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The expectation for any result (eg bank) is independent of whether the trial follows 12 player wins or 12 bank wins. HOWEVER, if my study of 1,000,000 baccarat shoes tells me that only 20% of the times a bank seq hits 12 does it go beyond 12, then I am putting my money on player when I see 12 consecutive bank wins.

In any small sample there are patterns that don't represent the population, and if you look long enough you'll find them. However, then you have a multiple hypothesis problem in that you don't know whether 20% is real or just a likely outcome of being able to chose the best among a variety of strategies. Now, if you don't know the grand model that generates the population a small sample is the best you can get and you really have to take the data mining into account before you are able to judge the 20%. This is the typical problem we face in designing mechanical investing strategies. However, in this particular case when studying baccarat shoes we know the true population return generating model. That model implies independence between trials. Therefore, we can learn absolutely nothing from a small sample of trials. We know that any pattern we see is bogus. Howardroark is 100% right. Also, the right to walk away is worthless because the trials are independent.

By the way if you don't believe me collect another 1,000,000 trials and you'll see that the probability is not 20% I can't believe you are discussing this!

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