Good morning. Concidering a mid-pocket pair
Consider being dealt pocket 10's. A player acting before you moves "All In" but the good news is he has a much smaller stack than you and he appears to be a loose player.
You begin to calculate whether to call but first you think about him having an overpair and if he does, what is your probability of making trips without him making trips.
Recognizing that there are boards that negate any probability of you winning we focus only on you making trips without him making trips.
First, what are the chances he has an overpair, A's, K's, Q's or J's?
C(4, 2)<-[Him making a pair] * 4<-[Number of pairs better that 10's]
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C(52, 2)<-[Possible pocket cards]
Last, if you mis-read your opponent and he does in fact have an overpair what are your chances of you hitting trips without him hitting trips? (Math assumes both players have pairs)
C(2, 1)<-[Trips] * C(45,1) * C(44,1) * C(43,1) * C(42,1)
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C(52,5) <- [Possible boards]
Does this math look correct?
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