE study performed on
only ONE sample and other samples may give different results, but
only within the boundaries of +-3 SD.
How I know? From personal experience (
years...) plus results from all serious studies I have ever seen or read about. To date.
I ask:
* Do you think math is
very different from reality?
* Do we really
need to do such
tiresome, time-consuming empirical studies or can we use a
calculator?
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
21. FAVORABLE SITUATIONS - Part 1
-
BUT NO! You can't just blindly look for Red - or whatever! In a casino you bet when the table is
FAVORABLE to you.
- And when is that, then?
- Listen. I'll use your own math to show you a really
GOOD method, based on a
COMBINATION OF SEVERAL FAVORABLE situations: A method that will, in average - yes, but you use averages too - bring you
AT LEAST 98 units per
106 events of
7 trials each.
(See; I can use your vocabulary)- And how's that done?
- I'll use your
OWN math: The probability for an "even" bet like Red to miss seven tries is calculated as:
(19/37) x (19/37) x (19/37) x (19/37) x (19/37) x (19/37) x (19/37) = well, something like
1/106.
So the probability to miss seven trials is
one single event in every 106. In average.
Is this correct?
- Yes, it's absolutely correct. 100%...
-
YES! I knew it! Now, here's my
SPECIAL TWIST to find
FAVORABLE SITUATIONS: I
WAIT until I have
SEEN FOUR NON-RED spins in a row and
THEN I start betting Red. The first bet is 1 unit.
If that bet is lost because Red didn't hit I bet 2 units on Red. I have now bet a total of 3 units.
If that bet is also lost I make a third bet that is 4 units. On Red. I have now bet 7 units.
- So if all three bets are lost I have
lost 7 units.
But this will happen
ONLY ONCE in
106 - in average, that's your
OWN math - and if any one of my three bets hits I have
won 1 unit and that will happen in the other
105 cases.
So I
win one unit 105 times and
lose 7 units once =
98 units in profit for every
106 times I try it:
Wait for four non-Reds and then bet Red for up to three times.
Plus and Minus that "
3 SD" you
mathboyzzz like to use as a safety-net. Now I'll do that too. Hah! And so I have calculated the
Standard Deviation like:
3 SD = 3 x SQR(trials x (1/106) x (105/106))...because the chance to
HIT a seven-spins
MISS =
1/106... Got that?
(Y'see - I learn!)
SO! YOUR OWN math shows that I will win. And win
A LOT!
I have
ANOTHER thing working for me here as well: When Red hasn't shown for four sprins, it
GENERALLY comes within three more.
I have seen this in the casino sooo many times it must be considered a truth.
HAH!
And a last thing:
Empirical studies! They show that events
even out over time and therefore Red
SHOULD hit more than average after not been seen for a while. As you have collected sequences that have no Reds
AT LEAST in the first four results, there is a
BIG difference between Red and Black so it
HAS to even out in the last three results.
There you are!
What do you say? Do you
DARE check it? I've got
YOUR math on
MY side now!
- OK... So you want me to collect
7-spins sequences where there is
no Red within the
first four.Then check the
next three for Red.
I will collect them in the same manner as the 3-results sequences: I'll start at the first result each day and if there are any left-overs so I cannot collect a complete 7-results sequence at the end of the day I will discard the last spins. Each and every day.
- Exactly! And do it for Black as well!
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
22. FAVORABLE SITUATIONS - Part 2
I looked into the file and...
...for the four
non-Reds, I found a total of
21,355 events in the file.
...for the four
non-Blacks, I found a total of
21,157 events in the file.
This is due to how I collected them: I looked for the four non-Red, recorded them and the next three results. Then I started at the
NEXT result, looking for another sequence of four non-Reds.
It is possible to find
more events if I, after recording one event, went
BACK to the result
IMMEDIATELY AFTER the first one of the last recorded event.
That way gives us a considerably
larger sample-size and that would be an advantage but has the
disadvantage that many of the seven-spins events are
part of each-other and thus may influence the end-result in a non-preferred way.
We have to settle with the "discrete" events.
- You know; I'll make my own prediction for this study... Actually, I will predict that the results from this study will be very similar to the
THREE-results study above... Remember that one? That's my "prediction" for this study...
Exactly the same as above...SampSize Math Ave StdDev -3SD +3SD
-----------------------------------------------
100 No hits 13.54 2.56 5 - 21 ... You say: 0 - 3
500 No hits 67.70 5.73 50 - 84 ... You say: 0 - 11
1000 No hits 135.41 8.11 111 - 159 ... You say: 0 - 18
5000 No hits 677.05 18.14 622 - 731 ... You say: 27 - 67
10000 No hits 1354.11 25.66 1277 - 1431 ... You say: 66 - 123
21157 No hits 2864.90 37.33 2752 - 2976 ... You say: 158 - 241
21355 No hits 2891.71 37.50 2779 - 3004 ... You say: 160 - 243Who do you think is correct - our figures differ
A LOT...?
.
.
.
