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 Originally Posted by DJAbacus
Maths Question for Mojo.
2 players play infinite HU poker hands.
They both shove PF with KK and AA
Over an infinite sample who has won the most money if we only look at the AA vs KK hands. You must show your working out.
wikipedia - Binomial Distribution
Accounting for the +1/-1 value of win/loss means the expected value is
EV(X) = np - n/2
but p = 50% = 1/2
so
EV(X) = n/2 - n/2 = 0
check
The variance of X is
var(X) = np(1 - p) = n/4
So no matter how many times you play at even odds, the expected outcome (read the mode of the data set) is 0 or no change.
The variance is ever increasing with n. Meaning that the bell curve is ever widening with n. Meaning that the peak of the bell curve is getting smaller and smaller as the curve becomes more and more flat with increasing n.
Or to put it another way:
Originally Posted by Renton
If you flip coins for 1:1 odds approaching infinity times, there will be approaching infinity different outcomes that fall along a gaussian curve. It is extremely unlikely that you would break even.
... even though the most likely result would be to break even, the probability of having any specific amount becomes vanishingly slight.
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