Re: Maths question
Your method is definitely correct but it can be time consuming .
Here is one way of thinking about it by using an approximation.
A player with a top 10% range will be playing slightly more ace hands than kings hands and slightly more king hands than queen hands . We may say that they are about equal to make the problem easier for us . So the probability he has an A,K or Q are about equal . The probability he will be playing a pocket pair is ~ equal to the probability he would have an A , K or Q .
Therefore the probability your opponent flops exactly one pair of queens on a q-8-4 board is ~ equal to the probability he would flop one pair of kings on a k-8-4 board and ~ equal to the probability he would flop one pair of aces on a A-8-4 board . So if x denotes the probability he has an A,K,Q or a pocket pair , then we have that
x+x+x+x =1 and x=0.25 and we're done !
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