Bump. Three years later.
Part 20: Non-allin Semi-bluff, In Position on the Turn
Suppose that we are on the turn, and there are n cards in the desk that always give us the best hand on the river. The pot size is p, and we are considering making a semi-bluff with a bet size of b. Villain calls c percent of the time and raises r percent of the time. If Villain raises, we fold. If Villain calls, there will be no betting on the river.
n - outs on the river
p - pot size
b - bet size
c - Villain's calling percentage
r - Villain's raising percentage
Our opponent can call, raise or fold.
EV of the semi-bluff = EV of Villain calling + EV of Villain raising + EV of Villain folding
The EV of Villain raising is r(-b) since r percent of the time we will lose our bet.
The EV of Villain folding is (1-r-c)(p) since (1-r-c) is his fold frequency and p is the size of the pot we win.
The EV of Villain calling has two parts:
EV of Villain calling = EV of hitting an out + EV of not hitting an out
The EV of hitting an out is c(n/46)(p+b) since Villain has to call, we have to hit an out and we win the pot plus Villain's call on the turn.
The EV of not hitting an out is c((46-n)/46)(-b) since Villain has to call, we have to miss on the river and we lose our bet on the turn.
EV of the semi-bluff = r(-b) + (1-r-c)(p) + c(n/46)(p+b) + c((46-n)/46)(-b)
However, we have to compare this to the EV of checking since we can check with a chance to hit. The idea is to figure out which option is better and by how much.
Let's assume for the sake of discussion that if we check and hit one of our outs, we will win the pot plus the same size of bet we would have made on the turn 50% of the time. If we miss, then we win nothing.
EV of checking = EV of hitting + EV of missing
The EV of missing is simply zero since we never gain or lose anything.
The EV of hitting is (n/46)((b*0.5)+p) since if we hit, we pick up the pot plus a river bet the same size as our turn bet 50 percent of the time, for the sake of discussion.
(Note: Making a simple spreadsheet to do the math for you on these calculations is amazing.)
Download such a spreadsheet here: filehosting.org - download page for Part_20.xls
Reply With Quote