Answer
This is simply Bayes Theorem.
Let x be that a player doubles up and
y that the player wins the tournament. Then:
p(y|x)=p(x|y)*p(y)/p(x)
Since p(x)>1/2 follows:
p(y|x)<2*p(x|y)*p(y) and since p(x|y) is 1 (because if he wins the tournament he had to double up there (otherwise he would have busted out) follows:
p(y|x)<2*p(y)
So..guess I saved Sklansky some work.
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