Roulette Wheel Bias Theory vs Practice

As many of you know, there is much debate about wheel bias and detection systems.

I am hoping that this thread can help me separate fact from fiction.

Here is what I have:

7500 Data Points on an automated Wheel.

Number Occurrences Expected Value X2
19 163 196.2105263 5.621202281
35 163 196.2105263 5.621202281
16 164 196.2105263 5.287779535
33 171 196.2105263 3.239228033
27 173 196.2105263 2.745665801
9 175 196.2105263 2.292876101
24 176 196.2105263 2.081770951
26 177 196.2105263 1.880858934
14 177 196.2105263 1.880858934
31 180 196.2105263 1.339281681
11 181 196.2105263 1.179142196
32 184 196.2105263 0.759882539
6 186 196.2105263 0.531341766
23 191 196.2105263 0.138369663
34 194 196.2105263 0.024903998
2 194 196.2105263 0.024903998
10 195 196.2105263 0.007468376
100 197 196.2105263 0.00317653
12 197 196.2105263 0.00317653
25 198 196.2105263 0.016320307
4 200 196.2105263 0.07318726
18 201 196.2105263 0.116910436
30 203 196.2105263 0.234936187
36 203 196.2105263 0.234936187
21 203 196.2105263 0.234936187
50 204 196.2105263 0.309238762
20 205 196.2105263 0.39373447
8 207 196.2105263 0.593305286
3 209 196.2105263 0.833648633
15 210 196.2105263 0.969110007
28 214 196.2105263 1.612886831
13 217 196.2105263 2.202747346
1 217 196.2105263 2.202747346
29 217 196.2105263 2.202747346
17 222 196.2105263 3.389710865
7 223 196.2105263 3.657682968
5 224 196.2105263 3.935848204
22 241 196.2105263 10.22420657

7456 68.10193133

Note: This is a double zero wheel. 100 = 00 and 50 = 0

The critical value appears to suggest that if your hypothesis is that the wheel is fair then you would reject this hypothesis.

1: If you accept this data then how would you use this data similar to other players who have attempted these methods for taking advantage of wheel bias.

2: What other tests should be performed to prove or disprove any suggested bias.

Thanks

#22 ends up with the best EV (a whopping 16.36%) with the second best number being the #5 with an 8.15% EV. The fact that they are adjacent on the wheel would fit the hypothesis of this being a biased wheel.

So long as you have a sufficient sampling size, AND IDENTIFYING MARKS (so you're sure the wheel has not ever been changed out during your trials), then the minimum number of trials to identify a bias is usually around 7500-8000. If you've come this far due diligence would push for 10k, in which you could identify biases with simple mathematics as you've done. Don't really need another test as this is the brute force approach where the numbers don't lie anymore.

Quote: Bnitty

As many of you know, there is much debate about wheel bias and detection systems.

I am hoping that this thread can help me separate fact from fiction.

Here is what I have:

7500 Data Points on an automated Wheel.

Number Occurrences Expected Value X2
19 163 196.2105263 5.621202281
35 163 196.2105263 5.621202281
16 164 196.2105263 5.287779535
33 171 196.2105263 3.239228033
27 173 196.2105263 2.745665801
9 175 196.2105263 2.292876101
24 176 196.2105263 2.081770951
26 177 196.2105263 1.880858934
14 177 196.2105263 1.880858934
31 180 196.2105263 1.339281681
11 181 196.2105263 1.179142196
32 184 196.2105263 0.759882539
6 186 196.2105263 0.531341766
23 191 196.2105263 0.138369663
34 194 196.2105263 0.024903998
2 194 196.2105263 0.024903998
10 195 196.2105263 0.007468376
100 197 196.2105263 0.00317653
12 197 196.2105263 0.00317653
25 198 196.2105263 0.016320307
4 200 196.2105263 0.07318726
18 201 196.2105263 0.116910436
30 203 196.2105263 0.234936187
36 203 196.2105263 0.234936187
21 203 196.2105263 0.234936187
50 204 196.2105263 0.309238762
20 205 196.2105263 0.39373447
8 207 196.2105263 0.593305286
3 209 196.2105263 0.833648633
15 210 196.2105263 0.969110007
28 214 196.2105263 1.612886831
13 217 196.2105263 2.202747346
1 217 196.2105263 2.202747346
29 217 196.2105263 2.202747346
17 222 196.2105263 3.389710865
7 223 196.2105263 3.657682968
5 224 196.2105263 3.935848204
22 241 196.2105263 10.22420657

7456 68.10193133

Note: This is a double zero wheel. 100 = 00 and 50 = 0

The critical value appears to suggest that if your hypothesis is that the wheel is fair then you would reject this hypothesis.

1: If you accept this data then how would you use this data similar to other players who have attempted these methods for taking advantage of wheel bias.

2: What other tests should be performed to prove or disprove any suggested bias.

