Sometimes you’ve assessed your options as accurately as you can, and you still don’t quite know what to do. Maybe you are getting 4:1 on an all-in bet, and you think you have almost exactly 20% equity if you call. Maybe a call is hopeless, but a pot-sized raise of a pot-sized bet will work approximately two-thirds of the time. Maybe you flopped second pair against a tight preflop raiser on a board that is likely to hit a tight raiser’s range, and the arguments for and against calling a continuation bet seem equally good.
Poker writers from David Sklansky to Tommy Angelo have been fond of pointing out that if, in your best judgment, two plays have very similar expected values, the wrong choice is only a little bit worse than the right one; because of that, these decisions can be the wrong ones to worry about and spend time on, at least over the felt.
That said, however, many of these situations are not quite as close as we take them to be, and studying them can be useful. Here I will discuss some ways to make sound decisions when you have judged that a situation is extremely close. Your initial judgment might be right, or it might be wrong; I will first discuss how to try to correct your wrong judgments, and then discuss some further considerations to use when you decide that your initial judgment was in fact correct.
Refining your estimate
You might have decided that two plays (say, calling and folding) have very similar expectation, but such judgments are frequently incorrect. A first way to correct yourself is by re-assessing any equities you rounded off to zero the first time around.
Here is a simplified example of this sort of correction. Let’s say that the board is Q522 and you are holding pocket sixes. Your opponent has made a pot-sized bet all-in, and you think that he would have played this way with all combinations of KQs, AKs or AQs, and with no other hands. You reason as follows: “I am ahead 4/10 of the time, because there are three combinations of KQs, four combinations of AKs, and three combinations of AQs. AKs has six outs against my hand, so I will win between 86% and 87% of that 4/10 of the time, puts my equity very close to 33%. So calling and folding are equally good.”
If you are truly justified in the reads on which you based your reasoning, you should call here. A first reason is simple and arithmetical: 38/44 of 4/10 is actually between 34% and 35%, so you are getting your price against a pot-sized bet that lays you 2:1. More importantly, however, there is a small error in the reasoning above: you rounded off your chances of winning to zero in the case when you are up against a Queen. Pocket pairs are hands that do not easily improve, but two outs is not the same as zero outs. Properly accounting for your chances of making a set on the river puts your equity over 37% here.
There are subtler ways in which people make rounding-off-to-zero mistakes. In the example above, you excluded almost all hand types from the opponent’s range. This is sometimes justifiable, but more often, the less likely hand types are not strictly impossible. If you are wrong to exclude big pairs from the bettor’s range, your estimated equity will be far too high; if you are wrong to exclude some categories of bluffs, your estimated equity will be too low. When you believe that decisions are close, and when you have made a number of simplifications, you can ask yourself two questions:
First: Which of my assumptions is most likely to be wrong? Let’s continue with the example above. We have already seen that we rounded off a low probability to zero. We have also ignored the possibilities that the opponent is bluffing without overcards or that he has an overpair, a set, a weaker one-pair hand, and so on. In different situations, different ones of these assumptions should be called into question. If you decided that the opponent is unlikely to bluff without overcards in part because he has a tight preflop range (perhaps because he raised under the gun in a 9-handed game without antes), you might be very confident in that assessment. If you based your judgment just on the fact that the opponent bet several streets, or on a demographic read, you should be more inclined to re-assess that premise. Similarly, if you decided that overpairs are impossible because a very straightforward didn’t reraise before the flop, you might have reason to retain that part of your read; if you reached that conclusion because of a mild hunch that he might have tried to check-raise with his strongest hands, you should be much less confident.
Second: Which major assumption, if wrong, would have the greatest effect on the correct play? I have often heard from acquaintances and students obsess over the question whether their opponents could have been betting with a draw. This is a worthwhile question to ask, but in some of these hands, the equity of the student’s hand against a draw was not so different from the equity of the hand against the full range; meanwhile, they had ignored possibilities involving made hands that could have had an enormous effect on the overall analysis of the situation. In the example above, the assumption about overpairs is making a big difference to the equity calculation; changing that assumption even a little bit will rapidly change the equity we end up with. By contrast, our judgment about whether he is likely to bet a straight draw is far less important, because straight draws are likely to be rare (and they have some equity, too).
The examples we have considered are simple, but they demonstrate patterns of thought that can help in any close situation. Have you rounded a nonzero quantity to zero? Which of your assumptions is likeliest to be wrong? Have you made a questionable assumption that is making a big difference to your conclusion? These questions will help you “break ties” in the right direction when your first judgment was less accurate than it could have been.
Taking a broader view
Sometimes a more detailed and considered analysis leaves you still believing that the decision is close; in that case, it can be useful to take a broader view of the situation in order to find other considerations that can make one of the nearly-equally-good decisions better than the other.
Do note, however, that this should be a last resort. If a “broad view” consideration, such as a tournament ICM effect, is important to the EV of a decision, it should be factored in all along, and not as an afterthought. If not, you have relegated it as an afterthought for good reason, and it is wise to spend your extra energy on the more fundamental aspects of a hand. In my experience, players worry far too much about these less tangible broad effects, especially image creation, the potential to tilt an opponent, and the benefit of being the biggest stack at the table.
If such considerations are the only available “tiebreakers,” however, you should use them well. Here are a two “broader view” topics, along with cautionary notes about their common misinterpretation:
(a) Players often worry that one or another of two close plays will affect their images, but forget to consider whether those effects will be good or bad. If you worry about getting caught bluffing, force yourself to find concrete reasons why that would be a bad (or a good) thing; keep in mind also that many opponents are inattentive and forgetful.
(b) Players often worry about the effect on their stack sizes of a given play, even in a cash game. Before you give too much weight to such a consideration, ask yourself what would be specifically good or bad about having a bigger or a smaller stack. Even if you are a strong deep-stacked player, a deeper stack is likely only to do you harm if the other deep stack at the table is a strong player on your left. Buy-in rules can also be important to these decisions: If you double up from a $500 buyin to a $1000 stack and risk getting knocked down to $200, the effect of your losing that $800 is different if you are playing a game with a standard $500 cap, an unusual $300 cap, or no cap at all.
There is no substitute for improvement at the nuts and bolts of hand analysis–that is, for being as accurate as possible at the sort of calculations that lead you to deciding that a decision is close in the first place. The ability to refine your calculations intelligently in difficult spots, however, is an important secondary skill-set. Developing these skills will benefit you not only in the close decisions but will have the indirect effect of making your overall poker thought processes less lazy and more comprehensive.