And NOW <drum-roll here> the
REEESULTS:
[
For COMPLETE tables incl all three sample-sizes: See the Appendix - Table #2]
No
RED in the first four:
Bet SampSize Math Ave StdDev -3 SD +3 SD Real SD Diff Diff %
-------------------------------------------------------------------------------------------
RED 100 No hits 13.54 2.56 5 - 21 15 +0 +1.45 +10.77
RED 500 No hits 67.70 5.73 50 - 84 64 -0 -3.70 -5.47
RED 1000 No hits 135.41 8.11 111 - 159 131 -0 -4.41 -3.25
RED 5000 No hits 677.05 18.14 622 - 731 649 -0 -28.05 -4.14
RED 10000 No hits 1354.11 25.66 1277 - 1431 1323 -0 -31.11 -2.29
RED 21355 No hits 2891.71 37.50 2779 - 3004 2882 -0 -9.71 -0.33Bet SampSize Math Ave StdDev -3 SD +3 SD Real SD Diff Diff %
-------------------------------------------------------------------------------------------
BLACK 100 No hits 13.54 2.56 5 - 21 10 -0 -3.54 -26.15
BLACK 500 No hits 67.70 5.73 50 - 84 66 -0 -1.70 -2.51
BLACK 1000 No hits 135.41 8.11 111 - 159 128 -0 -7.41 -5.47
BLACK 5000 No hits 677.05 18.14 622 - 731 639 -0 -38.05 -5.62
BLACK 10000 No hits 1354.11 25.66 1277 - 1431 1330 -0 -24.11 -1.78
BLACK 21355 No hits 2891.71 37.50 2779 - 3004 2849 -0 -42.71 -1.47No
BLACK in the first four:
Bet SampSize Math Ave StdDev -3 SD +3 SD Real SD Diff Diff %
-------------------------------------------------------------------------------------------
BLACK 100 No hits 13.54 2.56 5 - 21 15 +0 +1.45 +10.77
BLACK 500 No hits 67.70 5.73 50 - 84 73 +0 +5.29 +7.81
BLACK 1000 No hits 135.41 8.11 111 - 159 132 -0 -3.41 -2.51
BLACK 5000 No hits 677.05 18.14 622 - 731 676 -0 -1.05 -0.15
BLACK 10000 No hits 1354.11 25.66 1277 - 1431 1331 -0 -23.11 -1.70
BLACK 21157 No hits 2864.90 37.33 2752 - 2976 2840 -0 -24.90 -0.86Bet SampSize Math Ave StdDev -3 SD +3 SD Real SD Diff Diff %
-------------------------------------------------------------------------------------------
RED 100 No hits 13.54 2.56 5 - 21 10 -0 -3.54 -26.15
RED 500 No hits 67.70 5.73 50 - 84 60 -0 -7.70 -11.38
RED 1000 No hits 135.41 8.11 111 - 159 118 -0 -17.41 -12.85
RED 5000 No hits 677.05 18.14 622 - 731 679 +0 +1.94 +0.28
RED 10000 No hits 1354.11 25.66 1277 - 1431 1365 +0 +10.88 +0.80
RED 21157 No hits 2864.90 37.33 2752 - 2976 2913 +0 +48.09 +1.67Again, I ask:
* Do you think math is
very different from reality?
* Do we really
need to do such
tiresome, time-consuming empirical studies or can we use a
calculator?
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
23. ...WHERE ARE THEY?
- But then your math
DOESN'T WORK!!! Why did I miss so many? You said that my calculations were correct!
- No, I said that your calculation that "
Red wouldn't hit for seven spins in 1/106" (approximately) was correct. And I say again that it is.
BUT!Then,
after that, you said that you were going to
WAIT for four spins without a Red... You didn't ask me about that.
What you didn't realize was that you all of a sudden had
four KNOWN results. Do you remember what I said about known results, in the beginning?
A known result is a certainty and as such we always calculate it as 1/1.Look here:
ALL the sequences that
hadn't got a Red in the first four trials, could be said to look like this if we put all of them in one big
HL (High-Level - remember?) combination:
Result 1: B0 <--- Black or Zero hit here
Result 2: B0 <--- The same
Result 3: B0Result 4: B0Result 5: ? <--- Result not known yet
Result 6: ? Result 7: ? Now this
HL group consists of a lot of
LL 4-number results, for example "
17-24-0-8" or "
33-11-2-29"... And this is where you are when you start betting.
Now: By
which three-result combinations can that four-spins, non-Red, sequence you have just seen,
end to make it a
complete seven-spins sequence?
What are the possible results
AFTER "
17-24-0-8" or "
33-11-2-29"?
- Well, "
B-B-B", "
B-B-R", "
B-B-0"... Wait a minute! I
remember this...?
- Yes, we've seen this before: All of a sudden we're back at this table:
B-B-B - 5,832 p = 5832/50653 = .115136 (11.5%)
B-B-R - 5,832
B-B-0 - 324 p = 324/50653 = .006396 (0.64%)
B-R-B - 5,832
B-R-R - 5,832
B-R-0 - 324
B-0-B - 324
B-0-R - 324
B-0-0 - 18 p = 18/50653 = .000355 (0.036%)
R-B-B - 5,832
R-B-R - 5,832
R-B-0 - 324
R-R-B - 5,832
R-R-R - 5,832
R-R-0 - 324
R-0-B - 324
R-0-R - 324
R-0-0 - 18
0-B-B - 324
0-B-R - 324
0-B-0 - 18
0-R-B - 324
0-R-R - 324
0-R-0 - 18
0-0-B - 18
0-0-R - 18
0-0-0 - 1 p = 1/50653 = .00002 (0.002%)
---------------
RC: 50,653 =
(37 x 37 x 37) = Correct
Are
OTHER combinations or other numbers of
LL in this
HL possible, to end our seven-spins sequence
after the first four results are known...?
No, of course not -
there are no other or no less - and that's why I could simply use the same figures I used to "predict" the number of lost 3-trials events. Because there were only three trials left
AFTER you had seen the first four.
None of these combinations (not
HL nor
LL) can be excluded or changed in any way because you have
happened to see a four non-Red or non-Black sequence, right?
And if none of them can be excluded or changed,
no other combination can have a higher probability than usual to hit, can it? Will the sum still be
100% if that is the case?
Or the four spins you have just seen; can they in
some way influence the results of the
coming three?
("Hey Ball" says the wheel, "Red didn't hit for four spins, now jump to a red number - it is due, you know")
No, of course not.
The sad truth is: When you
HAVE seen the first four results of seven, only three results are
FUTURE and so the seven results can only end in
(37x37x37) ways.
Please study this empirically on a sufficient number of your own results (remember what I said about a
fair study?) if you don't believe me...
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
24. IT WILL EVEN OUT IN THE LONG RUN
- But it happens so often in the casino. I have seen it a gazillion times! We
ALL have.
- No, in reality not. You're a victim of something called "
selective memory" - you notice things that you are looking for or that is special to you but you
DON'T remember all the gray dull stuff that happens all the other time.
Do this: Bring pen and paper to the casino and record every time the Red comes within three spins and every time it doesn't, after not been seen for four spins. It will not take long before you realize things: When you record, the phenomenon doesn't occur that often at all.
