Roulette Wheel Bias Theory vs Practice

Quote: MDawg

A few people throughout history might have made money off biased roulette wheels. But definitely more have lost money off what they Thought were biased roulette wheels.

As far as the ones who might have made money off biased wheels, there are documented stories of people hitting the same number or quadrant repeatedly and making vast sums, and claiming it was on a biased roulette wheel. You've never read the "Thank you, old sport" story of the guy in Europe, I believe it was in Monte Carlo, who did that and retired? supposedly never to gamble again.

As far as the ones who have lost money off what they Thought were biased roulette wheels I personally observed, over the course of a week, a small party dump somewhere around two million USD on a European roulette wheel in Vegas they were convinced was biased. They did actually hit the number they claimed was supposed to come up a lot at least twice that I saw myself, but not enough times to matter.

MDawg,

I suspect that you're mistaking some short term observations of hot numbers being played for actual biased wheel play. Over the course of a week your observations are going to mislead you if you're just looking at what appears to be sections of the wheel or numbers that appear to sometimes repeat.

I think kubikulann understood what I was saying, which was:

1 - there have been such things as biased wheels over the course of time and perhaps some people have benefitted from them. The cases I have read of, were many years ago, in Europe. I don't mean ten or twenty I mean like a hundred years ago, and even further back in time. Back then, it seems far more likely that wheels could be biased.

2 - However, there are many more people who have THOUGHT that they were before biased wheels, and lost their arses betting the same number or quadrant. My story of the little "team" that dumped a couple mill is an example of that - they told me Exactly what they thought was going on, and put a lot of money behind their thoughts, to their detriment. This was in a modern Vegas casino.

Your story sounds a little made up.

I've spent a lot of time in Vegas and Tahoe, playing. It doesn't really matter what you think though.

I'm not a fan of roulette myself.

I think it somewhat comes back to what Sean Connery said to Kevin Costner in The Untouchables, "Who would claim to be that, who was not?" If I wanted to make up a story, I could come up with a better one than that. But, truth is sometimes stranger than fiction. I had a group of friends and a girlfriend with me during most of my trips, and any of them repeating some of the things we saw and experienced might be looked at in wonder, but it wouldn't make the stories any less true.

When and where did it supposedly happen?

There's a reason why I post the way I do, but you'll have to figure that out for yourself. Goodbye for now.

Thanks for the replies.

The point of this post is to take the raw data and present ideas on how to analyze it effectively to prove or disprove bias.

As Wizard noted in an earlier post, there may be something here but its likely small (if it exists at all).

I will provide the data and analysis for anyone to critique and lets see what we find.

Quote: Bnitty

The point of this post is to take the raw data and present ideas on how to analyze it effectively to prove or disprove bias.
As Wizard noted in an earlier post, there may be something here but its likely small (if it exists at all).
I will provide the data and analysis for anyone to critique and lets see what we find.

SN Ethier did a paper way back in 1982
Testing for Favorable Numbers on a Roulette Wheel
Author(s): S. N. EthierSource: Journal of the American Statistical Association, Vol. 77, No. 379 (Sep., 1982), pp. 660-665Published

and again in his college textbook 'The Doctrine of Chances'

Quote:

"Suppose we have “clocked” a roulette wheel for n coups, and the most
frequent number has occurred a proportion 1/25 of the time. Is it a biased
wheel? Although we can never be absolutely certain, we can nevertheless
quantify our degree of confidence. It will of course depend on n."
pg 472
"Actually, we are not concerned simply with whether the wheel is biased. The relevant
question is whether there is a favorable number, that is, one that results in
a superfair bet;"

Here is a table from the calculations for the math presented in that book.
"We saw that, if the most frequent number in n coups has occurred
a proportion 1/25 of the time, we can conclude with 95% confidence that
one or more favorable numbers exist if n ≥ 1,618."
k=1/k

↓k, CL→	99%	98%	95%	90%	80%	50%
19	522	465	392	337	282	212
20	652	582	490	421	353	265
21	818	730	614	528	443	333
22	1,031	920	774	665	558	419
23	1,306	1,166	981	843	707	531
24	1,669	1,489	1,253	1,077	903	679
25	2,156	1,923	1,619	1,391	1,166	876
26	2,821	2,517	2,118	1,820	1,526	1,147
27	3,755	3,350	2,820	2,423	2,032	1,526
28	5,111	4,560	3,838	3,298	2,766	2,077
29	7,161	6,389	5,377	4,621	3,875	2,910
30	10,431	9,305	7,832	6,730	5,644	4,239
31	16,038	14,308	12,042	10,348	8,678	6,517
32	26,703	23,821	20,048	17,229	14,447	10,851
33	50,484	45,036	37,903	32,572	27,314	20,514
34	120,577	107,565	90,528	77,796	65,238	48,995
35	511,095	455,941	383,726	329,758	276,525	207,677

your collected data shows the most frequent number at about 1/31

from the table, the confidence level is about 65%
the sample size, to me, looks way too small

others think it is ok and fine

others have collected way more spins than you have and some do not need to collect spins, so they say.
enjoy the ride

