[5NL] AKs OOP against UTG 4bet

Originally Posted by Cobra_1878

Are we happy to get it all-in here? If I call his 4bet it makes me look like exactly what I have got. If I flop an A or K, I am getting no action from JJ or QQ and I am probably way behind if I do get called.

If you 4bet and someone flats, does that really scream out he must have AK? I'm not so sure it does.

Anyway, I've been inspired to actually work out the EV of shoving. First algebraically and then in the second spoiler exactly for your reads.

Spoiler: Show

We will say folding has an EV of 0. We will assume that the Villain has you covered (which he does)

F = Villain Folds to Shove
E = Equity Against Villains Calling Range
P = Pot Size (before you shove)
B = How much you shove over the top
C = How much it costs to call villains raise

There are 3 results which can happen if you shove.
1)Villain Folds
2)Villain Folds, You Win
3)Villain Folds, You Lose

Profit of Each
1)We win P
2)We win P+B
2)We lose B+C

The EV is our profit * how likely the outcome is

1) (P) * (F)
2) (P + B) * (1 - F) * (E)
3) (-B-C) * (1 - F) * (1 - E)

So our EV in this situation is

(P)(F) + (P+B)(1-F)(E) + (-B-C)(1-F)(1-E)

Spoiler: Show

So we have our formula from the spoiler above. Let's go about working out our EV in this situation.

Our EV is = (P)(F) + (P+B)(1-F)(E) + (-B-C)(1-F)(1-E)

P = $2.07 (1.55 from Villain, 0.55 from you, 0.02 from SB)
B = $5.57
C = $0.95

We now need to calculate how often he folds and our equity against his calling range. We'll start with the latter.

Equity, if he only calls with QQ+ and AK, pokerstove says

E = 0.34586 (i.e 34.586%)

Now how often he folds.

If he 4bets with JJ+ and AK, combination wise that's
JJ = 6
QQ = 6
KK = 3
AA = 3
AK = 9

He 4bets with all of them (27) and folds only JJ (6)

F = 6/27

All together (formula and variables) that's

(P)(F) + (P+B)(1-F)(E) + (-B-C)(1-F)(1-E)

P = 2.07
B = 5.57
C = 0.95
E = 0.34586
F = 6/27

Using the magic of a calculator

EV Shoving = -0.80 (2dp)

I quite enjoyed that so I may even attempt to set up a simple scenario to work out the EV of calling at some point later today. Although it depends how complicated I can be arsed to go.