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 Originally Posted by Imthenewfish
You are dealt A,K, Q. Your opponents bets B into a pot of $1. You call with an ace, fold with a queen. With a king when you call you must be correct B/B+1% of the time. We call if villain has a queen at least 1+B/B% of the time.
We want to bet a queen B/B+1% of the time.
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Is this equilibrium?
<@spoonitnow> like ok the pot is 1 and the bet size is B
<@spoonitnow> assume we bet a queen x% of the time
<@spoonitnow> then for villain the EV of folding a king is 0
<@spoonitnow> if we bet a queen x% of the time
<@spoonitnow> then when we bet we have a ratio of ace:queen of 1
<@spoonitnow> so the % of time we have an ace is 1/(1+x) and the % of time we have a queen is x/(1+x)
<@spoonitnow> so the EV of villain calling a bet is (1/(1+x))(-B) + (x/(1+x))(1+B)
<@spoonitnow> set that equal to zero and solve for x
<@spoonitnow> note it's (1+B) b/c when we have a queen and villain calls he wins the pot of 1 plus our bet size of B
<@spoonitnow> so multiply both sides by (1+x)
<@spoonitnow> that gives
<@spoonitnow> 0 = -B + x(1+B)
<@spoonitnow> and
<@spoonitnow> x = B/(1+B)
And yes this is the kind of shit we sit around and talk about in IRC on a Sunday afternoon.
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