[Hobbs.]

I was thinking about doing an EV calculation for the turn raise in class today so I'll try to step through things below. I don't do these that often so feel free to correct me if things are wrong.

Opponents Range:

AK: 16 combos
AA-TT: 27 combos

In general our EV calculation will be the following:

EV = Equity*(bets invested + implied odds) - (1-Equity)*(bets invested) + Other

In this current example the other term will be represented by our fold equity. For the case with no fold equity we can see that our EV is negative.

EV(no FE) = 15/46*(+3BB) - (1-15/46)*(2BB) = -0.37 BB

No lets try and quantify FE.

Assume FE = F(x,y)*15/43*(6BB)

F(x,y) represents a function that will be dependent on both the percentage of times villian bets AK unimproved on the turn as well as the percentage of times he folds to our raise. For this problem let F(x,y) = x*y (with x equal to percentage villian leads with AK and y equal to percentage of times he folds AK). the ratio 15/43 represents the number of combos that he will potentially fold to a turn raise (it is 15 and not 16 because he will not fold AhKh). The 6BB represents the number of bets we stand to win the times we get our villian to fold the best hand.

Lets now look at the neutral EV case:

0 = x*y*(15/43)*(6BB) - 0.37BB

Limiting Cases:
1) villian bets AK on the turn 100% of the time:
This implies he needs to fold to our raise
y = 18% of the time.

2) villian will fold to our raise with AK 100% of the time
obviosly he then needs to only bet the turn 18% of the time.

Of course villian is not going to do either of these things 100% of the time, but Entity's estimate of villian folding AK to our raise around 25% of the time probably reflects a realistic situation.