DJTeddyBear
DJTeddyBear
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September 28th, 2011 at 5:42:17 AM permalink
Quote: statman

3. You object to using a random number generator to simulate a roulette wheel. Do you know of a better way? Do you know a source of real roulette data?

In one of the deleted threads, I suggested that the RNG in Excel was not adequate for your job.

Of course, at the time I didn't really understand what you were doing. I still don't but I've got a better idea.

It seems to me that if your goal is to discover biased roulette wheels, the system / procedure / program / whatever that you're using, will only prove that the RNG is biased or inadequate.

For what it's worth, LONG before you manage to discover a biased wheel, the casino will discover it, and fix it. Or, at the very least, move the tables around so you'd have a hard time being sure of your analysis.

TCS John Huxley manufactures roulette wheels, history displays, and a variety of other items. One of the tools they provide is wheel analysis.
http://www.tcsjohnhuxley.com/en/gaming-systems-and-security/roulette-wheel-analysis.html
Admin note: removed image www.djteddybear.com/images/wheel_analysis.JPG
It seems to me that, on this chart, the green dotted line is the median, the green solid lines are the standard deviation. I.E. Within the green is the safe zone. Between the green and the red line is the danger zone, and beyond the red line and you've got a bias. If those assumptions are right, the wheel in this chart is biased towards #11 and it's neighbor, #30.

The piece of the puzzle tht I can't read is the number of spins in this analysis....
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗
CrystalMath
CrystalMath
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September 28th, 2011 at 5:57:05 AM permalink
Quote: statman

To date I have been doing simulations only with fair wheels. Some have suggested I simulate a biased wheel. Here are some results. The hot number on this wheel is 00. Its probability of coming up is 3/76 and its expectation is +0.42105. This was arranged by taking some sample space away from No. 37 and giving to 00.

This was done with a Quattro Pro spreadsheet, which I'll be glad to share with anybody. Just send me your personal e-mail address and I'll include it as an attachment. The number of plays is easily changed and the probability of any number can be changed in increments of 1/152 provided that the probability of some other number is changed the same amount in the opposite direction.

Games of 1000 Plays
Game No. Most HitNo. of Hits
11739
2 00* 59
3 9 41
4 00* 44
5 5 39
6 00* 43
7 15 41
8 6 39
9 00* 40
10 00* 49
11 6 39
12 00* 41
13 16 35
14 00* 42
15 27 36



This just shows that if you have a very biased wheel, in which one single number has a 50% more chance of happening than any other number, you still require at least 2000 spins to show some evidence of bias. Right?

Unfortunately, assuming that you have all of your statistics right, the product is just not useful.
I heart Crystal Math.
MathExtremist
MathExtremist
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September 28th, 2011 at 8:47:16 AM permalink
Quote: statman

Perhaps you also will make an original contribution to the theory and win the admiration of your colleagues.


What theory? The multinomial distribution completely describes the probability of a specific distribution of roulette numbers in M spins for a fair wheel. Summing these probabilities for all sets of coefficients which meet your criteria (at least one roulette number occurring N times) yields the overall probability. Standard statistics can describe the likelihood that a sampling from a real-world wheel is also fair based on the assumption of equiprobable outcomes. This isn't novel. What exactly do you think you've discovered, invented, or solved?

As to your typo, it appears you made it in your post, not your spreadsheet. You previously wrote "RAND()*39".

Quote:

3. You object to using a random number generator to simulate a roulette wheel. Do you know of a better way? Do you know a source of real roulette data?


No, I object to simulating a roulette wheel at all. It's unnecessary if your goal is to detect biases in a real physical roulette wheel. The chi-square test, for example, requires two sets of data: observed results and expected results. For roulette, you should sample the physical wheel in question to get the observed results, and you should ideally calculate the expected results. You shouldn't simulate the expected results unless you can't derive them properly. In this case, you can -- see above.

The point is that you don't need to be mucking around with virtual roulette wheels and plotting histograms and running random trials with spreadsheets. You can directly calculate F(N,M) = probability that at least one of 38 equally-likely outcomes appears N or more times in M trials.

But why would you? Are you planning on doing K samples of M-length trials and comparing each sample to F(N,M)? Why is that approach better than simply doing a chi-square test on a series of observed results vs. the expectation that each number appears with p=1/38?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
boymimbo
boymimbo
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September 28th, 2011 at 10:55:42 AM permalink
I have to agree with MathExtremist. There's nothing new in the field of statistics at all. The measure of bias in a wheel can only be done through established statistical analysis means as Math describes. There is no way of shortening up the testing for bias. What you can do is lower the degree of confidence and claim that a wheel is biased by saying that the degree of confidence is say, 50% instead of 95% (or say 1/2 standard deviation above expectation). That would allow you to claim that the wheel is biased towards these numbers with a smaller sample size and with a smaller degree of certainty. But of course it runs a greater risk of being completely false.

This is the same argument that dice controllers use. What degree of certainty do I have that I'm actually controlling the dice versus randomness? What sample size is required to know that I'm beyond the randomness? With a sample size of 144, if I roll 12 sevens instead of the expected 24, am I controlling the dice?

Math is saying that the RNG in Excel and many other spreadsheet programs are faulty. There have been studies on this, but none on the current version, and none on QuarkExpress.
----- You want the truth! You can't handle the truth!
statman
statman
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September 28th, 2011 at 12:56:37 PM permalink
MATERIAL REMOVED

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Rancocas Valley Journal of Applied Mathematics
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Many thanks to those who have been helpful.
A fool is someone whose pencil wears out before its eraser does. - Marilyn Vos Savant
DJTeddyBear
DJTeddyBear
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September 28th, 2011 at 1:52:37 PM permalink
I go to AC occasionally. Before PA got table games, I went there often. I think I've been to AC twice in the last 18 months.

Since you're new here, I'll direct you to one of my threads - pretty much all about A.C.
Atlantic City Casinos and Points Of Interest Map



Quote: statman

The history of roulette exploitation shows that they do this after they have been taken for a bundle, not before.

I'd bet that much of that history was before TCS John Huxley and others came out with the sensors and history displays. After all, incorporating a histogram like the one pictured in my post above, seems like an obvious and cheap add-on once you go thru the expense of the sensor and dislplay. Hell, it might have been one of the original selling points of the history board.
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗
statman
statman
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September 28th, 2011 at 1:55:21 PM permalink
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Many thanks to those who have been helpful.
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MathExtremist
MathExtremist
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September 28th, 2011 at 4:50:50 PM permalink
Quote: statman

MathExtremist:

"You can directly calculate F(N,M) = probability that at least one of 38 equally-likely outcomes appears N or more times in M trials."

Yes, that is precisely what I do, and that is what goes into the tables, but I haven't seen anybody else do it.


That might be because it's not useful. Suppose you compute the likelihood that 100 spins yields 3 or more appearances of at least one number. Call that P. Then you watch a wheel for 100 spins. That's about 2 hours. Then what? You're comparing two hours' of results with a single probability to determine what exactly? You can't make a credible assertion that the wheel is or is not biased based on P and the past 100 spins.

So what are you getting at?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
statman
statman
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September 28th, 2011 at 5:04:56 PM permalink
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Many thanks to those who have been helpful.
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buzzpaff
buzzpaff
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September 28th, 2011 at 7:59:57 PM permalink
"inclusion-exclusion principle." + statman = THIEF

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