Bnitty,

Yes your wheel is likely a WEAK biased one.. The chi square is a little low, but the large number of numbers close to, or below two standard deviations between the numbers 27 clockwise to 14... and the numbers close to or above two standard deviations from the numbers 7 clockwise to the number 1 that makes the wheel interesting. Sometimes it's not just the raw data that can show significance but also the way the numbers are hitting, as they are placed around the wheel. I wouldn't be surprised if it was a wheel with an indexable pocket compartment that has a pocket compartment that's not tightly bolted down over one semi circle of the wheel or one that's breathing. (The loose area would absorb energy from the bouncing ball.) On wheel like this I would trace the movements of the lights being reflected in the pocket compartment to narrow down the cause.

If you're going to play on just raw number data, then you need an out of sample set of data ( at least a few thousand or more spins to confirm your find). The lead number shows as 3.24 standard deviations, but that's a little misleading because that number wasn't narrowed down as being the best before testing the data. (Meaning, that it's not really the true standard deviation of the number just yet. ) It's likely just a number that's hitting hot in a possibly weak biased section. If the wheel is biased, then the chi square and the standard deviations will grow as the sample size grows.

Overall though the wheel looks pretty weak for a bias play.

Quote: Bnitty

I have more data on this endeavor and I’m willing to go all in to prove or disprove what everyone is proposing.

Let’s make something happen with this or else it’s all talk.

Let’s do it.

Can you post the new data?

Quote: MDawg

I think kubikulann understood what I was saying, which was:

1 - there have been such things as biased wheels over the course of time and perhaps some people have benefitted from them. The cases I have read of, were many years ago, in Europe. I don't mean ten or twenty I mean like a hundred years ago, and even further back in time. Back then, it seems far more likely that wheels could be biased.

2 - However, there are many more people who have THOUGHT that they were before biased wheels, and lost their arses betting the same number or quadrant. My story of the little "team" that dumped a couple mill is an example of that - they told me Exactly what they thought was going on, and put a lot of money behind their thoughts, to their detriment. This was in a modern Vegas casino.

Dear MDawg,
I am in no way busy about the gist of the matter, are there or are there not biased wheels.
My point is about epistemological methods.

Your approach consists of what is known as « the law of small numbers »: « what I have personally seen is more important than statistical data ».
A classical example is, trusted magazine ABC published a poll showing model XYZ has the best record in terms of breakdowns (or failures? Translation problem, I mean ‘’panne’’ In French). Yet your brother-in-law had a XYZ and complained to you about some breakdown he experienced. Most people in this situation would conclude that model XYZ is prone to breakdowns, in contradiction with the statistical data.

Science doesn’t care a bit about your expérience, your story. It requires objective facts, large numbers of repeated observations and demonstrable proofs. Be wary of a much too easy tendency to assert things without support.

Secondly, the fact that many people have made errors is totally irrelevant to the question whether something is real. Many people THINK they should plant vegetables when the moon is rising. Does that info cause you to change your appreciation of whether there is a real effect?
Worse. You tell us you witnessed an amateur farmer who planted some lettuce on a rising moon and had a bad harvest; and you want us to conclude that the moon has no effect. Sorry, but that is not statistically sound.

My evidence is anecdotal as far as what I observed, or what I have read.

But still - stepping aside from all that , it stands to reason that a roulette wheel is going to be accurate in modern times with no bias, while a wheel from a hundred years ago would be less accurate. So without doing any statistical research at all we could say that a pair of dice from a Vegas casino today is going to be perfectly shaped versus dice that the Romans tossed two centuries ago.

That roulette wheel in a modern Vegas casino is like a Swiss watch that is maintained perfectly. I don't have to do a lot of tests to know that it keeps accurate time. Since the chances of its being biased are statistically insignificant, I may indeed say that there are more people who have thought they found a biased wheel than those who actually found one.

Quote: MDawg

My evidence is anecdotal as far as what I observed, or what I have read.

