Big Blind play against a minraise, 10-15bb deep

by mersenneary

Playing the big blind correctly against opponents who will minraise, limp, openshove, and openfold 10-15 big blinds deep is one of the most difficult (and controversial) theoretical discussions in the endgame of HUSNGs. Deeper than that, we have many players with a large sample of flatting with medium strength hands, and we can determine how good those plays are based on the results – the proof is in the pudding. However, it's tough to apply the same analysis 10-15bb deep, as pretty much everybody agrees that your flatting frequency should go down at this stack depth. But how much? How often should we be 3-bet jamming?

The traditional poker theory approach of plugging in ranges and coming up with expectation becomes wildly imprecise at this stack depth. Minraising frequencies go down, which means that the difference between 30% and 40% is massive, compared against the difference between a 50% and a 60% opening range 20bb deep. Futhermore, it's now a bad assumption to believe that a minraising range of 40% is a range that's close to the strongest 40% hands. Good exploitative ranges 12bb deep from the small blind, for example, mean that good players are often minraising a polarized range with a good amount of junk, and openjamming other hands like 66 and A7, which makes it a mistake to include those hands in the button's range for 3-bet jamming calculations.

But enough about the problem being hard. What can we figure out? Well, the first conclusion is that the more frequently your opponent minraises, the less likely you should be to flat. For example, let's play against the following minraising range 13bb deep (the blue lines show his boundaries for minraise/calling:

This opponent is minraising a pretty wide range for this stack depth, considering he's also limping some middling hands and openjamming some aces and low pocket pairs. In fact, he's managing to play 82% of hands from the small blind – a strong, aggressive strategy. There are some changes I'd make to it as a default play, but if we go up against a player who does play like this, what should our 3bet jamming range look like?

Before that, let's do a quick exercise. Order these six hands from best expectation to worst expectation from jamming (ignore for a minute the expectation from flatting), and indicate whether or not you would guess that folding is a better option than jamming:

Q8o

54o

J5s

76s

T9o

K4o

Different hands play differently than you might think, because our notions about what are good hands to play are heavily influenced by conclusions about hands from other stack depths.

K4o leads the way with -0.25bb from the start of the hand, a full ¾ of a big blind better than folding. K4o is a borderline hand playing against a minraise 20bb deep, but once you get down to 13bb deep, our opponent is actually raise/calling with worse enough that plus the fold equity from jamming, mucking is a large mistake against this opponent.

76s (-0.3bb), T9o (-0.4bb), and J5s (-0.5bb) are the next three on the list. 76s is 37% against the calling range, which is not bad at all. T9o and J5s similarly do OK. Q8o (-0.6bb) lands at 5^th in the list, which will be a surprisingly poor showing to many. The problem is that Q8o, unlike K4o, isn't getting any worse hands to call, but like K4o is dominated frequently, leading to 31.9% equity. Even 54o (-0.75) isn't far behind.

Notice that it's actually significantly better to jam 54o here than fold it. While it's not true that any two cards can be jammed (72o is -1.2bb from the start of the hand, where folding is loses us our one big blind), it's very true that against a wide minraising range, we can do a lot of expanded jamming.

Despite some hands performing worse than expected, against this opponent, we should be jamming all six of these hands listed. Q8o is the closest on the list to a flat (you'll have to trust my intuition here), but even that hand is a jam when we're getting a fold 61% of the time. There's just no room for flatting when we have that much fold equity from jamming, with pretty much anything in our range (in fact, the only hands that are correct to flat here are probably aces and kings).

Now let's look at a second opponent, who isn't minraising so much of his junk:

This is a 44.3% minraising range compared against 57.6% in our last simulation. It makes a massive difference in the expectation from jamming. Basically everything goes down around ¾ of a BB in expectation, leaving K4o at -0.95bb, 76s at -1bb (the same as folding), T9o at -1.2bb, J5s at -1.3bb, Q8o at -1.4bb, and 54o at -1.55bb. Against this opponent, wide 3-bet jams are not an option.

There's actually some sexy stuff you can do here against regs against this polarized raising range. For example, let's take 86s 13bb deep, t390 effective. What happens when you 3bet to t130? Well, all of that junk is still folding, because you look strong as hell. Suddenly, the weaker hands in that raise/calling range shrink up: Do you really love your life with Q9o? Aren't you tempted to hero fold (it's probably correct against most)? Additionally, you'll get a lot of flats from people with Kx hands they would have called jams with, and you get to jam blank flops and get a decent amount of folds. That often can do much better than jamming, as just look at all those hands we improved our expectation against. You do need some pretty good reads about your opponent before this sort of play should be implemented.

As for the main question of flatting vs. jamming, we've hit the crux of the argument – When jamming is clearly -EV, is flatting better than folding? This isn't a question we can answer with straight numbers. Who am I, as mersenneary the numbers lord, to tell you that you can't do better than folding by making creative plays postflop like bet/calling on dry boards? If you can exploit your opponent's postflop tendencies, there's going to be an extra justification for playing pots. In general, though, it should be with connected hands that flop well.

In conclusion, 10-15bb deep, you need to be hyperfocused on your opponent's button opening behavior. Part of the reason why it's so good to play so many hands from the small blind at this stack depth is that most people aren't reactive enough, and don't 3-bet jam (or jam over limps) appropriately. And so, from the big blind, you need to be that reactive. Against a wide minraiser, you should hardly be flatting at all, and against someone who is frequently inducing, you can choose to call with some of your more connecting hands.