How to spot wheel bias - the math way

[TierPlayer]

A very good site explaining how to find wheel bias is at nolinks://nolinks.genuinewinner.com/roulette-wheel-bias/

I'm talking about wheel bias on specific *numbers* here - for specific sectors it must be slightly different.
Well first of all you will need at least 300 spins to get somewhat reliable results. The reason is that each number will need to have an expected frequency of at leats 5-6 times.

The procedure goes like this (hugs to my stats teacher at the Uni) :
1) Find the expected frequency of every number under the assumption that the wheel is not biased, ie. divide the spins by 37. If you have 300 spins , the expected frequency is 300/37 = 8.11.
2) For every number from 0 to 36, calculate the difference  between observed frequency and expected frequency. Let's call this number Diff. Eg. Suppose the number 0 was spun 10 times, the Diff = 10-8.11=1.89. Suppose the number 1 was supun 5 times. The Diff for 1 is 5-8.11=-2.89.
3) Sum all the squares of the Diffs from 0 to 36. (remember the squares are always positive numbers)
4) Divide the result by the expected frequency (the same number as above, here it was 8.11)
5) If the number is bigger than 58.6, the wheel is most probably biased. Otherwise there is no reason to believe it is.

The method used is called "goodness of fit using the chi-squared distribution".
The number 58.6 that I used gives us a 99% confidence that we correctly believe the wheel is unbiased (if the result says so). If we need a better confidence level the number will be higher.

I did a test using spins from a land based casino (about 10,000 spins). It appears the wheel is not biased.

[Marven]

Nice. 300 spins is meaningless though, you need at least 1000 to give you an idea about the wheel. We use SD and chi-square tests for all numbers and sectors.

[GARNabby]

The best way to look at all of this in specific, followed by the best in general:

1.  nolinks://nolinks.stat.yale.edu/Courses/1997-98/101/confint.htm , nolinks://nolinks.surveysystem.com/sscalc.htm , and nolinks://nolinks.isixsigma.com/library/content/c030430b.asp ;

2.  Flipkart.com: Probability And Statistical Inference: J. G. ...Book Review of Probability And Statistical Inference by JG Kalbfleisch. 0387961836 9780387961835. ... Models For Probability And ... by James H. Stapleton ...
nolinks.flipkart.com/probability-statistical-inference.../0387961836-pvw3fdox0e - India - Cached , which is only another link for

Probability and statistical inference / J.G. Kalbfleisch ...Kalbfleisch, J. G. 1979 Probability and statistical inference / J.G. ... Probability and statistical analysis [by] Edgar P. Hickman [and] James G. Hilton ...

[TierPlayer]

I think there is a catch : if you use a confidence level 99% and you find that the wheel is not biased, then you are 99% sure it is so.
But if you conclude it is biased, your confidence is not necessarily 99% - probably it is less than that.

[Davey-Jones]

Playing numbers based on 300 previous spins is a bad BAD idea.

[Kelly]

Chi square is an essential part in all statistical analysis,  including tracking results in VB. Having said that, the correct way to bias spot, is to find the bias first, visually, and then from this assumption measure the Std/Chi Square.  If the the Std is peak picked from random numbers its not quite valid. Laurance has recently done a very good explanation on advantageplayer.com heres a copy and paste, you will then as a bonus get the formula for
calculating the standard deviation.

Laurance writes:

The formula for STDEV is: SQRT(N*P*Q)

In this case, N = 6 * 37 = 222

I assume you are playing a single zero wheel, so the probability of winning (P) = 2/37, and the probability of losing (Q) is 35/37. P = .054, Q = .946

SQRT(222*.054*.946) = SQRT(11.34) = 3.37

So, 3.37 hits represents one Standard Deviation (STDEV) from expectation given 222 trials and two numbers bet.

So, we now need to know what expectation is. Expectation = N * P (Number of spins * Probability of winning).

E = 222 * .054 = 11.988. Let's call it 12. Your expectation is 12 wins in 222 trials.

You have 21 hits, so you are 21 - 12, or 9 hits above expectation.

9 / 3.37 = 2.67 STDEV from expectation.

But wait ... there's more.

The 2.67 STDEV only has meaning IF you predicted the two numbers in advance of the 222 trials.

If you just took 222 trials, and then "Peak Picked" the top two numbers, the traditional STDEV does not apply. It only applies in the case where the outcome is predicted IN ADVANCE of the sample taken.

So, how rare is it to find two numbers which, combined, have a 2.67 STDEV over 222 trials? To answer this question, we need to run a simulation. I have a simulation program, and these are the results:

I ran 10,000 games of 222 trails each on a single zero wheel. I counted all of the games where there were at least two numbers, which combined, had a STDEV >= 2.67 (e.g. there were 21 hits or more).

