Roulette UNIQUE NUMBER ODDS

No, not the same chance
this is easily solved using math in pari/gp calculator for example
pari/gp is also online

10 spins 10 unique numbers: 1 chance in about 3.8
11 spins 11 unique numbers: 1 chance in about 5.2
12 spins 12 unique numbers: 1 chance in about 7.4
20 spins 20 unique numbers: 1 chance in about 598
37 spins 37 unique numbers: 1 chance in about 766,879,127,067,901

Code:

gp > \\\no match. ALL uniques
gp > n=37;
gp > s=10;
gp > b=prod(i=0, s-1, ((n-i)/n));
gp > bDec=1.*b;
gp > b1chanceIn=1/bDec;
gp > b
%6 = 34162713446400/129961739795077
gp > bDec
%7 = 0.26286746776603321944611410580187708246
gp > b1chanceIn
%8 = 3.8041983989059309993440041454797969195
gp >
gp > n=37;
gp > s=11;
gp > b=prod(i=0, s-1, ((n-i)/n));
gp > bDec=1.*b;
gp > b1chanceIn=1/bDec;
gp > b
%14 = 922393263052800/4808584372417849
gp > bDec
%15 = 0.19182220620764586283905623936893733045
gp > b1chanceIn
%16 = 5.2131607688710906287306723475093513341
gp >
gp > n=37;
gp > s=12;
gp > b=prod(i=0, s-1, ((n-i)/n));
gp > bDec=1.*b;
gp > b1chanceIn=1/bDec;
gp > b
%22 = 23982224839372800/177917621779460413
gp > bDec
%23 = 0.13479398274050790361663411415114515113
gp > b1chanceIn
%24 = 7.4187287864703982024244183406863845908
gp >
gp > n=37;
gp > s=20;
gp > b=prod(i=0, s-1, ((n-i)/n));
gp > bDec=1.*b;
gp > b1chanceIn=1/bDec;
gp > b
%30 = 1045843337171591729971200000/624931990990842127748277129373
gp > bDec
%31 = 0.0016735314438190086465631678815347885811
gp > b1chanceIn
%32 = 597.53881750676526835046051282250993012
gp >
gp > n=37;
gp > s=37;
gp > b=prod(i=0, s-1, ((n-i)/n));
gp > bDec=1.*b;
gp > b1chanceIn=1/bDec;
gp > b
%38 = 371993326789901217467999448150835200000000/285273917723723876056171083405292782327767461712708093041
gp > bDec
%39 = 1.3039864624082512267293095836071052523 E-15
gp > b1chanceIn
%40 = 766879127067900.99759596072834531831580

some will say yes and some will say no
most HATE doing math

 

So if I am reading that correctly, it's 766 trillion, 879 billion, 127 million, 67 thousand and 9 hundred to one odds of seeing all 37 numbers appear consecutively in any order. In other words, not something you see every day, but sure, it can happen according to the AP guys!
I wonder how many lifetimes that is and if all the past and present people that live or have lived on planet earth have reached that figure combined.

 

good observation.
in any order is correct.

I doubt it has happened one time in the history of mankind.

IF I was to program a Roulette machine (easy enough), I would code it to do just that - one time - to see if anyone even noticed, of course, that would be illegal in most gaming jurisdictions.

 

kraps2727, thank you very much for posting this. I know how to calculate the probability of x unique hits in x spins (x!), but not the probability of x unique hits in >x spins. I'm afraid I don't know R or pari/GP, so I can't read your code. I'm looking for a formula so I can code it in Javascript. Can you help?

 

Thought I recognised that name,, couldn't think where from,

Hi Michael, the guy who got the Wizard up and running many moons ago, the man behind the scenes coding the software. Welcome to Gambling Forums. Roulette is not my game, so I'll bow out, nice to see you here

 

Thank you very much, Junket King. To be honest, the Wizard already had a site when I met him in 2000, but his then-business partners weren't generating any revenue for him. He split with them in 2003 and I started managing the website, then in 2004 I started selling the adspace and exploded the revenue. I left circa 2010, but we're still good friends.