Do you think the results are influenced by the fact that you or someone else are
recording or do you think the results were, in fact, the same
all the time?
- But it should even out! At least a little and that
SHOULD have been noticeable in the study. The Blacks are so many more in the first four...
- Well, actually probability theory
doesn't say that anything
WILL even out. It says that you can
calculate a PROBABILITY for it. A high probability? Let's use an example for this:
Suppose that you, after seeing
10 spins have counted
6 Reds,
3 Blacks and
1 Zero. Now you have a
3-hits difference between Red and Black. For this to even out you will need
3 more Blacks than Reds. So to even out you will need
AT LEAST 3 spins -
more if they are not all Blacks. Now, do you know the probability to have
MORE Black hits than Red, in three spins? (As that's when you will
at least start to even out - and at least by one hit)
Yes you do! You can see that in the three-trials table above. Look for all combinations that have more "
B"s than "
R"s.
B-B-B - 5,832
B-B-R - 5,832
B-B-0 - 324
B-R-B - 5,832
B-0-B - 324
B-0-0 - 18
R-B-B - 5,832
0-B-B - 324
0-B-0 - 18
0-0-B - 18
---------------
24,354 / 50,653 -
less than 50%...
Because the probability to hit is only
18/37 - not 50% - there is a
greater chance that you will
STAY or even be
MORE BEHIND, than that you will
at least START to even out...
But if you look at it in
PER CENT it will probably be correct: A difference of
10 in 200 is
5% but a difference of
50 in 2000 spins is half;
only 2.5%. In this case you have to ask yourself: Do I
hit in per cent or do I
hit in numbers? Is the per cent DEcreasing? Is the number of hits really INcreasing?
Which question is more interesting to you???I used this example as we already had done all the maths. It is, however, possible to extend it to any bet and any difference and the results will always be the same:
If the probability to hit is LESS than 50%, the chance to even out IN NUMBERS is also less than 50%...The opposite is of course also true:
If the probability to hit is HIGHER than 50%, the probability to even out IN NUMBERS is also above 50%.Ask yourself:
Can I have a higher probability to hit, just because I try to even out?
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
25. THE WAKE-UP
I did a special study to show that the "even-out" theory is, in fact, a myth if you have less than 50% probability to hit:
On a day-basis
* I checked numbers that hadn't hit for
at least 74 spins. When they hit for the
first time after that (the "
wake-up hit") I counted how many times and when it hit again, within the
next 37 spins.
The theory being that a number that hasn't hit for a long time should even out.
It is also to show that saying things like:
"
We have all seen sleepers hit like crazy after waking up, haven't we? It happens all the time"...
...in reality is the result of a
selective memory.
There were a total of
52,408 "wake-ups" in the file, of which
33,401 had
at least one hit within the
next 37 spins.
An excerpt of the results:
[
For a COMPLETE table incl all spins: See the Appendix - Table #3 (Also shows distribution of the first and all hits)]
How long before the
FIRST hit comes
AFTER the
wake-up hit? (37 spins max wait)
Spin Math ave StdDev -3SD to +3SD Real SD Diff Diff %
------------------------------------------------------------------------
1 1416.43 37.12 1306 - 1527 1443 +0 +26.56 +1.87
2 1378.15 36.61 1269 - 1488 1394 +0 +15.84 +1.15
3 1340.90 36.12 1233 - 1449 1343 +0 +2.09 +0.15
.
.
.
35 557.98 23.30 489 - 627 543 -0 -14.98 -2.68
36 542.90 22.98 474 - 611 524 -0 -18.90 -3.48
37 528.23 22.67 461 - 596 548 +0 +19.76 +3.74
------------------------------------------------------------------------
Sum: 33401
0 hits 19016.31 22.67 18948 - 19084 19007 -0 -9.31 -0.04
------------------------------------------------------------------------
Sum: 52408Frankly:
Nothing hits like crazy here. Math average estimated
9.31 losses too little - estimating in the
19,000 misses range!
Four
hundredths of one percent wrong.
(To really see that nothing out of the ordinary happens, you should study the complete table in the Appendix)
So (for the last time) I ask you:
* Do you think math is
very different from reality?
* Do we really
need to do such
tiresome, time-consuming empirical studies or can we use a
calculator?
(Well... that second question is really asked by my friend who is making these tables...)*) What I mean by "
day-basis" is that I ended everything at the end of the day and
discarded everything that was
not complete. The reason to discard was that I didn't want "broken" 37-spins results. A number that hits for the first time
after 180 spins and gets
only 20 possibilities to occur because the day ends - that isn't
fair.
And I want to do this in a fair way.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
26. MISDIRECTED INTUITION
To sum it all up:
You did one of the
most common mistakes in the business... You mixed
STATISTICS and
PROBABILITY - you mixed
certainty and
UNcertainty...
And you simply cannot handle those two the same way, like you did.
The method to
wait some spins in order to
detect something (like 4 non-Red spins, a "wake-up hit" or actually whatever) in order for something else or the same
to happen because it is "
due to happen", is generally called "
Gambler's fallacy", partly because that's what it is -
a true fallacy, as you could see for yourself - and partly because mostly (ignorant and/or greedy)
gamblers fall for it.
It is often seen in gambling forums (I heard it's called "
Forum mathematics" by some...) posted by members who don't know how the logics, math and reality work and so they do it out of ignorance.
Have mercy on them...The figures you get, calculating like you did, are
very enticing and the math looks
really sound, I admit that.
But nevertheless it has
nothing in common with
reality.
This kind of enticing logics and math has even got an
official name ("Gambler's fallacy" aside) and that is "
Misdirected intuition", named by
C G Hempel (1905 - 1997).
(A translation from my language - maybe not the exact English name. Please enlighten me...)Misdirected intuition...Says it all.
And here's a friendly warning:There is one group of people who
FREQUENTLY use and defend "
Misdirected intuition / Gambler's fallacy" arguments and the adherent
skewed logics and math:
Roulette Systems Peddlers!
As I said; the "probabilities" are
enticing and the logic and math looks
sound so
of course they use it! But do you think that the peddlers don't know it's a
fallacy?
