The Haig Plan

“Doing precisely what we’ve done 18 times before is exactly the last thing they’ll expect us to do this time!”

Here’s a very general question: if someone did A last time, are they more likely to do A or not-A this time?

How you answer this question will have a lot to say about how you play poker. If someone just showed down a big bluff and they’re betting into you again, do you think they’re more or less likely to be bluffing this time? Do you call or fold?

The question depends on what they think of you, what you think of them, and what you believe about human nature in general.

If you take a generally accepted view of empirical evidence, it seems the more times someone has done A, the more likely they are to do A in the future. Football teams that have won a lot of games in the past are expected to keep winning. The value of the stock market is expected to keep rising because it has risen in the past. If someone we know has behaved rudely in the past, we expect him to behave rudely in the future.

In poker it becomes more complicated because our opponents are incentivized to surprise us and confound our expectations. A football team tries to win every time, but poker players (some of them, anyway) try to trip us up by reversing course. How to balance observed tendencies against the desire to reverse those tendencies?

If our opponents were machines that played the same way every time, their past behavior would indeed be good evidence of how they would likely behave in the future. Not perfect evidence, but in general, the more we saw them do something, the more confident we would be that they’d keep doing it. But since we’re dealing with people, it depends on how they think.

Experiments show that people are bad at simulating random sequences. Specifically, they discount the possibility of long runs too much. So people asked to simulate a random series of coin tosses produce too many sequences like this:

HTTHHTHTTH

and not enough like this:

HHHHTHHHHH

Long runs like the second sequence show up more often in actual random trials than in people’s attempts to simulate randomness.

Many players have a sense that they want their bluffs to simulate strong hands, which show up randomly. Therefore they time their bluffs to look like the first sequence of heads and tails above: spread out fairly evenly. If they haven’t raised in awhile, they think the time is right for a bluff; and if they’ve been raising a lot (probably because they’ve been getting good hands) they won’t bluff. This actually makes them less random. The strategy of bluffing sporadically works well not because it imitates randomness, but because it imitates most people’s idea of randomness. As long as you only raise occasionally, most people will give you credit for having a good hand.

I’ve seen a scenario play out like this many times: all of a sudden someone who’s been playing tight for a long time raises three hands in a row. Often when this happens, someone will re-raise him the third time, thinking he can’t have a strong hand three times in a row. This rarely works out for the re-raiser. If someone’s been playing tight for a long time, he probably really is a tight player. He could be a loose player with a truly terrible run of bad cards, but it’s unlikely; and if he were really loose, he wouldn’t let bad cards stop him anyway. What’s more likely is he just got dealt a strong hand three times in a row. It can happen… more often, as the experiments show, than we think it should.

In fact, if he was getting out of line, it was probably on the first raise, not the third one. Maybe he thought all his folding bought him some credibility and he could sneak one by. But the second time? A tight player wouldn’t try his luck again. He’s trying to simulate the flow of strong hands, which he doesn’t imagine would show up twice in a row. The third time is probably the strongest hand of all. By now he’s probably feeling somewhat sheepish about all this raising, so he must have a hand so strong that he has no choice but to raise. This is the worst time to go after him.

This situation taps into what’s known as the gambler’s fallacy, which is basically the belief that things balance themselves out. For example, someone who falls prey to the gambler’s fallacy might think that if a coin has come up heads three times in a row, it’s more likely to be tails the next time. In reality as long as it’s a fair coin it’s still 50/50 to be heads or tails the next time, no matter what came before. While in the long run you’ll tend to get a roughly equal number of heads and tails, there is no force that makes sure things balance out in the short term.

In poker, the chance of being dealt pocket aces is one in 221. The chance of being dealt aces twice in a row would be one out of 221 * 221, which comes out to one in 48841. Very unlikely! But if someone got aces last hand, they are no more or less likely than anyone else at the table to have aces again. Everyone’s looking at the same one in 221. Sometimes someone will justify a play by saying, “How likely was he to have it twice in a row?!” As far as the probabilities go, the previous time has nothing to do with it, although it will certainly affect both players psychologically.

What if you’re playing someone who knows all that? Then it might be a good idea to bluff immediately after you raise. That’s the time most people are least likely to bluff, so if your opponent knows that, he’ll give you a lot of credit for having a good hand. In fact, I’ve seen a video in which a strong player raised twice in a row against another strong player using exactly that reasoning.

But what if we’ve both read the preceding paragraph? Well it’s clear that now we’re getting into a deadly guessing game. Poker players call this dynamic “leveling”: we’re each trying to guess which level the other is on, and each level deeper we go the best strategy flips. Some players try to opt out of this kind of guessing game by basing their plays on ranges. A range is the set of hands with which you perform a certain action.  So maybe I re-raise with pocket jacks or better and ace-king, but also seven-six suited. This way my “bluffs” (seven-six) show up truly randomly, not just my imitation of randomly. Most people associate “playing your cards” with not bluffing, but you can create a strategy based on your cards to bluff at a pre-determined frequency. If you fear that your opponent is at least as sharp as you are, you may want to play this way, but if you consider yourself sharper, you might prefer to play the guessing game.

Some players are obsessed with establishing tendencies for the purpose of reversing them. I associate this strategy with former Michigan football offensive coordinator Mike Debord. Debord would establish a tendency all season — for example, every time he sent the tight end in motion to the left, he’d run left — only to break it in a key game, usually against Ohio State. This sometimes confused the defense, but they usually adapted pretty quickly. In fact, I suspect opposing defensive coordinators picked up on Debord’s meta-tendency of grandly rehearsed reversals to the point where they had a pretty good idea when they were coming.

As with many things in poker, it makes a big difference what your opponent is aware of, and the tendencies they don’t even know about themselves are usually the most reliable. Those are the ones that they’d never think about reversing. So if someone showed a bluff after taking a very strange line in a huge pot, the next time he takes that line, he probably has the nuts. Unless he’s a moron, or he thinks you’ll think that (but now we’re into the leveling war again). But someone might not bluff raise often enough on the flop and not even be aware of it just because he doesn’t know that’s something he’s supposed to do. In that case he’ll never change his tendency unless something forces him to change how he thinks about the game.

Some people imagine that a “wild man” strategy of raising, calling, or folding essentially at random would be hard to play against, but such a strategy usually ends up being extremely unbalanced (way too many bluffs, or not enough). I’ve heard people say, “How can you know what I’m doing? I don’t even know what I’m doing?” Everyone I’ve ever heard say this had strong and exploitable tendencies. In fact, to be effectively unpredictable requires a lot of work and planning. You have to be very intimate with your own ranges to know how often you ought to be bluffing and with which hands.

As to the original question — if someone did A last time, are they more likely to do A or not-A this time? — it’s hard to offer a better answer than “it depends.” In general, most people pay too much attention to short-term history and not enough to long-term tendencies. Dramatic events in recent history are the ones your opponent is most likely to remember and try to confound, while long-term tendencies are less salient and he may not even be aware of them. Perhaps it’s helpful to think of your opponent as a snowboarder: he can do a lot of tricks, twists, and jumps along the way, but eventually he ends up at the bottom of the mountain.

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