Re: Poker Math Question - Implied odds EV on the turn w/river bluffs
let's say
P = pot size on turn, including villian's bet
TB = how much you have to call on turn (eg villian's turn bet size)
RB = how much you will bet on river (let's assume you bet the same size whether you're bluffing or not)
XC = probability villian will call river bet
XB = probability that we bluff on a missed draw
X = probability of our draw coming in
Then expected value of calling the turn bet is:
EV = X(P + RB*XC) + (1-X)*(XB*(XC*(-TB-RB) + (1-XC)*(P)) + (1-XB)*(-TB))
kind of a long formula but it makes sense. If we make all bets pot sized, then TB = P and RB = 3P, and the formula reduces to
EV = X*P*(1+3*XC) + (1-X)*P*(XB*(2-5*XC) - 1)
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