Not in a long shot.
They know.
Because they
HAVE tested their systems/methods in a
FAIR way, haven't they?
Using a sample of a size that makes it fair? Sure... (Ask them how big the sample was...)
Either they have, and in that case they
KNOW they are
LYING.
OR they sell a system/method they haven't studied properly.
And how great is that?Have mercy on their customers...Misdirected intuition...Something is due to happen.
Says who?Logics? No.
Logics says "
There are 37 numbers each spin with equal chances to hit."
Math? No.
Math says "
p = covered bets / 37"
Fair empirical studies? No.
Fair empirical studies say: "
We agree with Logics and Math... +-3 SD, that is"
Roulette system peddlers? Yes.
I wonder why...
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
27. THE END
Now, my friend, we are at the end of this... We've returned to our 3-results table and it means that that's all - from now on it's only
variations of the theme.
You can use the same logics and math on any kind of bet and any sample-size of significance - they are the same in all situations.
I really hope I have been able to enlighten you a little and shown that logics, math and reality in fact are close to the same.
(Well, plus/minus 3 SD...)And I hope you've learn how you can use logics and math to calculate the probabilities of different events and be comfortable with the results you get -
whatever they are. And that you
DO it, of course.
Also; I hope that you know how to
interpret the results you get correctly.
And thus it's also possible for you to, in a very simple way, decide if a system/method is at least worth a study.
And you can do
FAIR empirical studies and know how to interpret the results in a correct way, because you understand the value of a fair study that gives fair results.
I hope.
And last, but not least, I hope I have given you an arsenal of weapons against those systems peddlers who's income from "roulette" goes via your wallet.
At least you can see through their "99.9% winning rate" promises in no-time.
(You can do even better: Simply betting on the 1st dozen and High for six times gives you a 99.995% chance to hit!
Sell it to them!)As a final hint for you, that will
help you A LOT through the every-day basic calculations that we've done above:
Use
Grabb's tools! You find them here:
nolinks://vlsroulette.com/grabb/ (nolinks://vlsroulette.com/grabb/)
The "
Hit or Sleep" and the "
Standard Deviation" tools are super for those simpler calculations you do every day.
For the more complicated, though, you'll still need your calculator.
- But... but... WAIT! You can't stop now, because now I've done all sorts of calculations on all sorts of bets and I have studied recorded spins empirically and I simply CANNOT find anything that is winning... That's no fun. Do I have to give up roulette???
- No, of course not. If you like to play, why not play? The difference from before is that you now know that it's a LEISURE-game. It's a MATH GAME with the odds in favor of the casino, and I told you in the beginning that the math works - and will work - "
as long as the wheel and ball are fair and the dealer doesn't aim for certain parts of the wheel (with more success than random)...".
That may be something to remember.
Maybe you should, while you are leisure-playing, study the wheel, ball and dealer in close detail to see if maybe, just maybe, there is something making the game not-so random. Is the dealer shooting the ball in a consistent way? Is it predictable? Does the ball hit only a few deflectors? Is the wheel level? Is the wheel and ball in perfect condition? Is that spot grease?
Ask yourself these and more questions -
be curious. And why not? You are just leisure-playing anyway, so you can think more of the future games than on the present - and maybe you'll go from playing a math-based game to a physics-based game.
Methods based on logics and math cannot -
WITHOUT LUCK - give you a real advantage as REALITY shows.
Maybe methods based on physics can?
But that's a completely different story.
Good Luck, my friend, and I hope YOU will find that method that for ever breaks the +3 SD barrier.
See You On-Board!
Kon-Fu-Sed
VLS forum member
If s**t can happen, s**t will happen.
- But when it hits the fan, probability theory is like having an umbrella.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
PS - Hit or Win
As you may have noticed, I didn't use the words "winning" and "losing" - only "hitting" and "missing" - with the exception of a few paragraphs.
This is on purpose to have no confusions about what I say.
In my terms a "hit" is when a number/bet I select is also the result of the spin. Otherwise it's a "miss".
A "win" on the other hand is when a number/bet gives a positive net after the pay-out. Otherwise it's a "loss". Or "even".
The difference can be shown clearly as if I bet 1 unit on all the 37 numbers, the result will always be a "hit".
But as I bet 37 units and I get only 36 back I cannot "win" that way - only have a "loss" of 1 unit.
So I can "hit" and "lose" the same spin.
No confusion.
That's why.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
PPS - Misdirected intuition; a classic
Regarding "Misdirected intuition"...
The literature is full of examples of it and a real classic is this one (not roulette-related, though):
Three men enter a hotel and ask for a three-bed room.
- It's $25, says the clerk. Shall we have a look?
They go to the room and the three men are satisfied so they give the clerk one $10 bill each.
The clerk gives five $1 back.
The three men keep $1 each and give the clerk the remaining $2 as a tip.
So the three men gave the clerk $10 each and got $1 back; they payed $9 each.
3 x $9 = $27.
The clerk got $2 as a tip.
$27 + $2 = $29.
Where did the 30th $ go?
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
Appendix - The files
The files that were used are included in a 820K zipped archive. Download it from the member's area:
nolinks://vlsroulette.com/downloads/?sa=view;id=165 (nolinks://vlsroulette.com/downloads/?sa=view;id=165)
The archive contains the following files:
***
AllSpinsDate.txtThis file contains all the spins from Wiesbaden I used.
It is formatted in this fashion:
01.04.2003
23
1
25
.
.
.
10
15
35
02.04.2003
12
3
31
.
.
.
19
25
21
18.04.2003
19.04.2003
19
25
28
.
.
.First there is the date and then comes all the numbers from that date on one line each, until a new date.
If there are no spins one date it is immediately followed by a new date: As can be seen above, there were no spins 18.04.2003.
The file contains 655,941 spins distributed over 1,903 days that had at least one spin.
***
BR33.txtThis file contains all the three-results events.
It is formatted in this fashion:
RRR
BRB
R0B
BBR
RBB
.
.
.One three-results event on each line.
There are 218,010 events.
***
NB47.txtThis file contains all the seven-results events that have no Blacks in the first four results.
