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.Quote:BnittyAs 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

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.

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?

Quote:RomesSo 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?

The problem is separating fact from EMOTION.Quote:BnittyI am hoping that this thread can help me separate fact from fiction.

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.

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.

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.