Simulation Results
I wrote two quick simulations. Here are the results for the probability that at some time in a sequence of 1000 hands, there exists a 100 hand window with 14 or more pocket pairs.
In the first simulation of 10000 1000 hand sequences, I got 14 or more pairs 1091 times. The second simulation I got 1040. So, I think the correct answer is around 10% or 11%.
For the second simulation I copied the following formulas into excel:
cells c1 to c1000 >>>> +IF(RAND()<1/17,1,0)
cells d1 to d1000 >>>> +SUM(C1:C100)
cell e1 >>>> 0
cells e2 to e1000 >>>> +MAX(E1,D1)
Each time you hit the F9 button, the worksheet shows the maximum number of pairs in a 100 hand window in cell e1000.
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