While the method below will collect data and allow it to be analyzed, the real key is that, in the end, that particular sample of data will have a probability, not a certainty, of being correct -- this is not a fault, it is an intrinsic problem of using data collection to draw conclusions, not only in gaming, but in any scientific study. In the end, there will be a "p" value representing the probability that the results came SOLELY by chance.
In medical studies, a "p" of 0.05 is felt by some to be a sufficiently low level to make the study credible -- even though this "p" means that the results have a 1 in 20 chance of having occurred by chance alone.
Such statistical analyses also assume that the study is well-designed; if there are obvious confounding factors that have not been well-controlled (equalized in the control and experimental groups, or at least factored in during the calculations), then the validity of the study and the "p" value become somewhat meaningless.
A very interesting example has just occurred in Indiana, where the Hoosier Lottery jackpot was just hit after 54 weeks without a jackpot winner. VERY roughly, the probability of hitting the jackpot is one in 12,000,000. There is a drawing twice a week. I sent an email to the lottery commission and they gave me the figures for how many tickets they usually sell for each drawing, and they told me:
When the jackpot is closer to $1 million we may sell only
approximately 450,000 tickets and if you assume that all of the
people have taken different numbers, than the odds of a winning
number being drawn are 450,000/12,271,512 or a little less than a
4% chance. When the jackpot is high, such as our current $49
million, we may sell approximately 1,500,000 tickets and then
again assuming that each number is different, the odds of a
winning number being drawn are 1,500,000/12,271,512 for a little
better than a 12% chance.
Using their LOW figure of 4% chance of a winner for each drawing, I calculated VERY roughly that, at the time I wrote them (49 weeks into the series / 98 drawings), the chances of having gone that long being totally due to chance was only 0.02 - a TWO PERCENT chance.
In reality, since ticket sales were undoubtedly up quite a bit during the series, the probability of having gone 48 weeks without a winner was probably much less.
If it were a medical study, this would be conclusive evidence that there was something "real" causing the long run of no winner. In fact, I am reasonably confident (although not totally, with such a low "p") that it was actually due to an unusual run of no winners - very unusual, but a run that will happen on rare occasion (this was the record by about four months over the previous record run without a jackpot winner).
If one ran a study as described on a VP machine, a "p" of 0.01 or 0.02 would also be convincing, but there is never ABSOLUTE proof that the event was NOT due to chance alone -- but, obviously, the lower the "p", the more convincing the data would be.
The only "real" way to determine if there was something fishy going on with CERTAINTY would be for a talented programmer to be able to somehow analyze the firmware and see if the programming itself was set to provide some events to return at a frequency other than what is advertised.
--BG
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9a. Determining if a vp game is gaffed
Posted by: "greeklandjohnny@aol.com" greeklandjohnny@aol.com johnnyzee48127
Date: Thu Nov 8, 2007 7:20 pm ((PST))I'll take an initial stab at this.? There are several factors to consider.? The
most important one is deciding what you are looking for before you start.? The
second most important factor is accurate record keeping.? If you play for a
couple of hours, keeping track of dealt trips can be tough if you don't write
things down.Here are the steps I would take.? Actually, if I thought a machine was non
random I wouldn't play it.? For the sake of discussion, here's how I would
approach the problem:1) State?the suspect characteristic of the machine, i.e 3 Aces never fill into
Quads.2)? Figure out the frequency of a success.? In this case, you are dealt 3 aces
about once is 650 hands.? You fill in once in 23.5 hands so on average, you will
convert 3 aces into quads 1 in 2470 hands ( rounded).3) Figure out a decent sample size.? This is easier said than done.? Nyquist
Theory says a minimum of 2 times the frequency.? I have heard Dan Paymar mention
he likes 10 times the frequency.? The appropriate sample size is also determined
by how badly gaffed the machine is.? If it never gives quad aces from trips,
that is a much easier event to detect than saying it gives them one out of 50
times instead of 1 out of 23.5.? I'll use 10 times the success frequency as a
starting point.4) Collect accurate data.? Once again, easier said than done, especially if
keeping track in your head.5) Apply the appropriate statistics to the data.? The binomial distibution is
useful but you also need some other information, like the?Z Test.?The Z-test is a statistical test used in inference which determines if the
difference between a sample mean and the population mean is large enough to be
statistically significant.This will tell you how likely it is that your result is a 'valid' result.
Wow, this is a pretty good question.? I will work on it some more and sent the
file to VP Fae for discussion.Why is it that working stats problems for video poker is more interesting than
doing them for work?