But still - stepping aside from all that , it stands to reason that a roulette wheel is going to be accurate in modern times with no bias, while a wheel from a hundred years ago would be less accurate. So without doing any statistical research at all we could say that a pair of dice from a Vegas casino today is going to be perfectly shaped versus dice that the Romans tossed two centuries ago.

That roulette wheel in a modern Vegas casino is like a Swiss watch that is maintained perfectly. I don't have to do a lot of tests to know that it keeps accurate time. Since the chances of its being biased are statistically insignificant, I may indeed say that there are more people who have thought they found a biased wheel than those who actually found one.

Cars are the same. Cars don't break down these days because they are assembled and run like a Swiss watch. Cars a hundred years ago did, but that was then. The chance of them breaking down now is statistically insignificant.

Quote: MDawg

My evidence is anecdotal as far as what I observed <…>

But still - stepping aside from all that , it stands to reason that <…>.

So without doing any statistical research at all we could say that <…>
…
That roulette wheel in a modern Vegas casino is like a Swiss watch that is maintained perfectly. [evidence, please?]

I don't have to do a lot of tests to know that <…>

Since the chances of its being biased are statistically insignificant, <…> .

Utter drivel. 😂
At the same time you profess that ‘anecdotal’ evidence ‘stands to reason’, that you ‘don’t need tests to know that’ something is ‘perfect’ ‘without doing any statistical research’, and then assert that is ‘statistically insignificant ‘.

Also, you ignore that biasedness results can be proved *significant*, but ‘’insignificant’’means you cannot prove any statement. ( you confuse ‘’statistical insignificance’’ with ‘’negligible’’)


Sutor, ne supra crepidam.
Please don’t play Ivanka and mix with experts on subjects you boast knowing nothing about.

Quote: Keyser

Cars are the same. The chance of them breaking down now is statistically insignificant.

No.
It is negligible.
But it is statistically significant.

If I let go of a hammer I'm holding, I don't need to look down to know that it has dropped. Unless I'm standing on some other planet that has negative gravity.

What is the end game here?

If you're trying to find a biased roulette wheel in a modern casino you are not going to find one. I don't need to analyze anything to know that.

It's becoming increasingly clear to me that a lot of you here are just armchair gamblers, spending long hours spouting theory. That's fact. Your insults, just prove that. :-)

I understand perfectly what you're getting at and I understand clearly that my anecdotal evidence doesn't prove anything definitively. But it offers more than any numbers you've churned because your numbers do not establish a biased wheel.

In case you didn't notice, the title of this thread is "THEORY VS PRACTICE" - I offer the practice that I've seen.

Modern Roulette is a loser game, so knock yourself out looking for something that doesn't exist. Which you won't end up playing anyway, because you're apparently not interested in reality (practice). Just theory.

Quote: MDawg

It's becoming increasingly clear to me that a lot of you here are just armchair gamblers, spending long hours spouting theory. That's fact. Your insults, just prove that. :-)

In case you didn't notice, the title of this thread is "THEORY VS PRACTICE" - I offer the practice that I've seen.

. Which you won't end up playing anyway, because you're apparently not interested in reality (practice). Just theory.

Yes, we meet here, agreeing to disagree.

I and others are not even armchair gamblers. We are statisticians and/or epistemologists.

The original question looks like: theory says wheels are unbiased; what does practice say?
Keyser offered very interesting info on the physical aspect. Others worked on the possibility of using statistical practically.

This in turn led to epistemological questions about the efficiency and trustworthyness of statistical tests.

Non you come and reverse the question. You claim Theory (we) assert a priori that wheels are biased and that Practice (you) can assert a priori they are not and our efforts are futile, without the least appeal to a safe scientific method.
Clearly the discussion at hand passes way over your head. You are perfectly correct in saying we don’t give a dime about true, life, practical wheels. We THINK.
You, on the other hand, gamble billions on real world tables. Not roulette, if I understand your criticisms. But of course this does not prevent your being an expert on roulette...

One final question: why do you bother? What is so important to you in our scientific-philosophical discussion?

You're quite right, I was carrying over the argument from the other thread where people were challenging my posts as untruthful. In this case, this thread, I agree that my posts related to this mathematical analysis are anecdotal, and not relevant scientifically because obviously, not enough data.

I understand your analysis, just not the need for it. Similar to your final Q actually. :-)

I’ll post the data soon. I need some time to organize everything. I’ll share all the data points and take advice on the next steps.

