What’s Your Play? Big Draw, Short Stack Results

Thanks to everyone who commented on What’s Your Play? Big Draw, Short Stack. It got a lot more attention than I expected!

Folding is an Opportunity, Not a Cost

Props to those of you who mentioned the relevant toy game from Mathematics of Poker. That was the first thing I thought of when playing this hand, and it was the impetus for my posting it.

For those who aren’t familiar, Chen and Ankenman demonstrate that when you have a big draw against a made hand, it can actually be correct for you to move all-in on the flop, knowing you are behind and have no fold equity, rather than give your opponent the opportunity to blow you off of your equity on blank turns.

The critical difference between that toy game and this hand is that in the toy game, we assume that the made hand knows his opponent is drawing and can play perfectly on the turn. In other words, not only can he force the draw out on blank turns, but he can also correctly check and fold on turns that sharply improve his opponent’s equity. No commenters suggested that Villain might check and fold a 6 or a heart on the turn with any hand that would have called a flop shove, and rightfully so.

There was, however, a lot of talk about how Hero will “have to” fold some turns, as though it were a cost or penalty of some sort. You should see this as an opportunity! In our example, checking back means that Hero will get to benefit from additional information about the hand he’s likely to hold at showdown. Because Villain is not in a position to make similar use of this information, this is an opportunity for the Hero.

The turn card is going to be what it’s going to be. It’s already sitting there on top of the deck, waiting to be dealt. Essentially, you are given the opportunity to peak at that card before you decide whether you want to get all in. Why wouldn’t you do that? Sure, it will be disappointing to see the Ac, but if you are going to see it either way, wouldn’t you prefer to know that it’s coming so that you can avoid putting $300 out there?

Put another way, assume that Villain never folds to a flop shove and will always shove any turn. In this case, shoving flop and calling a shove on any turn are functionally equivalent. The only question is whether Hero can make use of the additional information that the turn brings in order to avoid committing his stack on particularly bad runouts.

Fold Equity

All of that operates under the assumption that Villain never folds the flop. This was my expectation when playing the hand, though I do think that Gavrik makes a very good point (which also has some connection to a discussion in Mathematics of Poker):

Let’s see what happens if we base our play on trying to guess if we have any fold equity or not.

1) We assume we have ~10% fold equity. We are wrong and in reality we have 0% fold equity. We shove, get called and flip for it. We have lost a tiny amount of equity by being wrong.

2) We assume we have 0% fold equity. We are wrong and in reality villain would have folded ~10% of his range. We check back the flop and from there all sorts of bad things can happen – villain can “bluff shove” all the hands he would have folded on the flop, villain can hit a pair on the turn and shove for value, in addition, if villain shoves on a brick turn we are not really getting the right price to call. Seems like a recipe for disaster.

So, a lot depends on how confident you are that you have no fold equity. I was pretty damn confident.

Villain simply has to be strong based on the pre-flop action. If someone re-raises him pre-flop, he’ll be getting well over 2:1 to call. He just can’t make this play with any hand that isn’t ready to get all-in pre-flop, which means he’s functionally jamming $500 into a pot of $150 and an early position raise from a somewhat nitty player. Except that he’s not jamming, he’s deliberately offering his opponents good odds, which if anything only strengthens his range. Also, as Diane points out, the fact that Villain is in the big blind makes an “air squeeze” even less likely, as he could just call $40 more and see a flop.

Some commenters are suggesting that Villain might have KQ or KJ, but I just don’t see that based on the pre-flop action. Even if he did, I think there’s a fair chance he’s shove the flop as opposed to checking and folding. Just as Villain shouldn’t have any hands that will fold pre-flop, I also don’t think he should have any hands that will check-fold this flop. That means that when he does check, it has to be a trap.

I agree with Chris C. that many Villains will just shove AK on the flop, but I actually think it’s a pretty good hand for inducing, as he can’t really expect better to fold. It doesn’t matter, though. Whether or not Villain’s range includes JJ or AQ doesn’t change Hero’s play as long as Villain isn’t folding (and is planning to jam over a small bet, which I also expect to be the case).

The strength of Villain’s pre-flop range is certainly an argument for folding my hand. Against a range of only overpairs, I should fold. With AK in the mix, I have a call. With only a chance of AK being in there, I should probably fold. However, if Villain is going to make mistakes like this on the flop, my call is a little more appealing.

Turn Plan

Hero will need about 30% equity to call a turn shove. Although I think his ranges are too wide, I want to give props to Sean F. for using Pro Poker Tools to graph Hero’s equity across all turns. Here are graphs of Hero’s equity vs AA and vs KK+,AK.

Even against Aces, Hero can call almost 40% of turn cards. That would be any 7, and 8, any 6, and any heart, 18 cards total, 37.5% of the deck. The tricky thing is that Villain has all combinations of AK in his range, Hero should actually call more than twice as many turns, probably folding only on non-heart Aces and Kings. Putting only suited combinations of AK into Villain’s range again makes Hero call only on turns that clearly improve his hand, which was my plan (like Chris C., I’m skeptical that Villain would play AK this way, and don’t want to assign more than a small chance to that).

It’s worth noting that we might even get a check on some bad turns. Both AA and KK might want to check the Ac, for instance, and KK might choose to check Kc. I think shoving would still be a mistake for Hero, but occasionally getting to see a free river when way behind is a pretty nice perk.

Results

I checked. The turn was the 7c, Villain shoved, and I called and caught an 8 on the river to beat his KK. He was not pleased.