It is formatted in this fashion:
RRRRBRR
RRRRBRB
R0RRBRB
RRRRBRR
RR0RBBR
.
.
.One seven-results event on each line.
There are 21,157 events in the file.
***
NR47.txtThis file contains all the seven-results events that have no Reds in the first four results.
It is formatted in this fashion:
0BBBRRB
BBBBRBR
BBB0RRB
BBBBR0R
BBBBBBB
.
.
.One seven-results event on each line.
There are 21,355 events in the file.
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
Appendix - TABLE #1Table 1A - Sample: Three-results events
Sample sizes: First 100, 500, 1000, 5000, 10000, 50000, 100000 and 218010 of the file
Each result is "B", "R" or "0"
Three trials to hit
Exit after a hit
Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
-----------------------------------------------------------------------------------------------------------
BLACK 100 1 48.64 4.99 34 - 63 54 +1 +5.35 +10.99 46
46 2 24.98 3.58 15 - 35 22 -0 -2.98 -11.93 24
24 3 12.82 2.56 6 - 20 16 +1 +3.17 +24.72 8
No hits 13.54 2.56 5 - 21 8 -0 -5.54 -40.92
BLACK 500 1 243.24 11.17 210 - 276 263 +1 +19.75 +8.12 237
237 2 124.90 8.00 101 - 148 115 -1 -9.90 -7.93 122
122 3 64.14 5.73 47 - 81 58 -1 -6.14 -9.57 64
No hits 67.70 5.73 50 - 84 64 -0 -3.70 -5.47
BLACK 1000 1 486.48 15.80 440 - 533 509 +1 +22.51 +4.62 491
491 2 249.81 11.32 216 - 283 243 -0 -6.81 -2.72 248
248 3 128.28 8.11 104 - 152 116 -1 -12.28 -9.57 132
No hits 135.41 8.11 111 - 159 132 -0 -3.41 -2.51
BLACK 5000 1 2432.43 35.34 2327 - 2538 2427 -0 -5.43 -0.22 2573
2573 2 1249.08 25.32 1174 - 1325 1278 +1 +28.91 +2.31 1295
1295 3 641.42 18.14 587 - 695 609 -1 -32.42 -5.05 686
No hits 677.05 18.14 622 - 731 686 +0 +8.94 +1.32
BLACK 10000 1 4864.86 49.98 4715 - 5014 4871 +0 +6.13 +0.12 5129
5129 2 2498.17 35.81 2391 - 2605 2542 +1 +43.82 +1.75 2587
2587 3 1282.84 25.66 1206 - 1359 1264 -0 -18.84 -1.46 1323
No hits 1354.11 25.66 1277 - 1431 1323 -0 -31.11 -2.29
BLACK 50000 1 24324.32 111.76 23990 - 24659 24263 -0 -61.32 -0.25 25737
25737 2 12490.86 80.08 12251 - 12731 12617 +1 +126.13 +1.00 13120
13120 3 6414.23 57.39 6243 - 6586 6358 -0 -56.23 -0.87 6762
No hits 6770.57 57.39 6598 - 6942 6762 -0 -8.57 -0.12
BLACK 100000 1 48648.64 158.05 48175 - 49122 48642 -0 -6.64 -0.01 51358
51358 2 24981.73 113.26 24642 - 25321 25090 +0 +108.26 +0.43 26268
26268 3 12828.46 81.16 12585 - 13071 12700 -1 -128.46 -1.00 13568
No hits 13541.15 81.16 13297 - 13784 13568 +0 +26.84 +0.19
BLACK 218010 1 106058.91 233.37 105359 - 106759 106207 +0 +148.08 +0.13 111803
111803 2 54462.68 167.23 53961 - 54964 54386 -0 -76.68 -0.14 57417
57417 3 27967.32 119.83 27608 - 28326 27910 -0 -57.32 -0.20 29507
No hits 29521.06 119.83 29161 - 29880 29507 -0 -14.06 -0.04Table 1B - Sample: Three-results events
Sample sizes: First 100, 500, 1000, 5000, 10000, 50000, 100000 and 218010 of the file
Each result is "B", "R" or "0"
Three trials to hit
Exit after a hit
Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
-----------------------------------------------------------------------------------------------------------
RED 100 1 48.64 4.99 34 - 63 43 -1 -5.64 -11.61 57
57 2 24.98 3.58 15 - 35 29 +1 +4.01 +16.08 28
28 3 12.82 2.56 6 - 20 14 +0 +1.17 +9.13 14
No hits 13.54 2.56 5 - 21 14 +0 +0.45 +3.38
RED 500 1 243.24 11.17 210 - 276 221 -2 -22.24 -9.14 279
279 2 124.90 8.00 101 - 148 131 +0 +6.09 +4.87 148
148 3 64.14 5.73 47 - 81 81 +2 +16.85 +26.28 67
No hits 67.70 5.73 50 - 84 67 -0 -0.70 -1.04
RED 1000 1 486.48 15.80 440 - 533 461 -1 -25.48 -5.23 539
539 2 249.81 11.32 216 - 283 270 +1 +20.18 +8.07 269
269 3 128.28 8.11 104 - 152 138 +1 +9.71 +7.57 131
No hits 135.41 8.11 111 - 159 131 -0 -4.41 -3.25
RED 5000 1 2432.43 35.34 2327 - 2538 2435 +0 +2.56 +0.10 2565
2565 2 1249.08 25.32 1174 - 1325 1277 +1 +27.91 +2.23 1288
1288 3 641.42 18.14 587 - 695 625 -0 -16.42 -2.56 663
No hits 677.05 18.14 622 - 731 663 -0 -14.05 -2.07
RED 10000 1 4864.86 49.98 4715 - 5014 4855 -0 -9.86 -0.20 5145
5145 2 2498.17 35.81 2391 - 2605 2514 +0 +15.82 +0.63 2631
2631 3 1282.84 25.66 1206 - 1359 1249 -1 -33.84 -2.63 1382
No hits 1354.11 25.66 1277 - 1431 1382 +0 +27.88 +2.05
RED 50000 1 24324.32 111.76 23990 - 24659 24392 +0 +67.67 +0.27 25608
