[5NL] AKs OOP against UTG 4bet

Originally Posted by Cobra_1878

UTG open he could have 99+, AJs+, AQo+ maybe KQs.

4bet narrows it down to JJ+, AKs/AKo.

If he calls a shove, I think QQ (maybe) KK+ and AKs/AKo.

{ 99+,AJs+,KdQd,KhQh,AQo+ } is 74 combos. (I eliminated 1/2 of the KQ combos since you said maybe.)

{ JJ+,AKs,AKo } is 40 combos.
So that means Villain folds 74 - 40 hands out of 74, or 34/74, which is 46%.

{ KK+,QdQh,QdQs,QdQc,AKs,AKo } is 31 combos. (Again, I took out 1/2 of the QQ combos, since you said maybe.)
So Villain folds (40 - 31)/40 = 23% of the time, and Villain calls (1 - 23%) = 77% of the time

When Villain calls, you have ~41% equity.

So, the EV of your jam is:
money you win when Villain folds * percent of the time Villain folds
+ money you win when villain calls * percent of the time Villain calls.
$2.02*23% + (money you win when villain calls)*77%

Right now you have $6.52.
If you win, you will have $14.16. You will net $14.16 - $6.52 = $8.54, which will happen 41% of the time.
If you lose, you will lose $6.52, which will happen 59% of the time.
(Note: this just splits the equity evenly for the case of chopped pots.)

So, the money you win when villain calls is
$8.54*41% - $6.52*59%

And the whole EV calculation is
EV = $2.02*23% + ($8.54*41% - $6.52*59%)*77%
which reduces to:
EV = $0.45 + ($3.50 - $3.78)*0.77
EV = $0.45 + (-$0.28)*0.77
EV = $0.45 + -$0.22
EV = $0.23

The EV of a shove, given those ranges (which have already been critiqued, so I wont add to it) is $0.23. Which is positive, or +EV.

Now, I've ignored rake, and in this case, rake is going to eat that small margin of $0.23, so it is a fair critique of my analysis.

If rake is 5%, then the amounts you win get smaller.
$2.02 becomes $1.92. $8.54 becomes $8.12.

The EV calc becomes
EV = $1.92*23% + ($8.12*41% - $6.52*58%)*77%
EV = $0.09

So the margin is smaller, but the EV is still positive. You will win almost 2 bb per shove over the long term.

Originally Posted by Cobra_1878

Let's say villain was a 22/20/6 (3bet) in this spot, what would we do differently?

Well, this one has (20 - 6)/20 = 70% fold to 3-bet, so I'd say 3-bet any SC's, suited Ax, broadways, small and mid PP's and call with 99+.
EDIT: that stuff in red is stupid and wrong.
I mis-read the stats again.
I would need the stats on open raise, 4-bet and call a 5-bet jam.
The only one in there is open raise (PFR) of 20%

Originally Posted by daviddem

edit: you most likely won't get the same results, because I see he counted JJ+,AK in villain's range as 40 combos, which is wrong (he forgot to take the blockers in Hero's hand into account).

With A K blockers:

{ JJ+,AKs,AKo } is 27 combos.

{ KK+,QdQh,QdQs,QdQc,AKs,AKo } is 18 combos.
So Villain folds (27 - 18)/27 = 33% of the time, and Villain calls (1 - 23%) = 67% of the time

When Villain calls, you have ~41.18% equity. (note: Hero has diamonds, and I left the QQ combos with Q in for this equity. If I use the other 3 combos, the equity is 41.24%.)

The EV calculation is
EV = $2.02*33.33% + ($8.54*41.18% - $6.52*58.82%)*66.67%
which reduces to:
EV(no rake) = $0.46
EV(w/ rake) = $0.31

...

I'm shocked that the blockers make such a huge difference. The "w/ rake EV" more than tripled. Is this right? Did I make a hasty error? I have to split for work, so I can't double check it right now.