Simulating Murphy's Extreme Bias Roulette Wheel

Simulating Murphy's Extreme Bias Roulette Wheel
A roulette wheel found to be biased in favor of three numbers, including No. 0, was examined at a casino in Oregon using the chi-square test with 20,000 spins.

Some of the comments below were made before the post was moved and are no longer appropriate.

Regarding bias.

There's no set number of spins required to detect bias because the strength of biased wheels varies so greatly.

Wow, this is awful simulating.

According to the article at the bottom of page 40, the number 0 was hit 628 times out of 20,504, the number 25 was hit 621 times out of 20,504, and the number 29 was hit 607 times out of 20,504.

Out of 100 spins then, the 0 should hit 3.0628 times out of 100.

Your "experiment" shows a minimum frequency of 6.

WRONG. Try again.

Quote: statman

Is there a good reason for the 39 numbers in the x-axis?

0=0
37=00
38=?

Exactly. Lousy simulation. First, the fact that there is a decimal frequency as if it's a continuous spectrum, and second, for the existence of the number 38. I didn't realize that a roulette wheel had 39 positions on it.

To help things along, this little ditty would produce a frequency of .04 on 1,2,3 and a even frequency on the remainder of the numbers (4-38). It doesn't matter what three numbers come up the most.

To simulate your experiment with the murphy wheel you would generate 0 when the number was less than 628 / 20504, 1 when it was y out 20504 and z out of 20504.

(B1 = rand())
=IF($B1<0.12,INT($B1*25)+1,INT(($B1-0.12)/0.88*35)+4)

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Trying to prove bias or prove lack of bias?
Yipes.
I guess if you have a frequent player each night and he goes home broke, the wheel ain't biased. Or atleast it ain't biased sufficiently to be detectable to those watching the annunciator and keeping a scorecard.

Remember the photograph of the pretty girl standing near the annunciator that had all those 14s on it that night.
I'd just love to a different photo that very next night: Different pretty girl, lots or repeats of some other number, no 14s at all ... and tell the folks later its the same casino, same wheel.

Only ONE instance of Seven Red, but look at all those times 29 hit. So do you really want to say bias? Or look at octets and then say bias?

Don't tell me I'm making it too easy.

Yeah, but you can't have a distribution of numbers where you are simulating 100 spins and having a frequency of a certain number NOT BE AN INTEGER, and have your simulation have 39 numbers and then claim that an American wheel has an "eagle". Since when?

What I am saying is that you publish a simulation which is clearly wrong and state this mathematical mumbo-jumbo to support it when clearly, you really don't know what you're doing. Any statistician or mathematician knows how to do a simulation and wouldn't publish something clearly as out to lunch as this.

Look, go ahead and take your theoretical results to a casino. Record 100 spins. Find what you think is a bias, and bet those numbers. What you are going to end up doing is following mrjjj's method of betting the numbers that come up most frequently. He claims to win. Why can't you?

Quote: statman

7craps: Good point! I wanted to generate 38 numbers but 1 through 38 is 38, add zero and that makes 39. It appears I put another number on the wheel.

Don't worry about it. Just round it off to an even
40 slots and we'll toss the results into the round file
receptacle that sits on the floor near the desk.
Did you go to the Alfred E Newman school of
jokes and gaffs?

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Quote: statman

I disapprove of gambling and I don't go to casinos

Casinos love guys like you. If you go, I guarantee
they will love you. And your money..

double post...

Quote: statman

boymimbo: Try downloading the interactive spreadsheet. If you think it's wrong, fix it! Forget about the eagle: he has flown. Your friend MathExtremist does simulations. I'd welcome him back if he'd mind his manners and stick to what he knows. The non-integer number of hits arises because I used weighting factors for the hot numbers and used two places of decimals for accuracy. Rounding the number of hits to whole numbers might look better and I might do it.

In no event should a Monte Carlo simulation of a roulette wheel, biased or otherwise, lead to an outcome distribution with fractional values. It is not possible for a roulette spin to result in "half of a 25". If your simulation does, it is not correct.

On the other hand, you derived and supported three different correct answers to a single problem, so clearly your understanding of "correct" is more refined than my own.

And I truly appreciate your offer to welcome me back -- it was only a few days ago that you were challenging me to a math fight, so it's good to know that I'm provisionally in your good graces again. After all, I would never deign to offend a potential Nobel laureate in Economics, someone who has made the important breakthrough of computing the odds of any of 39 roulette numbers appearing more than 12 times in a few hours' worth of roulette spins. I think if you simulated a wheel with only 38 spots you'd be a shoo-in. Even better, because the Nobel nominating committee is from Europe, use the European wheel with 37 spots. Please remember me in your acceptance speech.

Quote: statman

I think that gambling problems afford enticing mathematical challenges. I have never made money from a slot machine but I made a nice bundle on IGT stock (International Game Technology).

