The 4 Bet Preflop Shove

I've been considering the merits of the 4 Bet Shove and how to play optimally both with it and against it. It seems in the hand evaluation forum that people often want this clarified. I hope this post will allow us to discuss it a little.

What is it?
Basically the 4 Bet Shove is moving All In preflop over a 3 Bet. A typical hand might look like this:

Villain bets 4BB,
Hero raises to 12BB,
Villain raises to 100BB (All in),
Hero...?

Why is it useful?
It takes away the positional aspect in a hand and is generally a better alternative to calling a 3 Bet out of position. It is generally a move with strong hands because you are risking your whole stack but in higher stakes games can also be a bluff.

What I want to discuss?
1. Which hands is it profitable to call a 4 Bet Shove with?
- How do we adjust to different villains/situations?

2. Which hands it is profitable to make a 4 Bet Shove with?
- How do we adjust to different villains/situations?

This is NOT a discussion about whether Calling or 4 Betting smaller would be a better play. I agree that these are valid plays with their own merits but this post is purely about the mathematics of shoving directly. Hopefully it will make clearer the situations where this is profitable.

Mathematics is highly encouraged and so I provide some basic formulae to consider:

1. Calling an All In:
EV = E*P - C
Where E is the Equity our hand has against their range, P is the Potsize if we call less rake (~ 200BB) and C is the Cost of our call (~ 84BB). The call is profitable if EV > 0.

2. Making an All In:
EV = F*U + (1 - F)(E*P - C)
Where F is the probability the villain folds, U is the size of the Uncalled pot (~ 20BB), E is the Equity our hand has against their calling range, P is the Potsize if we they call less rake (~ 200BB) and C is the Cost of our All In (~ 96BB). The All In is profitable if EV > 0.

I hope these formulae are both clear and actually correct. If you need examples I can provide. Now... discuss!

fwiw comments. I'm not that great at math, so...

The biggest merit in making a 4bet shove imo is that it looks so bluffy/fishy. As a result, there's something to be said for reserving this play for your very strongest hands, especially if it's unlikely that any balance is required (I'd think this is unlikely at least through 50nl if not up through small stakes).

If we're thinking about stealing, though, we're risking 80bb's to win 20bb's, so if we're depending purely on a steal pf (i.e., with a hand that has terrible equity against Villain's 3bet range), we need Villain to fold 80% of the time to the 4bet to b/e as a pf steal. Since no hand has zero equity pf, our Ev goes up the better our equity is - so of the times that we get called, we only need to have some marginal equity to make it worthwhile IF villain folds somewhere around 80% of the time to the steal preflop - which allows us to drop the % of the time the outright steal has to work to a lower number - say 75% or so (I'm not basing this on math, pure guesstimate).

Whether doing this makes sense or not depends a lot on your read on Villain. A villain with a 3% or less 3bet range is going to call way too frequently for this to be profitable imo - he's not going to fold often enough to the 4bet shove because his range is going to be too strong, and our pot equity is going to suck (if we're stealing rather than value betting). A villain with a higher 3bet range who thinks your range is wide, or who simply likes to gamble, may also call too frequently for this to be profitable as a pf steal - but we're more interested in making this play against this villain type than the tight nit with hands that do well against a wide 3bet range, say 99-JJ, AQs+.

Calling 4bet shoves 100bb's deep - I want a read that Villain will make this play with a wide range before I consider calling 4bet shoves with less than hands that I'm willing to get it all in with in the first place. But with a read that he's sufficiently wide, I'm more inclined to stack off with 88+, AJs+, etc. c9 posted a solution for 4betting against wide 3bet ranges in HA recently, I forget which thread - but that would be a foundation for calling off as well imo.

Note that your own image plays a role in calling 4bet shoves as well. If villain is willing to 4bet light because he perceives your 3bet range to be light, ...

Caution - playing 3bet/4bet games can be high variance obviously, but also can get into huge leveling games (I'm doing this because Villain thinks this about me so I think he'll do that as a result etc.). Be careful that you don't level yourself (almost certainly my single biggest leak).

ok short anser: If someone 4 bet shoves, the almost always have aces or kings, and if you 4 bet shove you better have the same because you will get called down 9 times out of 10.

I saw C9's article which mostly dealt with light 4 Bet shoving as a means to countering light 3 Betting. You make that play with A2s - A5s because these hands have decent equity (30%) against most calling ranges and the Ace in our hand makes it less likely they have AA and should increase our fold equity. That sort of shove is certainly marginal at the best of times and more for metagame reasons (to make them think you are a bit mad).

However what if we are 3 Bet OOP when we have a hand like QQ or JJ. Is this a profitable shove? What about AK? (Those are the main "trouble" hands)

In a deep stack game,
If you have KK in the small blind. If your upfront opponent raises (2bet) and everybody folds and you reraise him (3bet), and your opponent puts in the third raise (4bet), and you have KK, you’re a huge underdog to most everyone. Probably you’ll be better off with QQ because you can dump it and not losing much. But if you got two KK for the third significant raise, and it’s against the same person, you are in big trouble most of the time. This is the most difficult situation in NL , without a doubt two KK in the deep stack scenario I just described above.

Again, my math sucks, so huge grain of salt.

Villain's 3bet range and his perception of our 4bet shove range are critical.

If Villain's 3bet range is 3%, our pot equity against that range with JJ is 45%. If he folds everything to a 4bet shove except KK+, our equity against his calling range is 19%.

There are 24 combos of KK+, while the 3% range of hands is a total of 76 hands (99+, AKs), so he's folding 68% of the time.

I think the math is:

.68*20bb's (when he folds to the 4bet shove) + .32*(.19*100bb's) (when he calls and we win) - .32*80bb's (when he calls and we lose) = 13.6bb's + 6.08bb's - 25.6bb's = -5.92bb's

Contrast w a Villain who's 3bet range is 8% and who still only calls a 4bet shove with KK+. Now he's got 164 combos of hands and only calls with 24, so he folds 85% of the time. Using the same JJ scenario:

.85*20bb's + .15*(.19*100bb's) - .15*80bb's = 17bb's + 2.85bb's - 12bb's = 7.85bb's

Obviously it helps a lot to know his 3bet range, but also what calling range for the 4bet shove is - that is going to be influenced by his perception of Hero and his willingness to gamble (some guys are convinced that a 4bet shove has to be AK, so pairs are more likely to call; some guys never fold AK; etc.).

Its not my article. It was originally written by Cole South, who plays nosebleed stakes and is a way better player than I am. I also find it funny that he has a blog on live journal.

Also, you can certainly 4-bet shove with hands that are non-bluffs. I do it any time a normal sized 4-bet would be silly. For example, anytime there's a decent amount of dead money in the pot, a normal 2.5x sized 4-bet is going to commit me anyways. So I just shove, rather than 4-bet to some weird amount.

I would definitely use the 4 bet shove for only the strongest hands like AA, KK here.