 

"probability of x unique hits in >x spins." not really understanding this...
can you give an example of what exactly you are after?
I would think you need a Max spin (maybe a Min spin) so 24 uniques from 37 to 150 spins? You would have some very small values there.
my R code does cumulative right now, not knowing what exactly you're after, I would not know how to proceed.
I think I have posted this B4. 37 numbers and 37 spins
uniques with probabilities

Code:

> cc.draws(37,37)#0 Roulette, 37 numbers and spins
[1] "Number of numbers:37, spins:37, mean numbers show:23.5745, mean numbers NOT shown:13.4255"
          not drawn       Probability           cumulative        
u=1                  36 3.505402835209287e-57 3.505402835209287e-57
u=2                  35 8.672020148914835e-45 8.672020148918339e-45
u=3                  34 3.314692573547716e-37 3.314692660267917e-37
u=4                  33 1.181828396058428e-31 1.181831710751088e-31
u=5                  32 3.000862968528566e-27 3.000981151699641e-27
u=6                  31 1.353451338520529e-23 1.353751436635699e-23
u=7                  30 1.768441721182332e-20 1.769795472618967e-20
u=8                  29 8.959214842349408e-18 8.976912797075598e-18
u=9                  28 2.122121911879776e-15 2.131098824676851e-15
u=10                 27 2.668810406674974e-13 2.690121394921743e-13
u=11                 26 1.950286896969477e-11 1.977188110918694e-11
u=12                 25 8.848652985269136e-10 9.046371796361005e-10
u=13                 24 2.620176869821741e-08 2.710640587785351e-08
u=14                 23 5.261661586746048e-07 5.532725645524582e-07
u=15                 22 7.383252426941282e-06 7.93652499149374e-06
u=16                 21 7.411821128636426e-05 8.2054736277858e-05 
u=17                 20 0.0005422692213502838 0.0006243239576281418
u=18                 19 0.00293391179997579   0.003558235757603932
u=19                 18 0.01187191625199462   0.01543015200959855 
u=20                 17 0.03623411297966621   0.05166426498926475 
u=21                 16 0.08391608620844208   0.1355803511977068  
u=22                 15 0.1480232196433522    0.2836035708410591  
u=23                 14 0.1991885036499151    0.4827920744909742  
u=24                 13 0.2043690022411817    0.6871610767321559  
u=25                 12 0.1594366767704862    0.8465977535026421  
u=26                 11 0.0940910790104586    0.9406888325131006  
u=27                 10 0.04167532060124458   0.9823641531143452  
u=28                  9 0.01370132987004642   0.9960654829843917  
u=29                  8 0.003293428397655762  0.9993589113820475  
u=30                  7 0.0005672008922863491 0.9999261122743338  
u=31                  6 6.81047323781154e-05  0.9999942170067119  
u=32                  5 5.492144751551008e-06 0.9999997091514634  
u=33                  4 2.821730077624601e-07 0.9999999913244711  
u=34                  3 8.540410436050481e-09 0.9999999998648816  
u=35                  2 1.342486662710851e-10 0.9999999999991303  
u=36                  1 8.684549839638909e-13 0.9999999999999988  
u=37                  0 1.303986462408241e-15                 1   
[1] "Number of numbers:37, spins:37, mean numbers show:23.5745, mean numbers NOT shown:13.4255"

and 37 numbers with 150 spins - unique probabilities

Code:

