A lot of poker players dislike playing against short stacks. While there are a number of reasons for this, there is ultimately only two solutions unless you want to keep bleeding money to them or stumbling by doing the best you can and winging it in tough spots. The first solution is to avoid these guys completely, but that's not always an option. The second solution is to learn to play a small stack as well as your opponents, or even better to learn to play a small stack better than your opponents!
Here we're going to look at a common spot that gives a lot of people trouble, and use some hold'em math to figure out an easy solution. It's folded to you in the small blind. The big blind has 14 big blinds after posting the blind (you have him covered). You were dealt King-Seven of hearts. You don't want to open raise to your normal amount because if he calls then you have to play the flop out of position when you're very unlikely to hit and he can just shove over you profitably with any pair and any draw (even with just overcards). So there has to be a better solution. What if you just open shove and raise all-in to a total of 15 big blinds. And even better, what if you turned your cards face up as you did this. Could your opponent make your play unprofitable? Let's do some poker analysis and find out. Your opponent would be calling 14 big blinds in a pot of 16 big blinds, so he would have to be calling with 14/(14+16) = 46.7% equity in the pot to make his call correct. So what all hands have at least 46.7% equity against King-Seven suited? Rather obviously, that's all Aces, all pocket pairs, and all Kings with a Seven or higher kicker. He will have these hands 27.6% of the time, and when he calls, you'll have an average equity of 37.7%. That means that he folds 72.4% of the time, and you will lose at showdown 62.3% of the time. A small amount of poker math will let us find the value of your raise all-in as follows. First we calculate what happens when our opponent folds, and that's pretty easy. He folds about 72.4% of his starting hands and those times we win 1.5 big blinds (remember that the small blind was already posted and is no longer ours). This portion of our average profit is 0.724 times 1.5 which equals 1.086 big blinds. Second we evaluate what happens when our opponent calls and we win. He calls about 27.6% of the time, and 37.7% of those times we profit 15.5 big blinds. The part this contributes to our total average profit is 0.276 times 0.377 times 15.5 which is 1.613 big blinds. Finally we check out what happens when our opponent calls and we lose. Since he calls about 27.6% of the time and we lose 14.5 big blinds 62.5% of the time, this affects our average profit by 0.276 times 0.625 times -14.5, and that comes out to -2.501 big blinds. Now to figure out what our total average value is, we add up the three parts that we just finished solving for with some analytical Texas hold em math. Here we have 1.086 plus 1.613 minus 2.501 which comes to 0.198 big blinds on average. So here, our play is worth about one-fifth of a big blind, even if we turn our hand face up allowing our opponent to play perfectly. If he calls any more than the range we assigned him above then we have less of a disadvantage on average at showdown which increases our profit. Similarly, if he calls any less than the range we assigned him above then we have more of an advantage in fold equity preflop, and this will also increase our profit.
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