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?
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