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Open Small, or Open-Shove

A mathematical analysis

by Matt Matros |  Published: Oct 15, 2010


Matt MatrosIt’s fairly easy to play a short stack in no-limit hold’em; if you like your hand, you go all in, and if you don’t, you fold. The difficulties arise, however, when you have a stack that’s just a little too big to be called “short.” What do you do with a stack that’s small enough to reasonably move all in, but big enough to reasonably open for a smaller, more standard raise? Some players simply pretend that this problem doesn’t exist. Even with a medium-sized stack and a marginal-but-playable preflop hand, they move all of their chips to the center and get on with their lives. For the more thoughtful tournament players, however, the dilemma of the “small-medium” stack (which, I guess, is what I’ll call it) is a tough one to ponder.

The temptation to just move all in with your small-medium stack is quite strong. After all, this play is almost never a big mistake. Here’s an example: You have K-10 offsuit in the hijack seat, and a stack of 3,000. The blinds are 100-200 with a 25 ante at a nine-handed table, everyone has you covered, and it’s folded to you. You decide to go the most basic route and move all in. If the players behind you are fairly typical, you can expect the cutoff to call you with something like 6-6+ and A-Q+, and the big blind with something like 3-3+ and A-10+. These ranges have the cutoff calling 6.2 percent of the time, and the big blind 10 percent of the time.

We’ll say that the button calls 8 percent of the time, and the small blind 8.5 percent of the time. To calculate how often at least one player will call, we need to figure out the chance that everyone will fold. To do that, we multiply the folding chances for each individual opponent. Everyone folds, then, .938 × .92 × .915 × .9 = 71 percent of the time.

If we automatically lost every time we got called, this all-in move would be a bad play, as we’re risking 3,000 to win 525 (100 small blind + 200 big blind + 225 in antes). Luckily, we don’t automatically lose when called. Depending on who calls us, we have between 33.6 percent and 35.7 percent equity when called. To simplify things a little and speed up the calculation, let’s just assume that we have 35 percent equity when called (this will be very close to the correct number). This means that when we move in, everyone folds 71 percent of the time and we win 525, we get called and lose 3,000 18.9 percent of the time (29 percent x 65 percent), and we get called and win somewhere between 3,325 and 3,525 10.2 percent of the time (29 percent x 35 percent). Let’s compromise and say 3,450. (I’m also ignoring the rare case of getting called in two or more spots.) Our equity from moving in, then, is (.71 × 525) – (.189 × 3,000) + (.102 × 3,450) = 158. So, the all-in play shows a profit of about three-quarters of a big blind against these typical players, which is an excellent result.

Many people get this far into the analysis and are satisfied that moving in is the best play. Yet, all we’ve really shown is that if the profiles of our opponents are correct, moving in is better than simply folding. What if we consider another play — namely, opening for a raise to 500? Could that be even better than moving in? It’s much harder to provide a definitive answer for how much value this play has. We’d need to make a lot more assumptions about how our opponents play, and then we’d need to do a lot more math. Here are some of the questions that we’d have to answer: How often would our opponents call? How often would they reraise? If they called preflop, how often would they fold on the flop? How often would they raise? Would they ever just call?

With all of these variables, I don’t feel comfortable in describing what a “typical” opponent would do when facing our small opening raise. But, I’ll try a couple of hypothetical situations:

Hypothetical situation No. 1: Your opponents are tough, aggressive players who will reraise you all in with every hand they would’ve called with if you’d moved in, plus a few others. Let’s say that they fold collectively 60 percent of the time, but move you in the other 40 percent of the time, and they never flat-call. When they move in, you fold, as you don’t have the pot odds to call against their ranges. The value of your play, then, is (.6 × 525) – (.4 × 500) = 115. It’s still better than folding, but not as good as moving all in.

Hypothetical situation No. 2: Your opponents are loose, passive players who will often call before the flop and then play a fit-or-fold strategy after the flop. We’ll say that they fold collectively 50 percent of the time, but the other 50 percent of the time, they call you instead of reraising. You bet 500 on the flop every time, and your fit-or-fold opponents check-raise only about 35 percent of the time — essentially only when they have a decent pair or draw. Even if you fold to a check-raise every time, the value of this play is, assuming that the big blind is the preflop caller, (.5 × 525) + (.5 × .65 × 825) – (.5 × .35 × 1,000) = 356. Obviously, this is an extreme example with opponents who play terribly, but that’s the point; sometimes your opponents’ poor play makes a preflop all-in move a significantly worse choice than a standard raise.

Clearly, the more your table is like situation No. 2, the more you should lean toward a small preflop raise instead of an all-in move. But there’s also an argument to be made that a small raise is better in situation No. 1. Since your opponents are assumed to be strong players in this scenario, they’ll be calling your all-in bet with a looser range than the one I suggested earlier for “typical” opponents.

Furthermore, if you’re planning to make smaller raises with your good hands, like A-A and A-K, but all-in raises with your mediocre hands, like K-10 offsuit, your stronger opponents will pick up on this and your all-in move with K-10 offsuit will lose value (as will your small opens with your good hands). The best way to balance your strategy for maximum value against tough opponents may be to open small with your entire opening range, even if, in a vacuum, you’d do better by moving all in with a hand like K-10 offsuit. We don’t play poker in a vacuum, and we especially don’t do so against good players who pick up on patterns.

If you’re content to always move all in when faced with a small-medium stack and a mediocre hand, you’ll probably do OK in those spots. If, however, you want to extract every bit of value that you can, you might earn a few extra chips by finding the right spots to open for a smaller raise. Those extra chips just might lead to a big difference on the payout sheet. ♠

Matt Matros is the author of The Making of a Poker Player. He is also a featured coach for