8,025 of those games passed. In other words, if you don't predict the numbers IN ADVANCE, there is an 80% chance you will encounter two random numbers that, combined, will have 21 hits over 222 spins.

But, what if the two numbers are contiguous? The 80% figure applies if you pick ANY two numbers on the wheel. If you are looking at a contiguous 2 number section, this becomes a rarer event, but not that rare. The chances of a 2 number contiguous section rising to the 2.67 STDEV level is 28% (again, determined via simulation).

So, if you predicted the number IN ADVANCE of the 222 spins, the chance of those two numbers having 21 hits is about 1 in 50 (98% = 2.67 STDEV). If you peak pick the top two numbers after the fact, the chances of randomly winding up with two numbers hitting 21 times is 8 in 10. The chances of randomly finding two adjacent number >= 2.67 STDEV is about 1 in 4.

Hope this answers your question.

[toby]

@Kelly, The "simple detail" of how to spot a bias visually is the hardest part to learn.
Do you know it?

[Kelly]

I know the tecknik, but can`t go into details. All i can say without revealing too much is, the wheel needs to be moving to spot anything.  You can look all you want when the rotor is standing still, you won`t find anything that any maintenance or ordinary player wouldnt`see.
Having said that,  i can asure everybody that there are no biased wheels in my area.  And if there were i would deny it to my death day. The same goes for tiltet wheels.

[toby]

Ok, we know the technique but it takes too much to put it into action.

Even if I have lot of information I can not still know how to use it.

[Kelly]

Im not sure what you mean, it takes 30 - 60  minutes at the most  to locate visible possible biases on a wheel and draw a map over the wheel.  There are no guarantee that these locations are either donators or receivers, but  the actual number tracking will show what is happening in these areas. Certain biases are most likely to be either receivers or donators, but a combo of 2 biases can alter that depending on which kind of bias it is.   

[GARNabby]

Could a roulette- table/wheel be intentionally biased against the player in some normally-unseeable way, other than by the house-edge?

A friend of mine claims the baccarat-cards are rigged with magnets... that he's seen some "jiggling around" after the cards were removed from the shuffler.

[Kelly]

A bias that causes some numbers to go hot, usually also causes certain other numbers/sectors to go cold. Can`t have one, without the other

A bias could do the casino a lot of harm if a player found out about it.  If the casino believes that some players will start to ignore numbers that comes more frequent than others and start betting on the ones that comes less, and its because of a regular bias, they would clean those players out. But they would probably at the same time, lose more to those who playes hot numbers because they would  be playing with a genuine physical advantage, without knowing it.  They would with the right money management be playing with maximum, where the losing players will be betting smaller and smaller. Except Mr J, who would be progressing like a mad ;-)

In the end i think the casino is better off with just a regular unbiased wheel.

[toby]

A bias that causes some numbers to go hot, usually also causes certain other numbers/sectors to go cold. Can`t have one, without the other

A bias could do the casino a lot of harm if a player found out about it.  If the casino believes that some players will start to ignore numbers that comes more frequent than others and start betting on the ones that comes less, and its because of a regular bias, they would clean those players out. But they would probably at the same time, lose more to those who playes hot numbers because they would  be playing with a genuine physical advantage, without knowing it.  They would with the right money management be playing with maximum, where the losing players will be betting smaller and smaller. Except Mr J, who would be progressing like a mad ;-)

In the end I think the casino is better off with just a regular unbiased wheel.

Absolutly true.

Sometimes you find a biased sector close to a group of extremely cold numbers, they are donors to the next sector for any reason.

It isn´t enough to have an edge, you need a proper MM.

Imagine +20% edge having 1000 units BR playing 200 units each spin, huge chance to sink.

Hard to determine what numbers "not" to bet when you have many to choose.

I don´t like leaving holes between biased numbers.

[GARNabby]

A bias that causes some numbers to go hot, usually also causes certain other numbers/sectors to go cold. Can`t have one, without the other

A bias could do the casino a lot of harm if a player found out about it.  If the casino believes that some players will start to ignore numbers that comes more frequent than others and start betting on the ones that comes less, and its because of a regular bias, they would clean those players out. But they would probably at the same time, lose more to those who playes hot numbers because they would  be playing with a genuine physical advantage, without knowing it.  They would with the right money management be playing with maximum, where the losing players will be betting smaller and smaller. Except Mr J, who would be progressing like a mad ;-)

In the end I think the casino is better off with just a regular unbiased wheel.

Thanks, K.  Your response has a lot of depth to it, a lot to "chew on" there.

[lucky_jkl]

Kelly I was wondering if I could get that software you used to calculate the 80%. . . .   I looking for anykind of roulette software available for study and practical use. . . .

[lucky_jkl]

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