[5NL] AKs OOP against UTG 4bet

Originally Posted by MadMojoMonkey

There is dead money in the pot.

You don't need 50% equity. There's over $2 dead in the pot on your decision.

You have
$7.07 - $0.55 = $6.52
behind

Villain has you covered, so f you jam and Villain calls, the pot will be
2*$7.07 + $0.02 = $14.16

So you'd be betting $6.52 to win a pot of $14.16
If you jam, AND IF Villain calls, you only need...
$6.52/$14.16 = 46%

So you will break even (ignoring rake) in the long run if you have 46% total equity. If you have 40% equity against Villain's calling range and a decent amount of fold equity, then you are making a +EV play.

What ranges do you put Villain on for a UTG open 5-handed, then the 4-bet range, then the call a 5-bet jam range?

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.

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

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.

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

Why do you think this particular villain (who is 41/22/17 [3bet] over 78 hands) is positionally aware and would only call a shove with QQ+, AK? Is his play otherwise solid, and you think his numbers haven't settled down to where they should be yet?

Originally Posted by Cobra_1878

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

This makes no sense. Also, he didn't open from UTG.

Originally Posted by spoonitnow

This makes no sense. Also, he didn't open from UTG.

He definitely opened from UTG.

Originally Posted by Cobra_1878

He definitely opened from UTG.

nup

table was short, duder.

Originally Posted by Cobra_1878

He definitely opened from UTG.

In 6-max games, UTG is three of off the button, and MP is two. This guy opened from two off of the button.

I just pointed it out because I lot of people don't notice things like that and make bad assumptions because of it.

The whole topic of whether or not AK is going to be a +EV 3-bet/4-bet/5-bet against tight regulars basically comes down to the whole argument between balance and exploitative play. If you're 3-bet/5-bet bluffing to some degree (like you should be against these players), then it's critical to have AK in your range because most of their adjustments to call wider will put AK against hands it dominates (ie: adding AQ is 12 combinations if you hold AK, but adding TT is just 6).

Raising AK in general is also interesting pre-flop because there are a lot of situations where you can expect your opponent to fold better and continue with worse in terms of hot and cold equity because hold'em hands equities aren't transitive. For the simple example I use a lot, you might get him to fold 22 and call with JTs.

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.