roulette math help

[toastblows]

I played roulette recently. I know that a live wheel can be biased unlike the software wheels which are all RNG driven. This was a live wheel.

I played 4.5 hours, average 25 spins an hour i would guess.

Bet was 2x on 1/3 of the board, 2x on a 2nd 1/3 and 1x on 1/3 and nothing on 0 or 00.

My conslusion was that the 1x 1/3 was being hit 1 out of 5 times instead of 1 of approx 3. and 0 and 00 were not being hit 1 of 19 times. 0 and 00 hit 5 times in 4.5 hours.

So based on my betting style, and a profit of 12 units, can anyone tell me what my risk of ruin was, and if i had any advantage based on a 12 unit gain betting that way...if indeed there was a bias? (obviously 4.5 hours at a wheel is not enough analysis to tell if its bias'ed, so it most likely was luck...just wondering though)

[Guynoire]

Yeah, you’re basically right it’s not enough data to determine an advantage. Also it would have been nice to have some real numbers instead of just guesses because I think we all have selective memories, here’s the analysis anyway.

Inference of Data:

Number of Spins 114:
Number of wins: 85
Number of losses one 1/3rd of table: 24
Number of 0’s losses: 5

This was just algebra using the fact that you won 12 bets and lost on the 0’s spin 5 times, it must have landed on the losing one third of the table 24 times if the total number of spins is 114.

From your data I’m going to change your system a little because it is not the optimum system for winning; putting money on the losing 3rd only gives the house an advantage because you lose more on the 0’s spins. You might have a reason to bet this way but I’m first going to look at what would happen with the strongest system, betting only on the two winning thirds.

Transform the data:

Wins 85
Losses 29

Using a binomial test the probability of results at least this extreme occurring is about 0.6% so there might be reason to believe the wheel is biased, but the question still remains as to whether it is biased enough.

95% confidence interval of player advantage: (-.3% to 47.9%)

Even with the strongest system imaginable and questionable data it is still inconclusive even at the 5% level whether you can attain an advantage from this wheel because the confidence interval goes into the negatives. If you really want to determine if the wheel is biased you’re going to need thousands of spins of data. It would be a lot better if you could record exactly which numbers hit as you might find that it is not exactly one third that is favored.

[toastblows]

Thanks for the analysis. My hunch was that i was just "lucky". And when I think back i selectively pick out 5 or 6 numbers that kept hitting in my mind but who knows. I do know that based on my 4.5 hours, one of the 1/3s was hitting more than the other 2 which is why it was always a 2x bet.

I did other variations with 2x on that 1/3, 1x on the 1/3 i felt 2nd most...but it was too inconsistant between the 1x 1/3 and the no bet 1/3 in that system. So my logic was that 2x, 2x, 1x winning on the 1x would cover the loss of one 2x...rather than a straight loss of 2x and 1x (so losing 2x each time instead of 3x each time). Of course in that system you cant have a 0/00 or you get screwed worse over. I was lucky to not have a 0/00 for over 1 hr toward the end and a lot of hits on 2x 1/3s....pure luck is my conclusion over 114 spins you calculated.

Thanks again

[Brock Windsor]

I am new to biased wheels so could use some help. Can one number be biased as opposed to a section of numbers? I recently tracked 622 spins of which the number 4 appeared 33 times! Its neighbours appeared only 11 and 12 times. Another section of the wheel (00,27,10) appeared 25-19-23 times respectively. I had thought if the wheel showed a bias there should be a section of numbers hitting such as the latter as opposed to a single number appearing many times. My plan right now is to bet the minimum $1 on number 4 until the data normalizes...should the advantage persist through 1000 spins I will be looking to bet some fraction of kelly (maybe 1/10th?) Any thoughts on this? I won't bet more than the minimum until I have at least 1000 spins and a 95% CI the wheel is biased to a player advantage. If CI drops below 95% after 1000 spins I would bet the minimum or quit altogether.
BW

[Sonny]

Originally Posted by Brock Windsor

Can one number be biased as opposed to a section of numbers?

Sure. If that particular number has damaged or improperly installed frets, or maybe the pocket is damaged or too deep for some reason.

Originally Posted by Brock Windsor

I won't bet more than the minimum until I have at least 1000 spins and a 95% CI the wheel is biased to a player advantage.