 cc.draws(37,150)#0 Roulette, 37 numbers and 150 spins
[1] "Number of numbers:37, spins:150, mean numbers show:36.3928, mean numbers NOT shown:0.607181"
          not drawn       Probability            cumulative         
u=1                  36 2.177424544122785e-234 2.177424544122785e-234
u=2                  35 5.593903481953029e-188 5.593903481953029e-188
u=3                  34 1.691806217552409e-160 1.691806217552409e-160
u=4                  33 7.917353455855316e-141 7.917353455855316e-141
u=5                  32 1.79732212463243e-125  1.797322124632431e-125
u=6                  31 7.224562549300243e-113 7.22456254930204e-113
u=7                  30 3.524468664093874e-102 3.524468664166119e-102
u=8                  29 6.60567133118469e-93   6.605671334709158e-93
u=9                  28 1.002191559641911e-84  1.002191566247582e-84
u=10                 27 2.049896079225596e-77  2.049896179444752e-77
u=11                 26 8.139605169720873e-71  8.139607219617053e-71
u=12                 25 8.216206407780575e-65  8.216214547387795e-65
u=13                 24 2.587978440302679e-59  2.587986656517227e-59
u=14                 23 2.983255293484949e-54  2.983281173351514e-54
u=15                 22 1.427881780683184e-49  1.427911613494917e-49
u=16                 21 3.141072332524691e-45  3.14121512368604e-45 
u=17                 20 3.44979520742426e-41   3.450109328936629e-41
u=18                 19 2.025068936374158e-37  2.025413947307051e-37
u=19                 18 6.723576407237209e-34  6.725601821184516e-34
u=20                 17 1.323795287964448e-30  1.324467848146567e-30
u=21                 16 1.608223449016317e-27  1.609547916864464e-27
u=22                 15 1.246460072185899e-24  1.248069620102764e-24
u=23                 14 6.338652290947639e-22  6.351132987148666e-22
u=24                 13 2.165107140962139e-19  2.171458273949288e-19
u=25                 12 5.064474486323305e-17  5.086189069062798e-17
u=26                 11 8.240693411766362e-15  8.29155530245699e-15 
u=27                 10 9.441856006721884e-13  9.524771559746454e-13
u=28                  9 7.684553070333018e-11  7.779800785930483e-11
u=29                  8 4.465897058034082e-09  4.543695065893387e-09
u=30                  7 1.855594798028902e-07  1.901031748687836e-07
u=31                  6 5.493716400334692e-06  5.683819575203476e-06
u=32                  5 0.0001148034098288437  0.0001204872294040472
u=33                  4 0.001663095455592935   0.001783582684996982 
u=34                  3 0.01618201085930923    0.01796559354430621  
u=35                  2 0.09998409037823851    0.1179496839225447   
u=36                  1 0.3514061684712526     0.4693558523937973   
u=37                  0 0.5306441476062024                     1    
[1] "Number of numbers:37, spins:150, mean numbers show:36.3928, mean numbers NOT shown:0.607181"

many, I think, would like to know over X spins the probability of 24 or less uniques (cumulative, about 69%) or maybe 24 or more uniques (about 52%)?

I have NOT worked with javascript in a few years so I would have to brush up on it, if the coding is not that difficult. You have way more experience with JS than I do looking at your site (My last JS attempt was 3 years ago with Google Docs and the Script editor - turned out to be a BIG waste of time 4 me)

see what happens from here. Thanks for asking.

 

the math guys say "you havent played enough spins"

 

Thank you for the reply. I'm sorry I wasn't clear. I'm not looking for the Javascript, I can code the Javascript myself, as long as I know the formula. So I'm looking for the formula. For example: probability of 37 unique numbers in 50 spins.

When the number of uniques is <= the number of spins, (e.g., 20 unique #s in 37 spins), I can use 17/37 x 16x37 x 15/37, etc.

 

ok. the formula would work for both examples. I doubt your method would work when uniques are less than the spins as the formula is inclusion/exclusion
The Wizard of Odds has shown how to use that kind of formula in Roulette B4.
binomial() is a function like combin() in Excel or Wolfram Alpha for the number of combinations

Code:

\\ exact X uniques
parameters:
s=50;\\spins
u=37;\\uniques
n=37;\\number of numbers
formula:
a=binomial(s,u)*sum(k=0,u,((-1)^k*binomial(u,k)*(u-k)^n)/n^s)

result should be (a very small decimal)

Code:

gp > print(a)\\exact result
132005744860403619273465663075319190095134720000000000/69483946829049631418732401130460520284154662726180186608059352312305811442277
gp > print(aDec)\\as decimal
1.8998020533458682265760010087476394918 E-24
gp > 1/aDec\\1 chance in
%8 = 526370628055082496719932.10223200564067

Code:

\\ exact X uniques
parameters:
s=37;\\spins
u=20;\\uniques
n=37;\\number of numbers
formula:
a=binomial(s,u)*sum(k=0,u,((-1)^k*binomial(u,k)*(u-k)^n)/n^s)

result should be

Code:

gp > print(a)\\exact result
279368847701443428182784557070977481264406609920000000/7710105884424969623139759010953858981831553019262380893
gp > print(aDec)\\as decimal
0.036234112979666185716031648686571915321
gp > 1/aDec\\1 chance in
%16 = 27.598302201055087273947871263347598783

hope this helps

 

Thank you again, but I'm far from following you.