Here's what we have:

Original data set is reposted here, New data set is the original set plus ~1500 data points. I am missing some data from the new set but I don't believe it will prove anything as the p-value to reject our null hypothesis has decreased with the new data added to the pool.

I will further segment the data as needed and have some questions for the forum on some observations and statistics for a potential repeat bias but I am open to any interpretations of the data here and will add to the discussion based on any feedback given.

Overall I do not appear to see the bias growing as the data set grows.

Thanks for the help!

Data Set 1: 7456 Data Points, X2 = 68.10193

Number Ocurrences 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


Data Set 2: 8985 Data Points, X2 = 59.29182

Number Ocurrences Expected Value X2
19 201 236.4473684 5.314146384
35 201 236.4473684 5.314146384
24 207 236.4473684 3.66740181
11 211 236.4473684 2.738742934
33 212 236.4473684 2.52772457
27 213 236.4473684 2.325164748
31 216 236.4473684 1.768236535
16 218 236.4473684 1.439243769
9 219 236.4473684 1.287435199
26 219 236.4473684 1.287435199
32 219 236.4473684 1.287435199
14 226 236.4473684 0.461614387
6 227 236.4473684 0.377474153
21 230 236.4473684 0.175804704
23 231 236.4473684 0.125498638
2 231 236.4473684 0.125498638
34 237 236.4473684 0.001291626
36 238 236.4473684 0.010195355
100 238 236.4473684 0.010195355
12 239 236.4473684 0.027557625
50 240 236.4473684 0.053378438
4 240 236.4473684 0.053378438
18 242 236.4473684 0.130395689
10 243 236.4473684 0.181592127
20 246 236.4473684 0.385932695
25 248 236.4473684 0.56445245
8 248 236.4473684 0.56445245
30 251 236.4473684 0.895671148
7 252 236.4473684 1.022994464
1 252 236.4473684 1.022994464
15 254 236.4473684 1.303016724
3 254 236.4473684 1.303016724
29 254 236.4473684 1.303016724
28 255 236.4473684 1.455715666
13 255 236.4473684 1.455715666
5 267 236.4473684 3.947869256
17 268 236.4473684 4.210529245
22 283 236.4473684 9.165454119
8985 59.2918197


DF 0.995 0.975 0.2 0.1 0.05 0.025 0.02 0.01 0.005 0.002 0.001
37 18.586 22.106 43.978 48.363 52.192 55.668 56.7359.893 62.883 66.633 69.346
38 19.289 22.878 45.076 49.513 53.384 56.896 57.969 61.162 64.181 67.966 70.703
39 19.996 23.654 46.173 50.66 54.572 58.12 59.204 62.428 65.476 69.294 72.055
40 20.707 24.433 47.269 51.805 55.758 59.342 60.436 63.691 66.766 70.618 73.402
41 21.421 25.215 48.363 52.949 56.942 60.561 61.665 64.95 68.053 71.938 74.745
42 22.138 25.999 49.456 54.09 58.124 61.777 62.892 66.206 69.336 73.254 76.084
43 22.859 26.785 50.548 55.23 59.304 62.99 64.116 67.459 70.616 74.566 77.419
44 23.584 27.575 51.639 56.369 60.481 64.201 65.337 68.71 71.893 75.874 78.75
45 24.311 28.366 52.729 57.505 61.656 65.41 66.555 69.957 73.166 77.179 80.077
46 25.041 29.16 53.818 58.641 62.83 66.617 67.771 71.201 74.437 78.481 81.4
47 25.775 29.956 54.906 59.774 64.001 67.821 68.985 72.443 75.704 79.78 82.72
48 26.511 30.755 55.993 60.907 65.171 69.023 70.197 73.683 76.969 81.075 84.037
49 27.249 31.555 57.079 62.038 66.339 70.222 71.406 74.919 78.231 82.367 85.351

The bias just isn't strong enough.

I took a look at the data again and I used a pivot table to analyze some different strategies on taking advantage of the numbers that were identified .

So far the results are fairly impressive but I think that it needs a long-term view to prove that this is exploitable.

I will continue to post every 10,000 data points that I gather and maybe this will be able to show that it’s more than just a theory .

Thanks to everyone for all of the guidance and advice.

Bnitty, weak biased wheels take huge effort to be beaten, many hours playing a wage that prevents you from ruin before taking advantage of the bias. But, it is better than playing random. You should pay detailed attention to every wheel part to notice any Casino countermesure.
The way Keyser detects wheels visually can only be accomplish by very very few biased wheel pro players, it saves time and money.

ybot