Unless the bias is very large it may take more than 1000 spins to get reliable results. Usually somewhere between 2,000 and 8,000 spins will give you a good indicator depending on the amount of bias. Also, be aware that the bias may change as time goes by. If the bias is caused by something small like dirt buildup or a slight tilt then the conditions can quickly change. Certain conditions may disappear while new conditions begin to form. A number that is biased today may not be biased next week. This is especially true if the casino services their wheels regularly and/or runs weekly tests on them. If you discover a bias, they might too.

Beating the Wheel by Russell Barnhart is a decent introduction to roulette biases. It covers how to tell if a wheel is biased and to what degree. It doesn’t directly tell how to detect a bias on certain numbers but it will give you the gist of it.

-Sonny-

[Brock Windsor]

Thanks Sonny. I'll stick to $1 betting and post my results at 2000 spins and try to get a consensus on how to bet my edge if one still exists....again this is my first attempt at advantage roulette so I only want to stick my toes in the water before I dive in.
BW

[Guynoire]

Wow, 33 times in 622 spins! That's as unlikely as rolling the dice 50 times before sevening out. More improbable things have happened in a casino but I would suspect a bias.

[Sonny]

Originally Posted by Sonny

Beating the Wheel by Russell Barnhart is a decent introduction to roulette biases. It covers how to tell if a wheel is biased and to what degree. It doesn’t directly tell how to detect a bias on certain numbers but it will give you the gist of it.

My mistake. The book actually does cover a method for determining the bias of a particular number or series of numbers. Based on your results above, the number 4 has over a 95% CI of being biased. It comes up about twice every 38 spins which gives you over an 89% advantage. The variance on a single straight up bet is pretty high (33.21) but you can safely play this number while you continue to clock the wheel.

The numbers 00, 27 and 10 do not have even an 80% CI. The book recommends at least an 80% CI before playing a particular number, although the exact percentage is up to the player.

-Sonny-

[Kasi]

[QUOTE=Sonny;69824]The book actually does cover a method for determining the bias of a particular number or series of numbers. Based on your results above, the number 4 has over a 95% CI of being biased. /QUOTE]

I don't know about the book or anything but, help me out here, in answering what are the chances of any number appearing exactly 33 times in 622 spins in an unbiased 0,00 wheel?

I get like 1 in 312?. Is that what you/anyone gets? Is it the right question to even ask? It just seems a little dangerous to me to log 622 spins, determine what number hit the most, and then potentially conclude it's probably biased and start betting on it for something that seems like it's going to happen randomly, with one number or another, every 1000 spins or so anyway.

If a number hits 5 out of 10 spins, I think a more rare event, would that be enough to conclude the number is biased and to begin betting on it?

Put another way, is this really only a 2-3 standard deviation event on a fair wheel when considering the chances of it happening to any of the 38 numbers?

I guess you got me wondering what this guy's CI index is based on. Are high tides involved?

Much more logical to conclude, as time goes by, after you've lost your money betting on that 4, that the wheel was actually biased for 4 back then, but, if and when the bias has apparently disappeared a few thousand spins later and everything is pretty normal, as can often happen as you say, and even maybe switch to a different number, that they must have fixed the fret or, more likely, that speck of dust blew out of the 4 and lodged in the next obviously biased number. Anything is better, from the author's point of view, than concluding the wheel was actually never biased at all.

That way, after you've lost your money, you were merely incredibly unlucky rather than stupid.

And, of course, should you win, it was pre-ordained and solely due to your ability to recognize a biased wheel. Really, when you think about, doesn't even qualify as gambling what with that 89% advantage. If you believe it, Brock, bet a lot more than a dollar before a speck of dust blows away that rare 89% advantage. Keep us posted on results of spins.

Just a starting point for discussion lol. I've eaten crow before lol.

[Guynoire]

Originally Posted by Kasi

I don't know about the book or anything but, help me out here, in answering what are the chances of any number appearing exactly 33 times in 622 spins in an unbiased 0,00 wheel?

The chances of landing exactly 33 out of the 622 possible is very very small, but this number really doesn't mean anything. The probability of getting any exact number out of 622 is pretty small. The real number you want is the probability of getting results at least that extreme ie.>=33

The distribution is just binomial so I used my calculator to add up all the possibilities. The probability of results at least this extreme occurring due to random chance is about 1.5*10^(-4) or about 3 out of 20,000.

If you construct a 95% confidence interval of your projected advantage the size of this interval is still pretty big because of the relatively small number of counts but I get a range of (27%-154%) with a middle of 90% just like Sonny's numbers.