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more PlayOK dealing analysis
#1
Noted elsewhere I was getting this all set up.  Right now I've only got 1 game, 12 deals, but there's already a very suspicious statistic.

I counted the hand shapes for all the hands.  I worked out the computation to know the frequency any shape should occur...see Pinochle Discussion sub-board.  

So, with my 48 hand sample, I got a bunch of shapes.  I took every shape where the probability of that shape was 2% or less.  It turned out that there were 9 such.  So, I defined a 'trial' as a hand being dealt with any of those shapes.  The probability that such a hand would be dealt, is the sum of the 9 probabilities.  In total, that sum was 10.3%.  So, in 48 hands, the expected number of hands of any of those shapes, would be 5.

There were 11.  To say this is an outlier is an understatement;  it should happen less than 0.6% of the time.
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