Win-Win Poker

by Daniel Kimberg | Published: Dec 31, 2004

At its heart, poker is a game about beating other people out of their money – or at least so it seems on the surface. Ignoring the rake, poker is a zero-sum game: For every dollar won, there is a dollar lost. It probably doesn't make sense to trace the ownership history of a given chip, and thereby to keep track of exactly whose dollars you're winning or losing. But, a core reality of the game is that in order for you to win, someone else has to lose.

Behind this seemingly obvious truth, however, is a bit more complexity. People play poker for all sorts of reasons. While monetary profit is the one that comes to mind most readily, there are certainly players who value the action, the intellectual challenge, the social contact, or the pure element of competition as much as or even more than they enjoy the potential profit. In cardrooms around the world, you can find many players who know they have no reasonable expectation of winning, yet they still keep coming back. Although the money is zero-sum, the value people derive from playing poker isn't. The broad array of motivations is one of the most important factors that drives poker's success.

To be sure, even if poker depended on losing players who think they're winners, the game would have a solid following. But understanding the different kinds of value people find in poker can be helpful in finding investments for your bankroll that meet your goals least painfully – both for you and for your opponents.

An ideal situation would be one in which your goals conflict minimally with those of the other players at the table. If the rest of the players at the table are treating the game like a slot machine – a reasonable gamble for the day, but one at which they have no expectation of long-term profit – you can happily play at positive expectation without feeling that your winning necessarily takes away from what other players at the table really want. To be sure, they'd sooner win than lose. However, since they're happy to play at negative expectation, even when they lose they're still getting what they wanted. And because of that, the game is stable. As long as they don't go broke, the game can continue to meet the needs of the entire table, week after week.

To turn things around a bit, imagine you're in a phase of your game where improvement is more important to you than profit. If you're trying to take your game to the next level, you may be perfectly willing to play at negative expectation for a while in order to gain valuable experience, perhaps with a new game or limit. In this case, the situation may not be stable for the long run; you won't be willing to pay a premium for lessons forever. But for the time being, your need for experience and your opponents' need for chips won't conflict – at least not as much as they would if you were both out to maximize profits.

Although it's common to see poker as a kind of adversarial pursuit, these kinds of win-win exchanges are evident in many areas of life. When you exchange money for services or goods, the transaction works because you're each happier to have what you're getting than what you're giving up. The two parties place different relative values on the items they're exchanging. And it need not be a fundamental disagreement on values. You might agree with the convenience store that your dollar bill is worth a dollar. But the bottle of soda you're buying is likely a lot more valuable to you as a drink than it is to the store as inventory. You'd feel the same way if you'd acquired a huge inventory of soda.

You also see the same thing in professional sports. When two baseball teams exchange pitchers, it might be because of a disagreement about the future prospects of the two players. But it might also be that the two teams have different needs that are better met after the trade than before. A team with extra right-handed middle relievers might make a trade with a team that has extra left-handed middle relievers. The trade might go more smoothly if the respective teams have middle relievers who aren't getting along with their teammates and who have families in the other team's city. Although there may still be haggling about ways to balance the trade, and it all could fall apart if one of the teams thinks it can get more compensation elsewhere, win-win trades can certainly occur when players are more valuable to one team than to another.

Examples in poker aren't limited to your broad goals for sitting down at a table. Tournaments provide a variety of situations for win-win transactions based on mismatched values. The most obvious example comes with just a few players to be eliminated out of the money. A player interested mostly in minimizing risk, or who places a high value on making it into the money, might be willing to pass up some high-variance positive expectation plays. At the same time, players who are willing to risk exiting just out of the money in order to improve their overall equity may be much more willing to get involved in big hands. The equity players are glad to benefit from conservative players who won't play their pocket queens, and the conservative players are glad to see the equity players battle it out in confrontations that are certain to help them slide into the money.

Sacrificing expectation to reduce variability is a recurring theme. It's frequently observed that professional poker players increase their earning rate because they're willing to weather the variance associated with pressing small edges, where nonprofessionals are less interested in investing huge sums with razor-thin edges. Outside of poker, it's easy to think of even clearer examples. A classic thought puzzle is to imagine what you'd do if someone offered you, say, 3-to-2 on a coin flip for your life's savings. Your expectation for a bet like this is, of course, better than anything else you're liable to get elsewhere. But if you take the bet, there's a 50 percent chance you'll end up stone-cold broke. Few would take the bet, because the downside would be too disastrous. More mundane examples of trading expectation to reduce variance abound, and, incidentally, keep the insurance industry afloat.

Whenever you make a bet you think will be profitable, it's important to know what the other party thought was so attractive about the bet. If both parties are making the bet for reasons of profit, one of you has to be wrong. In a heads-up freezeout, you both can't be the better poker player. But, if you can find opponents whose motivations don't conflict with yours, there's no reason you both can't go home happy.