I can´t translate this proof. If anyone is interessted search for HMM (Hidden Markov Movement Model) or HMS (Hidden Markov Sequenz)
Formal definiert man ein Verborgenes Markow-Modell als Fünftupel λ = (S,A,B,π,V) mit
* S = {s1,...,sn} - Menge aller Zustände
* A = {aij} - Zustandsübergangsmatrix, wobei aij die Wahrscheinlichkeit angibt, dass nach Zustand si in Zustand sj gewechselt wird.
* B = {b1,...,bn} - Menge der Emissionswahrscheinlichkeitsverteilungen bzw. Dichten
* bi(x) - Wahrscheinlichkeit im Zustand si die Beobachtung x zu machen
* π - Anfangswahrscheinlichkeitsverteilung mit π(I) Wahrscheinlichkeit, dass si der Startzustand ist
* V - Merkmalsraum (oft als Ausgabealphabet bezeichnet), also der Definitionsbereich von bi. Dieser kann diskret, oder kontinuierlich sein. Je nach dem ist bi eine Wahrscheinlichkeit oder eine Dichte.
S = Menge der RNF-Konstellationen nach Coup 37 = {14/13/10; 13/14/10;...}
bi(x) = Wahrscheinlichkeit an der Stelle x (13N lt. Empirik)
n-Anfangswahrscheinlichkeit n(I) Zahlen = Wahrscheinlichkeit von x Zahlen x/37
V = R oder N oder F
A = {aij} = (Vorläufer R N F = ai) (Treffer R N F = aj)
Tabelle n Emissionswahrscheinlichkeit
Treffer
TR TN TF
Vorlauf VR 0,415 0,342 0,243
VN 0,406 0,344 0,25
VF 0,383 0,379 0,239
Tabelle q Übergangswahrscheinlichkeit
Minderung bleibt
-1 0 nichtmöglich
14R 0,378 0,622 R wird F
13N 0,351 0,649 N wird R
10F 0,270 0,730 F wird R/N
das Markov-Modell sieht dazu so aus
P1 = 0,406
P2 = 0,344
P3 = 0,250
-> 0,622 -> 0
0,351 <- 0,73 <-
P1 = 0,415 -> 0 P1 = 0,383
P2 = 0,342 0,27 <- P2 = 0,379
P3 = 0,243 P3 = 0,239
Because the table is damaged I add a picture
I will try to explain in my poor english and obviously without using the correct stochastical/math-vocabulary.
1. Kolmogorof
He found and proofed and put this in math:
Example dice:
With an perfect device there are only 6 possible outcomes to achieve:
There is no 7 and there is no 0 possible
There has to be a result of any of the possible numbers 1, 2. 3. 4. 5. 6.
What we know: There shows 1 out of the 6 up or
any result is element of this group {1,2,3,4,5,6}
As the probability for each number is the same the probability is 1/6 for each number of this group
possible results are therefore
{1}{2}{3}{4}{5}{6}
If we group these outcomes like this
{1}{2,3}{4,5,6}
which are the probabilitis for any of these groups and he found that the probability just sums up due to the numbers of group
1/6 2/6 3/6
also it makes no difference if we build different multiple groups like
{1,6}{2,5}{1,5}{2,6}{1,2,6}{1,2,5,6}{3}{4}
for each group it is (number of members)*1/6
Second Markov:
let me explain Markovs idea by an example:
Today we know todays weather
and we know yesterdays weather
Tommorows weather is influenced by todays weather but not by yesterdays weather
Imagine we would live some hundred years ago and hadn´t no weather-forecast on TV. We just can have a look into the skies.
But at night we sleep and cannot see what is going on. We don´t see clouds coming, winds changing etc.
So the change of todays weather to tomorrows weather is effected by "Hidden Movements" (hidden to us)
If we transfer this to random results:
the last result (short: 0) effects the next result (short: +1). But the next result is not effected by the result before the last result (short: -1).
What is a RESULT?
Many would say the number that appeared is the result.
This is the idea behind: Each spin is independent
But if you read Markov you will learn that even a situation can be an result. Even when the (hidden) movement of one situation to the next is random.
This means for G.U.T:
The situation is: A crossing is to happen:
It doesn´t matter how we came to this point.
But this Situation is effecting the next result!
to be continued
Everythings logical and clear for all?
If there is no interest, I will stop.
br
winkel
Please continue Mr. Winkel.
Winkel,
Give it up. You're wasting your time. Start a new system or method designed to exploit the gaming device in some way, rather than the random game.
If you're going to post the few trials that Twocat tested, then you should also post the millions of trials the Konfused tested.
-Landis
QuoteToday we know todays weather
and we know yesterdays weather
Tommorows weather is influenced by todays weather but not by yesterdays weather
Imagine we would live some hundred years ago and hadn´t no weather-forecast on TV. We just can have a look into the skies.
But at night we sleep and cannot see what is going on. We don´t see clouds coming, winds changing etc.
So the change of todays weather to tomorrows weather is effected by "Hidden Movements" (hidden to us)
If we transfer this to random results:
the last result (short: 0) effects the next result (short: +1). But the next result is not effected by the result before the last result (short: -1).
What is a RESULT?
Many would say the number that appeared is the result.
