can anyone program this?

[gizmotron]

Before each four spin segment the odds are 2.3%. After the first spin the odds are a little better. Each spin works step by step toward the 25%,

[simon]

later on I will see if I can scan and upload a couple pages from the book I am referring to.  it is definitely something you have not seen before.  It should be read carefully and with an open mind, before concluding if the formula is valid or not.

[gizmotron]

I doubt that anything in a book will change my mind. On step one, there is a 2.34% chance that all the conditions will come true in all four steps. If step one comes true then there is a 3.12% chance that the next three things will take place. After that it will take 6.25% chance that the last two things will happen. Finally it will take 25% for the last step to occur. I think I did that right.

[simon]

here are five pages from an interesting out of print book.  I have been developing a system based somewhat on the author's remarks.  I would like an opinion if his formulas on pages 5 and 7 regarding 3 events and 4 events have any validity or not.  thanks.

p.3

[simon]

p.4

[simon]

p.5

[simon]

p.6

[simon]

p.7

[bombus]

the probability is 25%, no more or less. It has to be, because you are talking about independent trials, so whatever sequence has come before the arrival of the 4 will make no difference.

I think Tangram is correct here simon, sorry.

That said, I bet four groups of nine all the time, and one of my favoured scenarios is betting the fourth group after three spins with no group repeats, but I bet that group at least twice, and up to four times. Stopping after any win of course.

[simon]

Hi Bombus, I just posted above five pages from a book, did you read them? (carefully?)

[Tangram]

Simon,

There's nothing wrong with the maths, but the mistake comes from confusing a sequence of outcomes with a single outcome. For example, on page 5, the author correctly gives the probability of not getting a repeat in 3 spins, but then goes on to say:

Code Select Expand

It would certainly be logical to place bets that have already been selected because the odds are in favor of repeats

Implying that you can somehow get an advantage by waiting for no repeats in the first 2 spins and then betting for a repeat on the 3rd, which is a fallacy because the odds of a repeat haven't changed on any particular spin, it only seems as though they have when you look at the sequence as a whole. It's exactly this kind of thinking which leads people to believe that a black is more likely on the next spin because you have just seen 10 reds in a row.

[simon]

It's exactly this kind of thinking which leads people to believe that a black is more likely on the next spin because you have just seen 10 reds in a row.

well believe it or not a math major at a prestigious university personally told me that if red hit 10 times in a row he would definitely bet black and I said "but isn't that the well known gambler's fallacy?" and he basically told me that it's not a fallacy and there is still some debate about this because everything has to even out in the end, which was really surprising and confusing for me to hear, and yes I know about the law of large numbers, etc.  

Be that as it may, it is the author's specific statements and formula on p.7 under the heading THE FORMAL STATEMENT OF THE IDEA that I want to focus on and find out if the statements make sense and if the formula is valid.

[Tangram]

Asking the question - "are spins independent?" goes to the heart of the matter because if they truly are under all circumstances, then no system or method based on past results can possibly work. There does seem to be some evidence to the contrary but it's all anecdotal -  no objective test has ever been made that shows that spins are not independent. However it's not always easy to dismiss the arguments of those who say there is a degree of non-independence, despite the common-sense view that there can't be because every spin is a new event.

if every table game result is an independent event, how can we ever expect any particular number to come up at all? We can't, because there would be nothing to stop the wheel from selecting a different number, every time. And yet, the same people who say that these numerical events are immaculately independent, expect the numbers to conform with the probabilities. But if such events were truly independent, there would never be a moment, or even a sustained period, when any number could be expected to show up.

There is a causative force that compels numerical events to seek their legitimate place within their assigned probabilities. Whether the dice or wheel have a memory is irrelevant. The influence originates from the effects of statistical propensity, the authority that governs the probabilities of random numerical events.

The key to getting a clear handle on this lies in seeing the difference between viewing table decisions one at a time, or in groups. On a one-by-one basis, it is true that there will never be a time when any number is mandated to appear or not appear. But even in a sampling as small as 3000 spins, you will never see what might be regarded as a catastrophic deviation from the statistical expectation. There's not an unbiased roulette table on earth that can make it through that many spins without our number 8 coming up at least two or three dozen times times.

nolinks://nolinks.thegamblersedge.com/propensity.htm

There does seem to be a contradiction here, and I've never heard a satisfactory explanation for it.

Anyway, going back to the "formal statement":

Now, if we consider the random process from the standpoint of not repeating a selection we see that the situation is the same as that involved in a series of trials without replacement.

I disagree with this. It isn't the same thing at all. Just because the calculations happen to be the same it doesn't mean that the physical situation is too. The only way you could make roulette a game of "no replacement" is by covering each pocket on the wheel every time the ball lands in the corresponding number, analogous to removing cards from the deck in Blackjack.

[simon]

p.1

I am posting pages 1 and 2 so the other pages are not taken out of context and you can read the author's comments on randomness, etc. and see that he seems to have his head on straight.

(I trust that these pictures of the document are readable to the viewer and that after clicking on them once to enlarge, they can be clicked again to enlarge to the correct size.)

[simon]

p.2

[simon]

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