The Novice Poker Player's View From the Foothills

by Daniel Kimberg | Published: Dec 05, 2003

Three missionaries, three cannibals, and a boat sit on one side of a river. All six would like to be on the other side, but the boat holds only two, and if the cannibals ever outnumber the missionaries (on either side of the river), somebody's going to get eaten. Can you get everyone across safely? The answer doesn't involve having any of the people inside any of the other people, or any other trickery – it just involves people rowing back and forth.

In all likelihood, you first came across this classic problem in grade school. (But in case you didn't, or can't remember the solution, think about it for a minute. I've put the solution at the end of this column.) It's a cute diversion for kids, but it's also been used in academic circles to illustrate some tricky aspects of human and machine problem solving. One of these tricky aspects is that in order to solve it, you have to be willing to take a step that seems to be moving people in the wrong direction, even though it's actually getting you closer to your goal.

There are numerous more obvious (but less fun) examples of this kind of problem that are more likely to come up in the course of your life. Oddly enough, they're the kinds of problems people tend to solve easily, but dogs have trouble with. For example, if you want to retrieve a ball that's on the other side of a fence, you may have to move away from the ball to go around the fence, even though it seems within reach. The standard example of this kind of problem is hill climbing. Imagine a large hill surrounded by smaller foothills. A naïve approach to reaching the summit would just be to keep going up until you reach the top. But if you did that, you might get stuck at the top of a smaller foothill, what mathematicians would call a local maximum. So, you need to be willing to take steps that would seem (to a dog, say) to take you away from your goal. And although the right behavior seems obvious in simple examples, in real life it can be much more subtle. You don't always know when you're on a foothill, especially when the mountain is some nebulous and ill-defined goal, like financial security or happiness.

Poker is an interesting example of a game in which straightforwardly approaching your goal state (maximum profit) is liable to cause problems. The connection between the correct decision and profit is often obscured by the most salient aspects of a given situation. At some level, this simple observation encompasses all the difficulties that novice players usually have with strategy. Taking the hill-climbing approach – only taking steps that seem to move you closer to your goal – can play out as both weak and passive play. Folding doesn't always feel like the best way to get closer to your goal of winning money, and certainly in the short term it means accepting a loss. In fact, if your goal is to realize a profit in the next 30 seconds, folding is obviously a bad idea. Certainly, when you fold, there is generally some chance you'll find out later that you could have won the pot. The only way to eliminate this possibility entirely is never to fold. But if your goal is to turn a profit in the long term, not just this minute, folding is more likely to be a viable choice. At the very least, you need some awareness of things like odds and equity to make the right decision.

At the same time, playing safe and careful poker is also a bad idea that can have some short-term benefits. If you've decided to play your J-J or A-K in a loose hold'em game, flat-calling before the flop may seem like the low-risk way to keep your losses to a minimum, since there's a substantial chance of an unfavorable flop. If your goal is to avoid big losses, seeing the flop before making a bigger commitment seems like it might keep your losses manageable. To put it differently, throwing more chips out there with an uncertain hand isn't intuitively the right way to go about winning. The same applies to raising with drawing hands, or even made hands that could easily be outdrawn (say, A-10 with a two-suited flop of 10-9-2). Aggressive play doesn't always feel like the best way to find solid investments for your chips. Yet, virtually no hand is a sure thing, so the only way to minimize your exposure is to avoid aggressive plays entirely. If you see your goal as playing "safe" poker (that is, limiting your losses), you may find it difficult to pursue plays that have both positive expectation and obvious risk.

Although these modes of thinking seem contradictory, there are certainly players who suffer from both a reluctance to fold and a reluctance to raise. One seems like giving up, the other seems too risky. So, they call, and keep calling, making the minimum investment without giving up their interest in the pot. It's the definition of weak play, and the unfortunate consequences include giving your opponents long odds to outdraw you, failing to maximize profits on winning hands, and generally becoming more predictable in a way that helps your opponents steer clear of your winning hands. If this pattern feels comfortable to you, as it does to many novices, you may need to take a wider view of poker strategy. Focusing on the short-term implications of your decisions can be harmful when your goal is long-term profit. There are lots of reasons to play tight, aggressive poker, and to avoid flat-calling when a raise or fold might be more profitable. I've devoted this column to an analogy with hill climbing because I think most players intuitively understand those reasons, they just have a gut reaction to the moment that keeps them from making the right play. In that case, it may be most useful just to keep in mind that when you fold or raise without certainty about the outcome, you do so with an eye on the mountain, not on the foothills. Your goal isn't to do well in this hand, it's to do well in the long term, and that can involve some short-term outcomes that won't make you feel like you're getting any closer to your goals.

Before I leave, I want to add one more comment on flat-calling. Writers on poker strategy have often (and rightly) focused on the weaknesses of flat-calling. The examples I've given above focus on some of the reasons players tend to call when they should raise or fold. However, in the current poker climate, you're liable to run into a fair number of overly aggressive players, against whom flat-calling is sometimes the best strategy, and could even be described as aggressive. So, I want to avoid the impression that I'm substituting one simple answer for another. There's no shortcut to finding the best strategic decision. But, however you decide to handle a situation, it's important to avoid basing your decision just on the most immediately obvious consequences.

What about those missionaries and cannibals? Here's the solution, with M for missionaries and C for cannibals. I've put in boldface the step that causes people some trouble. MC cross, M return, CC cross, C return, MM cross, MC return, MM cross, C return, CC cross, C return, CC cross, and we're done. MMM and CCC all have a nice vegetable salad for dinner.