25608 2 12490.86 80.08 12251 - 12731 12383 -1 -107.86 -0.86 13225
13225 3 6414.23 57.39 6243 - 6586 6445 +0 +30.76 +0.47 6780
No hits 6770.57 57.39 6598 - 6942 6780 +0 +9.42 +0.13
RED 100000 1 48648.64 158.05 48175 - 49122 48665 +0 +16.35 +0.03 51335
51335 2 24981.73 113.26 24642 - 25321 24790 -1 -191.73 -0.76 26545
26545 3 12828.46 81.16 12585 - 13071 12788 -0 -40.46 -0.31 13757
No hits 13541.15 81.16 13297 - 13784 13757 +0 +215.84 +1.59
RED 218010 1 106058.91 233.37 105359 - 106759 105842 -0 -216.91 -0.20 112168
112168 2 54462.68 167.23 53961 - 54964 54374 -0 -88.68 -0.16 57794
57794 3 27967.32 119.83 27608 - 28326 28027 +0 +59.67 +0.21 29767
No hits 29521.06 119.83 29161 - 29880 29767 +0 +245.93 +0.83
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
Appendix: TABLE #2
Table 2A - Sample: Seven-results events without Red in the first four
Sample sizes: First 100, 500, 1000, 5000, 10000 and 21355 of the file
Each result is "B", "R" or "0"
Three trials to hit
Exit after a hit
Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
-----------------------------------------------------------------------------------------------------------
RED 100 1 48.64 4.99 34 - 63 48 -0 -0.64 -1.33 52
52 2 24.98 3.58 15 - 35 21 -1 -3.98 -15.93 31
31 3 12.82 2.56 6 - 20 16 +1 +3.17 +24.72 15
No hits 13.54 2.56 5 - 21 15 +0 +1.45 +10.77
RED 500 1 243.24 11.17 210 - 276 226 -1 -17.24 -7.08 274
274 2 124.90 8.00 101 - 148 132 +0 +7.09 +5.67 142
142 3 64.14 5.73 47 - 81 78 +2 +13.85 +21.60 64
No hits 67.70 5.73 50 - 84 64 -0 -3.70 -5.47
RED 1000 1 486.48 15.80 440 - 533 467 -1 -19.48 -4.00 533
533 2 249.81 11.32 216 - 283 252 +0 +2.18 +0.87 281
281 3 128.28 8.11 104 - 152 150 +2 +21.71 +16.92 131
No hits 135.41 8.11 111 - 159 131 -0 -4.41 -3.25
RED 5000 1 2432.43 35.34 2327 - 2538 2361 -2 -71.43 -2.93 2639
2639 2 1249.08 25.32 1174 - 1325 1302 +2 +52.91 +4.23 1337
1337 3 641.42 18.14 587 - 695 688 +2 +46.57 +7.26 649
No hits 677.05 18.14 622 - 731 649 -0 -28.05 -4.14
RED 10000 1 4864.86 49.98 4715 - 5014 4759 -2 -105.86 -2.17 5241
5241 2 2498.17 35.81 2391 - 2605 2545 +1 +46.82 +1.87 2696
2696 3 1282.84 25.66 1206 - 1359 1373 +3 +90.15 +7.02 1323
No hits 1354.11 25.66 1277 - 1431 1323 -0 -31.11 -2.29
RED 21355 1 10388.91 73.04 10170 - 10608 10326 -0 -62.91 -0.60 11029
11029 2 5334.85 52.34 5178 - 5491 5326 -0 -8.85 -0.16 5703
5703 3 2739.51 37.50 2627 - 2852 2821 +2 +81.48 +2.97 2882
No hits 2891.71 37.50 2779 - 3004 2882 -0 -9.71 -0.33Table 2B - Sample: Seven-results events without Red in the first four
Sample sizes: First 100, 500, 1000, 5000, 10000 and 21355 of the file
Each result is "B", "R" or "0"
Three trials to hit
Exit after a hit
Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
-----------------------------------------------------------------------------------------------------------
BLACK 100 1 48.64 4.99 34 - 63 49 +0 +0.35 +0.72 51
51 2 24.98 3.58 15 - 35 30 +1 +5.01 +20.08 21
21 3 12.82 2.56 6 - 20 11 -0 -1.82 -14.25 10
No hits 13.54 2.56 5 - 21 10 -0 -3.54 -26.15
BLACK 500 1 243.24 11.17 210 - 276 262 +1 +18.75 +7.71 238
238 2 124.90 8.00 101 - 148 125 +0 +0.09 +0.07 113
113 3 64.14 5.73 47 - 81 47 -3 -17.14 -26.72 66
No hits 67.70 5.73 50 - 84 66 -0 -1.70 -2.51
BLACK 1000 1 486.48 15.80 440 - 533 505 +1 +18.51 +3.80 495
495 2 249.81 11.32 216 - 283 255 +0 +5.18 +2.07 240
240 3 128.28 8.11 104 - 152 112 -2 -16.28 -12.69 128
No hits 135.41 8.11 111 - 159 128 -0 -7.41 -5.47
BLACK 5000 1 2432.43 35.34 2327 - 2538 2500 +1 +67.56 +2.77 2500
2500 2 1249.08 25.32 1174 - 1325 1247 -0 -2.08 -0.16 1253
1253 3 641.42 18.14 587 - 695 614 -1 -27.42 -4.27 639
No hits 677.05 18.14 622 - 731 639 -0 -38.05 -5.62
BLACK 10000 1 4864.86 49.98 4715 - 5014 4958 +1 +93.13 +1.91 5042
5042 2 2498.17 35.81 2391 - 2605 2485 -0 -13.17 -0.52 2557
2557 3 1282.84 25.66 1206 - 1359 1227 -2 -55.84 -4.35 1330
No hits 1354.11 25.66 1277 - 1431 1330 -0 -24.11 -1.78
BLACK 21355 1 10388.91 73.04 10170 - 10608 10458 +0 +69.08 +0.66 10897
10897 2 5334.85 52.34 5178 - 5491 5327 -0 -7.85 -0.14 5570
5570 3 2739.51 37.50 2627 - 2852 2721 -0 -18.51 -0.67 2849