Thanks

I plotted count on a simple excel line chart.It screamed bias.
Then I realised the counts had been sorted so it stopped screaming.
Armed with map of the wheel, I sorted by number position.
Got the rather subjective conclusion that the numbers near 5 and 22 were 'hotter' than those diametrically opposite.

If I were analysing this properly, I'd start by separating clockwise and anticlockwise spins.

Thanks for the replies.

In my case this wheel always spins clockwise but the speed varies on a pattern that I can't quite figure out.

Let's say that we can get 10-15k data points for this wheel.

Are we looking to flat bet the biased sectors or are we waiting for some mathematical inference that betting a certain number of times is profitable.

I assume that one could run a simulation on the presented data and try to optimize a strategy?

Once you have all the data points and do the basic math to show certain numbers probabilities are higher than others (re:biased numbers) then a simulation is pretty much a moot point. At that point you could simply bet the biased numbers, which have been shown to mathematically have an edge over time. I haven't done much more dabbling in betting the adjacent numbers of the biased numbers, but I'm sure an argument or some simple math from the previous probabilities could make sense.

Quote: Romes

So long as you have a sufficient sampling size, AND IDENTIFYING MARKS (so you're sure the wheel has not ever been changed out during your trials), then the minimum number of trials to identify a bias is usually around 7500-8000.

I have to admit this issue of adequate sample size is something that has been bugging me for several months, ever since I read Stanford Wong's book "On Dice". He seemed to be saying with carefully constructed tests, even a hundred data points would suffice. Granted, that was for dice rather than roulette, but it still seems a small number. It got me curious enough that even tho I hated statistics in college (my least favorite math course) I've started trying to learn more on the subject. From what I can grok, the greater the bias, the smaller the sample size required to generate a P-value that is sufficient to reject the null hypothesis. Sounds reasonable but until you sample a ton of data, how do you know if it is a biased wheel? The 7000 number FEELS right but is there any formula that can be used to figure out what a reasonable sample size should be in a given situation?

Quote: Bnitty

I am hoping that this thread can help me separate fact from fiction.

The problem is separating fact from EMOTION.
People WANT a biased wheel that they can walk up to and get rich with despite the fact that all the people who have been playing there do not see any bias, all the people working there do not see any bias, all the computers owned by the casino do not see any bias, all the managerial reporting programs from accounting do not see any bias.... but lo and behold when THEY walk up to the roulette wheel they will somehow detect and exploit that bias which only they themselves can see. And during that period of exploitation ain't nobody gonna adjust the thermostat or use a vacuum cleaner or nudge the wheel or even give it a good hard stare.

Data Points? Heck, if you really want to believe in something you don't need any datapoints at all. If the pornslapper's photocard says "Not An Agency" you can choose to believe it. If you want the wheel to be biased you can believe it. You don't need data points to feed a fantasy.

If you think the wheel is biased start betting octants, if your bank roll dwindles, it ain't biased.

TLDR: The more bias the fewer samples are needed. If my hypothesis is that this coin is weighted to heads is more likely to land, then I'm going to need far more flips to determine it's weighted if heads lands about 51% of the time, whereas if it lands on heads 90% of the time, I don't need such a large sample size of flips.


I haven't gone through the numbers posted above on this roulette wheel, but I saw someone post a 15% or 8% edge looking post. If that's the case, I'd go ahead and bet those numbers for a reasonable amount, such that if I'm wrong and there is no bias, I'm not giving up too much value, but if I'm right, then I'm still getting a fair amount of value. In doing this, I'd continue to track the numbers to verify or refute(?) the previous notion/data that the wheel is biased.

IOW: I just flipped a coin that landed on 15 heads and 5 tails. I think it very well might be biased. Instead of betting large amounts on heads, I'm going to bet a reasonable amount on heads AND continue to track it, to make sure heads is still showing up far more than 50/50. If it continues, then I'll continue. If it doesn't continue, then I'll do the math again and assume the probability is 15/20 then see how unlikely the new results are.

That number 22 is 3.24 deviations to the right of expectations, which is getting pretty convincing.

Only 1 in 1,675 chance this result just happens to be out there by luck.

There is no magic number for sample size. If this bias is true and you did 20,000 spins you could just state the same result with more confidence. But 99.94 % confidence (1674/1675) is pretty good...I would be betting heavily on number 22. Have to keep in mind though that single number bets are very high variance, so even with a huge 16.4% advantage, there's still over a 25% chance you will have lost money after 500 bets. So you might need a few days of playing to successfully exploit this.

The sample size needed to give confidence is going to vary based on how biased the wheel is and what kind of bet you're testing for. Testing a single number on a slightly biased wheel will take many more samples than testing a quadrant on a very biased wheel.

By the way the "quadrant" of the ten numbers 17-5-22-34-15-3-24-36-13-1 is even more biased than number 22. It comes up 2,113 times vs expected 1,962. That's 3.97 deviations out, and there’s only a 1 in 27,651 chance of that happening by chance alone.