Re: blackjack
To determine the chances of at least winning 1/3rd of the
total hands, it would be just 1-P(winning less than 1/3rd).
There is an approximation to the binomial distribution
using the standard normal curve which is better as the
trials become very large. For the exact answer, the chances
of not winning at least 1/3rd of the hands for 3m trials
(m an integer>=1) would be determined by:
Summing of the combinatorial numbers
C(3m,k) where k runs from 0 to m-1.
Then, dividing this sum by 2**(3m).
For example, with m=4 or 12 deals, you simply sum
C(12,0) = 1
C(12,1) = 12
C(12,2) = 66
C(12,3) = 220
giving the sum of 299.
2**12 = 4096 so the chances of NOT winning 1/3rd in this
case is 299/4096 or there is a 3797/4096 chance of winning
at least 1/3rd of the hands.
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