How many spins would you need to record to confirm a bias?

How many spins would you need to conform a roulette bias?

For example if an AP or a casino security person wants to investigate a wheel for a suspected bias, how many spins observed would be an ideal minimum?

Obviously the more the better, but nobody has unlimited time, but is there some minimum number of spins agreed upon to get a reasonably accurate idea?
Also, would I be correct in assuming the larger the bias the smaller sample needed?

Quote: Gandler

How many spins would you need to conform a roulette bias?

For example if an AP or a casino security person wants to investigate a wheel for a suspected bias, how many spins observed would be an ideal minimum?

Obviously the more the better, but nobody has unlimited time, but is there some minimum number of spins agreed upon to get a reasonably accurate idea?
Also, would I be correct in assuming the larger the bias the smaller sample needed?

If I tell you are you going to tell CET properties how to check their wheels to stop AP's?

Quote: Gandler

How many spins would you need to conform a roulette bias?

For example if an AP or a casino security person wants to investigate a wheel for a suspected bias, how many spins observed would be an ideal minimum?

Obviously the more the better, but nobody has unlimited time, but is there some minimum number of spins agreed upon to get a reasonably accurate idea?
Also, would I be correct in assuming the larger the bias the smaller sample needed?

As for your last question -- you are correct. The larger the bias the smaller sample size needed. And vice versa (the smaller the bias, the larger a sample size needs to be).

I learned all about this kind of thing a year or two ago. Unfortunately, I have forgotten how to do it. Although, it's kinda coming back to me.


First, imagine you have a coin and has 7 heads and 3 tails (out of 10 trials). Your expectation is 5 H and 5 T. If I remember correctly, you gotta find the variance and how many standard deviations that is away from expectation. From there, you can say something like, "There is an X% chance the coin is biased." You cannot completely 100% confirm a bias, but you can figure out the chance that something is biased.

I can flip a coin 10 times and always land on heads. That doesn't mean I'm 100% certain the coin is biased -- after all, 10 heads out of 10 tosses will occur 1/(2^10) sessions (where 1 session = 10 tosses)....or something like that.


Or maybe you gotta figure out the frequency such an event will occur (7 heads out of 10 trials) and use that figure.
Now i'm all confused.



But ultimately, it depends on how many spins you've done and how far away from expectation it is. Fifty 00's out of 100 spins would not require too many spins.....while 3 out of 100 spins would require a whole lot more spins. If it was 3,000 double zeros out of 100,000 spins....now you're getting somewhere.

If you google chi-squared roulette there are a few articles. Essentially you take how many each number come up and ensure the figures match a random wheel. If the numbers are too flat (i.e. every number came up the same number of times) or too outlandish then this test finds that. (You can use the same techniques for proving a RNG is generating random numbers.)

As to finding out whether a particular number is biassed, it is similar to the Heads/Tails concept. This time you look at the result (which normally would be N/37 or N/38) and compare how far it is from the expected value in terms of Standard Deviations. You also have to establish, beforehand, how confident you want to be. In the H/T example you might say that having seen 10/10 heads the coin is biassed, but in practice this could have happened to a fair coin. Sometimes you just have to be more sure!

Of course if you're looking for a wheel with bias opportunity you might be happy with a lower threshold accepting that sometimes you'll land up betting on a true wheel rather than a biassed one. But that's getting into Bayes theorem about how likely the wheel would have been biassed in the first place.

For instance if you suspected that only 1 in 1000 coins were double-headed (that's what I call bias!), but then saw 10 heads in a row, that would not enough. It would be [approx] 50:50 whether you'd picked a biassed coin landing heads*10 or a fair coin that was really unlucky.

Hello everyone!

Casino employees know that the wheel is not okay using the program's connected to the statistics available.

If the casino workers do not know that that there are such risks and do not need to worry : )