No hits 2891.71 37.50 2779 - 3004 2849 -0 -42.71 -1.47Table 2C - Sample: Seven-results events without Black in the first four
Sample sizes: First 100, 500, 1000, 5000, 10000 and 21157 of the file
Each result is "B", "R" or "0"
Three trials to hit
Exit after a hit
Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
-----------------------------------------------------------------------------------------------------------
BLACK 100 1 48.64 4.99 34 - 63 45 -0 -3.64 -7.50 55
55 2 24.98 3.58 15 - 35 32 +1 +7.01 +28.09 23
23 3 12.82 2.56 6 - 20 8 -1 -4.82 -37.63 15
No hits 13.54 2.56 5 - 21 15 +0 +1.45 +10.77
BLACK 500 1 243.24 11.17 210 - 276 240 -0 -3.24 -1.33 260
260 2 124.90 8.00 101 - 148 135 +1 +10.09 +8.07 125
125 3 64.14 5.73 47 - 81 52 -2 -12.14 -18.93 73
No hits 67.70 5.73 50 - 84 73 +0 +5.29 +7.81
BLACK 1000 1 486.48 15.80 440 - 533 475 -0 -11.48 -2.36 525
525 2 249.81 11.32 216 - 283 263 +1 +13.18 +5.27 262
262 3 128.28 8.11 104 - 152 130 +0 +1.71 +1.33 132
No hits 135.41 8.11 111 - 159 132 -0 -3.41 -2.51
BLACK 5000 1 2432.43 35.34 2327 - 2538 2386 -1 -46.43 -1.90 2614
2614 2 1249.08 25.32 1174 - 1325 1272 +0 +22.91 +1.83 1342
1342 3 641.42 18.14 587 - 695 666 +1 +24.57 +3.83 676
No hits 677.05 18.14 622 - 731 676 -0 -1.05 -0.15
BLACK 10000 1 4864.86 49.98 4715 - 5014 4821 -0 -43.86 -0.90 5179
5179 2 2498.17 35.81 2391 - 2605 2563 +1 +64.82 +2.59 2616
2616 3 1282.84 25.66 1206 - 1359 1285 +0 +2.15 +0.16 1331
No hits 1354.11 25.66 1277 - 1431 1331 -0 -23.11 -1.70
BLACK 21157 1 10292.59 72.70 10075 - 10510 10260 -0 -32.59 -0.31 10897
10897 2 5285.38 52.09 5130 - 5441 5353 +1 +67.61 +1.27 5544
5544 3 2714.11 37.33 2603 - 2826 2704 -0 -10.11 -0.37 2840
No hits 2864.90 37.33 2752 - 2976 2840 -0 -24.90 -0.86Table 2D - Sample: Seven-results events without Black in the first four
Sample sizes: First 100, 500, 1000, 5000, 10000 and 21157 of the file
Each result is "B", "R" or "0"
Three trials to hit
Exit after a hit
Bet SampSize Trial Math Ave StdDev -3 SD +3 SD Real SD Diff Diff % Did NOT hit
-----------------------------------------------------------------------------------------------------------
RED 100 1 48.64 4.99 34 - 63 54 +1 +5.35 +10.99 46
46 2 24.98 3.58 15 - 35 24 -0 -0.98 -3.92 22
22 3 12.82 2.56 6 - 20 12 -0 -0.82 -6.45 10
No hits 13.54 2.56 5 - 21 10 -0 -3.54 -26.15
RED 500 1 243.24 11.17 210 - 276 249 +0 +5.75 +2.36 251
251 2 124.90 8.00 101 - 148 135 +1 +10.09 +8.07 116
116 3 64.14 5.73 47 - 81 56 -1 -8.14 -12.69 60
No hits 67.70 5.73 50 - 84 60 -0 -7.70 -11.38
RED 1000 1 486.48 15.80 440 - 533 495 +0 +8.51 +1.74 505
505 2 249.81 11.32 216 - 283 264 +1 +14.18 +5.67 241
241 3 128.28 8.11 104 - 152 123 -0 -5.28 -4.11 118
No hits 135.41 8.11 111 - 159 118 -0 -17.41 -12.85
RED 5000 1 2432.43 35.34 2327 - 2538 2471 +1 +38.56 +1.58 2529
2529 2 1249.08 25.32 1174 - 1325 1248 -0 -1.08 -0.08 1281
1281 3 641.42 18.14 587 - 695 602 -2 -39.42 -6.14 679
No hits 677.05 18.14 622 - 731 679 +0 +1.94 +0.28
RED 10000 1 4864.86 49.98 4715 - 5014 4906 +0 +41.13 +0.84 5094
5094 2 2498.17 35.81 2391 - 2605 2492 -0 -6.17 -0.24 2602
2602 3 1282.84 25.66 1206 - 1359 1237 -1 -45.84 -3.57 1365
No hits 1354.11 25.66 1277 - 1431 1365 +0 +10.88 +0.80
RED 21157 1 10292.59 72.70 10075 - 10510 10297 +0 +4.40 +0.04 10860
10860 2 5285.38 52.09 5130 - 5441 5253 -0 -32.38 -0.61 5607
5607 3 2714.11 37.33 2603 - 2826 2694 -0 -20.11 -0.74 2913
No hits 2864.90 37.33 2752 - 2976 2913 +0 +48.09 +1.67
Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members
Appendix - TABLE #3
Waiting for a wake-up hit AT LEAST 74 spins
The hit after at least 74 spins without a hit, is the wake-up hit.
How many hits are there in the next 37 spins after the wake-up hit?
The sample:
All recorded wake-ups = 52408
with hits = 33401
(tot hits = 52478)
without hits = 19007Table 3A - How long before the FIRST hit comes AFTER the wake-up hit? (37 spins max wait)
Example:
The Math average says that the FIRST HIT after the wake-up will come at the fourth spin 1304.66 times in this sample.
One Standard deviation = 35.62 and the interval -3SD to +3SD is 1198 to 1411 times.
The real number of occurrencies found in the file was 1318 times and that was not outside the 0 SD range.