This is the idea behind: Each spin is independent
Winkel, each spin is independent. The weather is completetly different because yesterdays weather does influence tomorrows. In roulette, the dealer does not block each number after it hits, and the chance of hitting on the next spin is not changed because of what hit on previous spins in the random game.
We can built positronic brain and name it Mr. Data and go with him in casino. Future best friend, ha, ha.
So what we´ve learned is that landis doesn´t try to look any further than 1+1 = 2
Now let´s go further:
as we learned from Kolmogorof:
If we choose any 14 numbers the probability to hit is 14/37
as we learned from Markov:
The state now influences the next result. The state before NOW doesn´t influence the next result.
But Markov says:
It is more likely that the hidden sequence which formed the result NOW is repeating in a similiar way.
for example: If we imagine that the tranformation from result 23 to result 36 is made by an unknown formula, it is more likely that the same formula transforms 36 to the next result.
So we just have to find the previous formula to have a "more likely result" in the next spin.
This means if we take it very simple: 23 +13=36
but it also can be 23-20*12
The formular is hidden to us!!!!!
Is this theory understandable?
br
winkel
As the Formula is hidden we have to find a way to detect any information about it:
The way we know is:
Result A -> (hidden sequence) -> Result B -> (hidden sequence) -> Result C
How we can use it:
we know the situation is 14 13 10
The hidden sequence formed this situation from 3 possible further states:
A) 15 12 10 : A "0" is transformed to an "1"
B) 14 14 09 : A "1" is transformed to an ">1"
C) 14 13 10 : A ">1" has appeared again
if we came from A) then a probability of 15/37 did its job
if we came from B) then a probability 0f 14/37 did its job
if we came from C) then a probability of 10/37 did its Job
(btw: if we add we have 39/37!)
The next hidden Sequence can form also 3 new situations from 14 13 10:
A1) 13 14 10 : A "0" appears
B1) 14 12 11 : A "1" appears
C1) 14 13 10 : A ">1" appears again.
if we reach A1) a probability of 14/37 did its job
if we reach B1) a probability of 13/37 did its job
if we reach C1) a probability of 10/37 did its job.
br
winkel
ps: due to my bad english, i would like to read if there are misunderstandings or not
So, what is a probability to have in 37 spins ALL difrent numbers?
And what is probability to have those numbers be in order e.g. 0,1,2,3,4,5,6--36 ?
Is the odds of this two events the same? Yes, I thinks so.
what are main difrence beetwen those two event? In second we can aspect next number, so previus spin have influance on next.
Hi GogoCro,
The odds of those events aren't the same. There are many ways you can order the numbers 0,1,2,3...36, but only one set of numbers (order doesn't count). Which would be harder to predict: the names of the first 3 horses crossing the finish line in a race or the order in which they finished?
00-13763753091226345046315979581580902400000000
01-9166659558756745800846442401332880998400000000
02-1417012790124480288380845887872707854336000000000
03-90145184730246025892907271420329810984960000000000
04-29783741778105059444026916492559103171756032000000 00
05-57970329049287657719781576280879113815426334720000 000
06-71885464137813784536847011575656511147914297344000 0000
07-59868819651200001053099801425565015916297584640000 00000
08-34762581204447586766128168170075977030524175646720 000000
09-14461938585196940315555791016241509772262121668608 0000000
10-43988863327144295628455119614800310494950727457177 6000000
11-99314403709014104760333242459469784676539760954572 8000000
12-16828756402132029257761608807853825140919211026022 40000000
13-21571423994333250786619796187375647743212359516160 00000000
14-21024615376642894044456549483200633964092178038784 00000000
15-15624050599243186577664106109533697507830824488140 80000000
16-88574561489078877149151720891953299471144686971289 6000000
17-38245595250327605318223205863016817185097264898048 0000000
18-12530967822349466104288191215822395024582071699456 0000000
19-30967834997093364656576727119566555144104706314240 000000
20-57237248137167777811633467981012366039863905403289 60000
21-78232772280842619876129768406917976326662281691136 0000
22-77931225778939000694390819037276276993798373785600 000
23-55537548139736362650165721245628847247861411840000 00
24-27656320468975854551661981504668356215745258752000 0
25-9339872643636158806351478567442193463378891366400
26-205855413999978844470780459449127510202760140800
27-2816965401383850461200395609690655180465920000
28-22399283172504178506420208588596956078284800
29-94565721758805225307882215499643868211200
30-186661410285074412593290629857625492480
31-142858615341622458131514354387133440
32-31674513616614897584407615403640
33-1247435821496707522962937200
34-3498702745071044101500
35-91534343011020
36-37
from Top to Button the exakt number of possible combinations with exakt 0,1,2,3,...,36 sleepers
your questions is answered by the top-line
Thank you.
Then is this true?
odds for 37 all diffrent (unique) numbers in 37 spins(random display eg 1,5,2,9,27..)
1. spin - 37:37
2. spin - 36:37
3. spin - 35:37
4. spin - 34:37
.. etc..etc
odds for 37 all diffrent (unique) numbers in 37 spins (in order,like 0,1,2,3,4,5)
1. spin - 1:37
2. spin - 1:37
3. spin - 1:37
4. spin - 1:37
..etc..etc
Thanks for the explanation very interesting.
Regards
Max