Simple Maths Check: +EV 4betting

[The Bean Counter]

So I've downloaded Verneer's +EV 4bet calculator and hoping somebody can help clarify my interpretation below please. In the example:

- I can 3bet literally ATC in a vacuum as long as villain folds 59% of the time. Therefore if villain is 3betting me 10% but only continuing with 3% against a 4bet, I can profitably 4bet ATC (since villain will fold 70% of the time). Seems straightforward enough and hopefully this is correct...?

- If I'm planning to 4bet/call it off, I need villain to fold 76.5% of the time to 4bet A5s profitably. Therefore villain would need to be 3betting me at least~13% and continuing with only 3% for me to gii with A5s, otherwise A5s goes in to the 4b/fold category; is that right? Just seems pretty damn spewy to be calling off a jam with A5s..

Edit: this can't be right, surely? If villain jams 3% always no matter the initial 3betting range, I need more than 40% to profitably call given pot odds, so what is this stat telling me?!

[abelardx]

The stats you're looking at give us some idea of our fold equity when we 4-bet. To calculate the EV you also need to know the effective stack size and the raise size.

1. If you're 4-bet bluffing 2.5x, you need to fold villain 2.5/3.5 = 71% of the time to break even. This ensures you win 1 every 2.5 times for each 1 time you lose 2.5. This also assumes that we give up when called, or at least never lose by continuing. I'm not sure where the 59% figure comes from.

Oh I see Verneer is using a 4-bet size of 2.25x instead of 2.5x. In that case you'd need fold equity of 2.25/3.25 = 69% to breakeven on a cold 4-bet bluff.

2. Here's the setup: Suppose it's blind on blind so we don't have to worry about a spare 1.5 blinds any where. Suppose also that we each have 100 blinds in our stack.

We open to 3. Villain 3-bets us to 10. We 4-bet to 25 with A5s. Villain jams, which we know he only does with JJ+ and AK. Is the pot big enough to get it in?

Note that the pot size is really the only consideration. Our fold equity at the time we 4-bet has nothing to do with the EV of calling the jam. That's a different decision point with a different EV calc.

EV(calling the 5-bet shove)
= (times we win) * (size of pot when we call) - (times we lose) * (size of call)
= .31 * 125 - .62 * 75
= 38.75 - 46.5
= -7.75

So calling is not advised unless stacks are much shorter or his range is much wider.


There must be some more assumptions/interpretations behind what the calculator is saying. Don't change your play based on what it says until you thoroughly understand it.

Do you like DeucesCracked? Their micro/ss coach sthief09 also does a lot of math videos. I like him a lot. You might want to check him out too.

[abelardx]

I'm such an idiot. I got the first one wrong.

You raised to 3. He 3-bets to 10. You 4-bet to 25 say. You're not risking 25 to win 10. You're risking 22 to win 13 because your raise is already in the pot. So it needs to work 22/35 = 63%. Using Verneer's bet sizes his 59% figure now looks right. Sorry bout that.

[BorisTheSpider]

Thinking about it the opposite way round, if you want to have hands you bluff jam with (like A5s), you've got to consider what percentage of the time he 4bet-folds. That gives you the fold equity you get from jamming with A5s, then you want to put him in a situation where he can't effectively bluffcatch.

So, let's say his 4bet value range is [QQ+,AK], well his weakest hands (his bluffcatchers) are QQ and AK - they are the weakest hands in that range, and if he's going to call with QQ (or AK) when you jam, he is basically bluffcatching right?

So, if when he calls with QQ (or AK) he has just the right amount of equity vs. your overall jamming range (including A5s) that he breaks even doing that, he will be indifferent to calling - it won't matter whether he calls with QQ/AK or just folds, either way his EV is 0. Note that his EV is 0 after he's already put his 4bet in the pot - so the hand overall is not breakeven for him, but the situation once you jam is.

[The Bean Counter]

I'm such an idiot. I got the first one wrong.

You raised to 3. He 3-bets to 10. You 4-bet to 25 say. You're not risking 25 to win 10. You're risking 22 to win 13 because your raise is already in the pot. So it needs to work 22/35 = 63%. Using Verneer's bet sizes his 59% figure now looks right. Sorry bout that.

No worries. Thanks for working through some examples too - the results are interesting and I'd definitely recommend downloading the calculator from Google docs (for reference, those numbers are my own based on a typical 25nl scenario for btn vs bb).

Thinking about it the opposite way round, if you want to have hands you bluff jam with (like A5s), you've got to consider what percentage of the time he 4bet-folds. That gives you the fold equity you get from jamming with A5s, then you want to put him in a situation w'here he can't effectively bluffcatch.

Oh ffs, you're right - thanks. My brain seems to be on permanent fart now I'm "between jobs".

\thread.

[Pelion]

Maybe you're just asking about the maths, but if you are actually thinking about a poker situation where villain is 3betting a tonne and 5betting super tight, why would you ever want to get it in with A5s? Just 4bet bluff a tonne and fold a lot when he continues.

Also, I don't know what those stats are telling you without seeing the formulae, but it is perfectly possible for both 4b/c and 4b/f to be +EV. Just because one of them is +EV doesn't mean it is the best choice.

e.g. If villain opens 10000000 combos, and only continues with 3% (40 combos), then 4b/c will be +EV.

4b/f will still be better. This would be my guess at what is happening.

[griffey24]

I don't see why we would ever want to 4b GII with A5s?

You're choosing Ax as a 4b hand for blockers, so that he's more likely to be 3b/folding instead of 3b/5b jamming. You need some pretty good dynamic to be 4b/calling off A5s imo.