The difference between the real number and the Math average was +13.33 or +1.02% for the real number.
Spin Math ave StdDev -3SD to +3SD Real SD Diff Diff %
-----------------------------------------------------------------------
1 1416.43 37.12 1306 - 1527 1443 +0 +26.56 +1.87
2 1378.15 36.61 1269 - 1488 1394 +0 +15.84 +1.15
3 1340.90 36.12 1233 - 1449 1343 +0 +2.09 +0.15
4 1304.66 35.62 1198 - 1411 1318 +0 +13.33 +1.02
5 1269.40 35.14 1164 - 1374 1316 +1 +46.59 +3.67
6 1235.09 34.66 1132 - 1339 1185 -1 -50.09 -4.05
7 1201.71 34.19 1100 - 1304 1111 -2 -90.71 -7.54
8 1169.23 33.72 1069 - 1270 1160 -0 -9.23 -0.78
9 1137.63 33.26 1038 - 1237 1140 +0 +2.36 +0.20
10 1106.88 32.81 1009 - 1205 1189 +2 +82.11 +7.41
11 1076.97 32.37 980 - 1174 1079 +0 +2.02 +0.18
12 1047.86 31.93 953 - 1143 1072 +0 +24.13 +2.30
13 1019.54 31.49 926 - 1114 1074 +1 +54.45 +5.34
14 991.98 31.06 899 - 1085 1019 +0 +27.01 +2.72
15 965.17 30.64 874 - 1057 961 -0 -4.17 -0.43
16 939.09 30.22 849 - 1029 918 -0 -21.09 -2.24
17 913.70 29.81 825 - 1003 870 -1 -43.70 -4.78
18 889.01 29.41 801 - 977 942 +1 +52.98 +5.95
19 864.98 29.01 778 - 952 892 +0 +27.01 +3.12
20 841.60 28.61 756 - 927 789 -1 -52.60 -6.25
21 818.86 28.22 735 - 903 880 +2 +61.13 +7.46
22 796.73 27.84 714 - 880 748 -1 -48.73 -6.11
23 775.19 27.46 693 - 857 759 -0 -16.19 -2.08
24 754.24 27.08 673 - 835 694 -2 -60.24 -7.98
25 733.86 26.72 654 - 814 754 +0 +20.13 +2.74
26 714.02 26.35 635 - 793 683 -1 -31.02 -4.34
27 694.73 25.99 617 - 772 696 +0 +1.26 +0.18
28 675.95 25.64 600 - 752 648 -1 -27.95 -4.13
29 657.68 25.29 582 - 733 655 -0 -2.68 -0.40
30 639.90 24.95 566 - 714 619 -0 -20.90 -3.26
31 622.61 24.61 549 - 696 662 +1 +39.38 +6.32
32 605.78 24.27 533 - 678 610 +0 +4.21 +0.69
33 589.41 23.94 518 - 661 555 -1 -34.41 -5.83
34 573.48 23.62 503 - 644 608 +1 +34.51 +6.01
35 557.98 23.30 489 - 627 543 -0 -14.98 -2.68
36 542.90 22.98 474 - 611 524 -0 -18.90 -3.48
37 528.23 22.67 461 - 596 548 +0 +19.76 +3.74
-----------------------------------------------------------------------
Sum: 33401
0 hits 19016.31 22.67 18948 - 19084 19007 -0 -9.31 -0.04
-----------------------------------------------------------------------
Sum: 52408Table 3B - At what spin does the FIRST hit of TOTAL X hits come, AFTER the wake-up hit? (37 spins max wait)
X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Sums
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 529 510 516 512 566 489 485 541 544 592 546 537 530 546 524 538 493 583 534 505 572 499 514 485 536 524 540 508 507 516 562 526 488 556 514 513 548 19528
2 541 555 516 509 484 454 397 407 411 408 371 377 400 339 316 281 297 267 273 228 247 199 203 171 190 141 135 126 132 91 89 78 63 49 29 11 9785
3 266 239 225 225 194 181 176 160 142 160 121 131 121 104 97 81 58 76 70 53 53 43 39 34 24 16 21 13 14 11 11 5 4 3 3171
4 84 68 70 61 54 51 48 42 35 21 32 22 17 27 20 18 19 16 12 3 7 5 3 3 3 2 1 2 1 1 748
5 18 15 13 9 16 8 4 8 8 8 9 5 6 2 4 3 3 1 2 1 1 144
6 5 6 1 1 1 2 1 2 1 20
7 1 2 1 1 5
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Sums 1443 1394 1343 1318 1316 1185 1111 1160 1140 1189 1079 1072 1074 1019 961 918 870 942 892 789 880 748 759 694 754 683 696 648 655 619 662 610 555 608 543 524 548 33401Table 3C - At what spin did HIT # X come, AFTER the wake-up hit? (37 spins max wait)
X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Sums
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 1443 1394 1343 1318 1316 1185 1111 1160 1140 1189 1079 1072 1074 1019 961 918 870 942 892 789 880 748 759 694 754 683 696 648 655 619 662 610 555 608 543 524 548 33401
2 34 93 117 133 164 196 240 237 263 282 307 355 351 368 375 406 456 413 462 478 451 495 473 497 464 550 539 501 495 548 525 487 551 489 557 521 13873
3 1 5 13 13 21 19 44 35 41 45 50 80 66 73 88 85 126 123 140 141 142 173 159 183 183 186 194 232 234 225 225 261 243 239 4088
4 1 1 5 1 3 3 1 7 7 9 11 22 12 22 21 21 40 31 39 32 43 45 62 41 50 81 76 65 83 82 917
5 2 1 1 2 2 1 3 4 3 7 3 3 7 7 5 3 13 10 14 15 22 17 24 169
6 4 1 2 1 3 3 5 3 3 25
7 1 1 3 5
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Sums 1443 1428 1436 1436 1454 1363 1320 1422 1396 1501 1399 1423 1477 1421 1416 1367 1359 1499 1414 1390 1506 1364 1423 1357 1458 1348 1468 1422 1392 1374 1500 1429 1362 1478 1386 1427 1420 52478