On that, you and I agree. I got into gaming math over 15 years ago precisely because it affords enticing mathematical challenges. And I also make a nice bundle from IGT, though it's not as a result of holding their stock.

However, I did make roughly $20 on the Batman slot machine last week in the Venetian. For someone who writes so much about gambling, perhaps you should try it.

LOL.

If there are no half-bets on the roulette wheel, how come I can put my bet between 25 and 26? Doesn't 25.5 pay like 100:1? If I nudge my bet a little bit towards 26, does that cover 25.75? And I've been at the roulette table before when a result was 70% 18 and 30% 19. They paid the 18 at 24.5 to 1 (they rounded to 25) and the 19 at 10.5 to 1 (they rounded down to 10 -- I didn't get that). It was impossible to win there!

I don't have the time to fix one's mistakes for free. I spend my days getting paid to fix others' mistakes.

What I am saying is that for a theorist who has come up with a new way to detect bias, your simulation in the state it is only proves that you're a hack. If I presented this, to say, my statistics professor, s/he would hand it back to me with a big fat ZERO. If I presented this simulation to a prestigious publication like "Indian Gaming", they would send it back with a smiley face on it. If I was a university graduate student presenting this finding to my professor for submission to a real publication, my professor would grab me by the ears and throw me out the door!!!

I've done paid statistical research before, on Cepheid variables stars, using real observations, and had I provided decimal observations when a discrete integer was required or put the results in an invalid bucket, she would have yelled at me and ended my research scholarship immediately.

I would strongly suggest before bringing on mathextremist, dororthygale, the wizard, or crystalmath into these conversations that you check your research, and then check it again. These folks have put their reputations and their knowledge on the line, not just on these forums, but for a living.

IGT has a beautiful campus here in Reno (where I am stationed) -- drove by it a couple of times.

Quote: boymimbo

If there are no half-bets on the roulette wheel, how come I can put my bet between 25 and 26? Doesn't 25.5 pay like 100:1? If I nudge my bet a little bit towards 26, does that cover 25.75? And I've been at the roulette table before when a result was 70% 18 and 30% 19. They paid the 18 at 24.5 to 1 (they rounded to 25) and the 19 at 10.5 to 1 (they rounded down to 10 -- I didn't get that). It was impossible to win there!

Actually, that'd make an interesting roulette variation -- weighting the proportion of the wager by precise physical placement. You'd need some sort of electronics system to pull it off but it'd be possible. Imagine betting the 1,2,4,5 corner and having 33% of the chip in the 5 spot, 25% each in 2 and 4, and 17% in the 1 -- then a 1 shows and the bet pays 5 to 1 instead of 8 to 1. And then imagine the argument with the floorperson about it if the bettor intended to make a "normal" corner bet...

That's called cheating.

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Quote: statman

Quote:

MathExtremist: I also make a nice bundle from IGT, though it's not as a result of holding their stock.

I, and I'm sure everyone else would like to know exactly what you did. I wrote to IGT shareholder services saying I wanted to do an analysis of one of their machines and asked if they would care to reveal the probabilities of the various payouts of one of their machines. I included an analysis I had done of an old Mills machine. They replied that they did not give out that kind of information. I don't know of any way to force them to do it. In New Jersey the only legal requirement is that their machines must pay back at least 75% of the money put in. Usually it's over 90%. Occasionally a machine will clock in at over 100% for a month, but that's just a fluke.

It's not past tense -- I have ongoing business relationships with several gaming vendors, the details of which will not be discussed here. As for doing an analysis of their machines, no, they don't give out PAR sheets to the general public. The secrecy that is common in gaming machine mathematics is one of the reasons I have the job I do.

The 75% requirement is Nevada's minimum RTP, not New Jersey where it's 83% (and no more than 100%). And those requirements are based on theoretical hold, not actual numbers. The variance of a particular slot model often means it's not within 2-3% of the target RTP over a month of actual use, especially if it doesn't get much play, but that doesn't mean it's not compliant.

If you're looking to do outside analysis of slot machine PAR sheets, look up Dr. Kevin Harrigan at U of Waterloo and some of his papers. He was able to obtain PAR sheets via FOIA requests.

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Quote: statman

Many thanks for the lead to Dr. Kevin Harrigan. FOIA means "Freedom of Information and Protection of Privacy Act," which is a law of British Columbia. To follow Dr. Harrigan's route I would have to fly to Vancouver and file an action in a Canadian court. The last time I was in Canada I got into a conversation with someone who was fond of bashing Americans and wanted me to agree with him. I guess we look and speak pretty much alike.

FOIA applies in all of Canada - Waterloo is in Ontario. And the U.S. has it's own freedom of information act, so you could file here as well.

