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Are RNGs really random?15 September 2008
I asked Mike to define exactly what he meant by "RNG pattern." His reply follows.
Thanks for the clarification. It helps me see exactly where we disagree.
There are some who don't believe that, given an unbiased selection mechanism, as you take more and more samples, the characteristics of your sample nears the characteristics of the population with Random Sampling with Replacement. Hence your homework assignment to read the literature to see that that is true.
I see now though that our area of disagreement is whether the RNG is unbiased. I suspect that this is a point on which we will have to agree to disagree.
Let's imagine that you will take part in a Turing Test. Your goal is not to tell machine from human, but rather to tell pseudo-random number generator from true random number generator. You are presented with two number streams, one from the P-RNG and the other from the true RNG. You have to identify the source of each number stream.
There are many statistical tests you can apply against the number streams to help you decide. You can find them by searching on the Internet. You can also find a list of the statistical tests that Gaming Labs International uses to test P-RNGs in its GLI 11 - Gaming Devices in Casinos V2.0 document (section 4.3.3 Applied Tests).
The P-RNG mathematicians and programmers have designed their P-RNGs so they pass those statistical tests for randomness. You would not be able to tell the number stream from the P-RNG from that from the true RNG.
Now, I know you don't have access to slot machine performance reports, but if you did you would see that as machines get more and more play, their actual payback percentages get nearer and nearer to their long-term payback percentages (percentages that are calculated using the pay table and the layout of the symbols on the virtual reels). If the P-RNGs were biased, the actual percentages would be homing in on some other numbers than the machines' long-term paybacks.
Moreover, each slot machine has a PAR (or PC) sheet that details the virtual reel layouts and specifies the machine's long-term payback percentage. I've always been able to verify the long-term payback on the sheet by using the virtual reel layouts and pay table. Gaming jurisdictions want to ensure that machines are operating properly and that they are receiving all of the tax revenue to which they are entitled. The long-term payback on the PAR sheet is the metric against which a machine's performance is measured.
I agree that if the P-RNGs were biased, we would need to know the true probabilities of choosing each virtual stop in order to calculate a machine's long-term payback.
But I disagree that the P-RNGs are biased. On any given spin, each virtual stop on each virtual reel has the same probability of being chosen. Testing labs like GLI test the number streams from the P-RNGs to ensure that this is true.
As I said before, we'll have to agree to disagree about whether P-RNGs are biased.
Best of luck in and out of the casinos,
Send your slot and video poker questions to John Robison, Slot Expert, at email@example.com. Because of the volume of mail I receive, I regret that I can't reply to every question.
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