Poker Scenarios: Short-Stacked in the Big Blind

Poker Scenarios: Short-Stacked in the Big Blind
by Martell

In having poker discussions with some of my colleagues, it became apparent to me that there are many "endgame"-type of poker decisions that boil down to simple mathematics (for the most part). With all the poker literature out there, one would think that these types of decisions would have become routine; to the contrary, they turn out to be situations where players unknowingly are making mistakes.

The difficulties I see with these situations are 1) typically the calculations are too large to do them in the heat of battle, yet the average player isn't going to put in the time to solve them in advance, and 2) the solution that would be suggested by conventional wisdom is misleading at best, and in some cases downright wrong.

My goal with this series is to identify some of these scenarios and shed light on what the correct mathematical decision would be in each case. I will begin with a fairly common tournament scenario—you are short-stacked in the big blind. Over the next few articles, we will explore ways you should play that hand versus a variety of opponents. Our first scenario pits us against a tight, early-position raiser.

Poker Scenario #1

You are in the middle stages of a no-limit holdem tournament. The blinds are $100/$200 and you begin the hand with $800. A tight player in early position raises to 4 times the big blind. Everyone folds to you.

The key to this scenario (and many of the others we will be exploring) is putting your opponent on a range of hands. The best players will try to be a little tricky, which makes our job tougher, but in general, most good players will tend to be more careful when they are out of position. Since we have defined this raiser as a tight player and he's in early position, we will assume that he has some type of solid hand. Let's say that this type of player would raise with any pair 7s or higher, as well as with any AK, AQ or AJ (suited or unsuited).

In this situation, which of the following hands should you call with: pocket 5s, KJ offsuit, and 76 suited?

Conventional wisdom says that, in a heads-up situatuion, two high cards are preferable over most other hands. Suited connectors are generally not playable, because you can't get the implied odds for the few times that you hit your hand. Small pairs are either in a coin toss vs. two overcards or completely dominated by a higher pair.

Conventional wisdom is often right (thank goodness!), but in this case, it will lead you to make some mistakes. Let's look at the math.

You will be risking $600 to win $1100—your opponent's $800 bet, the small blind's $100, and the $200 you have already committed to the big blind. Another way to look at it is that you are risking 3 big blinds to win 5.5 big blinds. In order to break even, you need to win 3 times every 8.5 times you find yourself in this situation. That calculates to just a hair under 35.3%. Any hands that will win more than 35.3% of the time provide you with a positive expectation for the hand (in other words, you will come out ahead in the long run).

So how do our three prospective hands do versus an opponent that would raise with this particular range of hands?

KJ offsuit wins 27.7% of the time.
76 suited wins 30.1% of the time.
Pocket 5s wins 36.5% of the time.

This is an interesting discovery. I think many players, when facing this type of desparate situation, would be happy to pick up a hand like KJ. Yet they would clearly lose money in the long run with this call, and even a "drawing hand" like 76 suited will provide better results (though still not good enough to correctly call here).

And the pocket 5s? Despite being dominated half the time, they still do well enough to warrant a call here. Of course, 5s are the best of the small pairs, due to their strong strait possibilities, but even the worst pair—those lowly pocket 2s—win 34.9% of the time, narrowly missing our cutoff, but still performing much better than either KJ or 76 suited.

The lesson here seems to be not to underestimate the value of the pocket pair, even versus a variety of premium hands. The fact that it is already a made hand gives it enough of an advantage over the Ace high hands to make it playable in this situation.

Next time, we'll take a look at what kind of hands we could call with against an aggressive raiser. I'm expecting to find some really interesting options.

Martell can be reached at martell@babblog.com.