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Quote: statman

rdw4potus: Thank you for your encouragement. As I read The Freedom of Information Act, 5 U.S.C. § 552, it applies only to getting information from U. S. government agencies and would not apply to individual citizens or corporations. Please correct me if I am wrong.

I think it also is applicable to state governments in most cases. So, in the very few cases where there's state-run gambling in the U.S. (Boot Hill in KS is the only example I can think of), you might have success.

I'm not trying to come on to you, or anyone. The fact is that you posted a simulation that was entirely faulty and then faulted those who make a living at math. But I will stay out of your way!

Quote: statman

Another member of the forum wrote to me that there were people here qualified in higher math. I asked who and he mentioned the Wizard and Teliot - no one else.

I sincerely hope you're talking about an instance other than the one with me. I a)also included Math Extremist in my list and b) gave a list of gaming math professionals, not general math experts. The latter would include Dorothy Gale, Crystal Math, Miplet and others.

Quote: statman

Quote:

boymimbo: I would strongly suggest before bringing on mathextremist, dororthygale, the wizard, or crystalmath into these conversations that you check your research, and then check it again. These folks have put their reputations and their knowledge on the line, not just on these forums, but for a living.

I didn't initiate posts to MathExtremist or DorothyGale and invite them to express contempt for me - they did it of their own initiative. MathExtremist and I now are reconciled but I think DorothyGale has passed the point of return.

Your running commentary on who's in your good graces at any point in time is, quite frankly, bizarre. I don't know you at all and I have no basis to either love or hate you. However, you have made many outlandish and incorrect statements about your work on roulette, including the absurd notion that your work might qualify you for the Nobel Prize in Economics. I certainly haven't reconciled with those statements, and I maintain that many are false.

I also do not agree that you can detect a subtle roulette wheel bias in as few as 30 to 200 spins, even if you know exactly what the probability of a given distribution is, and indeed even if you know for a fact that the wheel is biased. As a direct analogy, you can't credibly claim to detect a bias in a coin after 100 flips, even though you can calculate precisely what the odds were of a particular coin flip distribution. There is a meaningful distinction between probability and confidence interval that I'm not sure you comprehend.

Also, for the most part, "gaming math" is not necessarily "higher math". Most casino games can be fully analyzed using simple combinatorics, and slot game math is almost always developed in little more than a spreadsheet. With the exception of estimating longer-term results, all casino games use discrete probability distributions so you don't even need calculus to look at them. A working knowledge of high-school algebra and the factorial function is, in most cases, sufficient.

As for the "best way to come on to anyone", I humbly suggest taking your own advice. By your own admission, you are relatively new to a great deal of the technologies used in analysis of casino games. The members of this forum are not. Asking intellectually honest questions will serve you far better than making wild proclamations -- or selling tables of numbers.

MathExtremist: Your comments are noted. I think that this forum suffers from lack of supervision and I have been the target of much abuse. DorothyGale has called me "A fine piece of work." Apart from her context, that might even be a compliment, however Buzzpaff has repeatedly call me a thief. That is a serious matter and I am following up on it.

I recognize you as an experienced gaming analyst and you have won my respect. As to being able to detect roulette bias in 30 spins, a friend once cleaned me out on my home roulette wheel in about 30 spins by playing the most frequently occurring numbers. I don't claim that that is possible in a casino. He didn't think so either

Quote: statman

MathExtremist: Your comments are noted. I think that this forum suffers from lack of supervision and I have been the target of much abuse. DorothyGale has called me "A fine piece of work." Apart from her context, that might even be a compliment, however Buzzpaff has repeatedly call me a thief. That is a serious matter and I am following up on it.

I recognize you as an experienced gaming analyst and you have won my respect. As to being able to detect roulette bias in 30 spins, a friend once cleaned me out on my home roulette wheel in about 30 spins by playing the most frequently occurring numbers. I don't claim that that is possible in a casino. He didn't think so either

Because Statman removes all his posts, thereby ruining the thread,
please quote him and it stays.

Quote: statman

DorothyGale has called me "A fine piece of work."

I didn't use the word "fine" ... my post is made September 30th, 2011 at 6:51:52 AM in this thread ... Post w/ quote

Here are some definitions of the common slang phrase "piece of work" from the urban dictionary.

1. Someone who -- although often interesting -- is difficult to get along with on an every day basis. They often make simple things overly complex, or argue points ad infinitum.

2. Unaware of one's foolishness. Originates from "What a Piece of Work is Man" monologue from Hamlet. More precisely an ironic reflection of how little most men achieve despite being endowed with relatively enormous powers to act and reason. Generally used as a sarcastic "compliment."

3. A person whose stupidity and ignorance never fail to amaze you.

You can't even quote correctly ... wrong again ... it just keeps getting worse for you ...

--Ms. D.