(1) My understanding of binomials is that I need three inputs:

(a) Probability of a single event
(b) Number of trials
(c) Number of successes

But both of your binomial functions take only two inputs.

(2) Your formula uses the variable "k" but it's not defined.

(3) Your formula uses the function "sum" which I'm unfamiliar with. Presumably it's a summation (sigma) but I don't know how the arguments correspond to a traditional summation.

 

and they should. you are thinking binomial probability.

How about binomial coefficient (n,k) "is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number."

(2)binomial(s,u)*sum(k=0,u,((-1)^k*binomial(u,k)*(u-k)^n)/n^s)
where k=0 to u
(3)it's a summation... Yep, it is
(-1)^k*binomial(u,k)*(u-k)^n)/n^s is the formula part in the summation
(-1)^k is the inclusion/exclusion part.

I have never seen a sum() in javascript and I think they have a way of doing it with 'reduce
stackoverflow shows some examples on how to do this, but a link can not be provided here

 

Looking at maTh Is FuN
dot
Com website and their javascript calculators, they create functions for these things.

Math.js has some advanced functions but I did not come across the sigma(summation) function, seems odd to me.

unless you can find a site that has some advanced JS calculators and look at the code, you will have to start by creating the sum and binomial (combinations) functions
good luck with that

 

Thank you again for the help. With that along with some self-study and help from others, I just published my Ultimate Roulette Calculator. Unfortunately, because of the forum rule against self-promotion, I'm unable to link to it. Maybe someone else will find it and link to it...

 

Petersone does this help?
Here are some great stats from a poster called Teorulte

I thought they were relevant to Colbsters post

I ran about 500 000 cycles of 37 spins and came up with the following:

(Number on left is number of unique numbers and next number is how many times a spin cycle had exactly that many unique numbers in the test)

37 spin cycle:

15 1
16 12
17 202
18 1417
19 6020
20 18309
21 41304
22 73951
23 98780
24 102814
25 80164
26 47276
27 20934
28 6706
29 1685
30 349
31 35
32 5

74 spin cycle:

25 46
26 304
27 1898
28 7536
29 22123
30 50675
31 88059
32 114050
33 107055
34 69801
35 29634
36 7735
37 1011

111 spin cycle:

29 31
30 181
31 1407
32 7570
33 29508
34 83849
35 151889
36 155781
37 69674

148 spin cycle:

32 15
33 828
34 8540
35 52625
36 181344
37 256499

Mean and median were approximately:

24 for 37 spin cycle
32 for 74 spin cycle
35 for 111 spin cycle
37 for 148 spin cycle

Or this?

This is a test I did in November. I tested over 1 million single zero RNG spins and got this:

2 3210
3 6251
4 9017
5 10906
6 12398
7 12852
8 12454
9 11478
10 10007
11 8619
12 6845
13 5243
14 3857
15 2730
16 1816
17 1128
18 687
19 355
20 246
21 96
22 61
23 29
24 16
25 5
26 3
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0

The most unique numbers in a row was 25 (The 26 means it hit on the 26th spin, so 25 unique numbers in a row) and this happened only 3 times.

 

Hi am new here i have been playing roulette for many years and i think am going to go the bias routh my question is how many spins do you need to track for a half wheel Section bias 18 numbers on one side and 18 on the other leaving out the zero its European wheel. i read on another website they say 500 spins should be about right but what with i consider a bias 240 on one side 260 on the other? Also do i need to play 500 spins 16, hours at 2 min a spin to get a bias out and win? One last question do i need to track 500 spins all at once? Or can i track 100 spins a day for 5 days on the same wheel of course

 

There is no magic number of spins. The way it works is, the more spins you have, the more confidence you have in the result.

For example, let's say I flip a coin and get heads. Do I conclude that the coin is biased from such a small sample? No. How about two heads? No, but it's more likely the coin was biased versus just one heads. How about three heads? Even more unlikely to be a random result, even more likely to be biased. And so on, and so on. At some point you might have a 60% chance that the game is biased, or with more data 75%, and even more data 85%, etc. You never get to 100%, because, say, 100 heads in a row is *possible* even though it's extremely unlikely.

You don't have to track the spins all at once, you can track them across various sessions.