# The Mini Max Strategy

When one is confronted with a situation that’s truly zero sum where one party is going to win and the other party is going to lose, a situation is very complicated and sometimes difficult to analyze. Game theory spent much of its early days analyzing zero sum games and trying to figure out what’s the best strategy. It’s a little complicated because it depends critically on how sophisticated you think the other party is. If they’re very, very, very smart, the chances that you’re going to outthink them are not very high. In such a situation often times the best strategy is very counterintuitive, because it involves flipping a coin or rolling a dice or doing something random. Professional poker players know this and they often times advocate in poker strategy books that one should occasionally do something completely counterintuitive in order to keep your opponents off guard.

And in fact game theory has shown that this is good, solid, mathematically well-founded advice, that often times what you want to do is engage in a kind of random strategy—game theorists call this a mixed strategy—in order to make sure that your opponent can’t get the leg up on you. The nice thing about these random strategies is that they ensure that your opponent can never outthink you. So even if you think your opponent is a little smarter than you or a little bit more sophisticated than you or has a little bit more information than you do, the fact that you’re being random to a certain extent means that they can’t outthink you. Now how do you figure out how to be random? I’m not saying just flip a coin all the time or whatever. What game theorists have figured out is that in zero sum games the best strategy to pursue when you’re against a sophisticated opponent is to adopt the strategy which minimizes your maximum loss.

This is sometimes called the mini max strategy. So the idea is you think: what’s the worst case scenario for me? What could my opponent do that would make me worse off? And then you figure out what’s the best strategy against that, so you’re minimizing your maximum loss. Game theorists prove that if you use this way of thinking, minimizing your maximum loss, you ensure that no matter how sophisticated your opponent is you’ve guarded against the worst case scenario. And not only that but in zero sum games you’ve done the best you can possibly do. That’s not true in games that aren’t zero sum, so one has to be very careful about employing this strategy, because if you’re mistaken and you’re not in a zero sum interaction you could end up ruining it for everybody. But if you’re truly in a zero sum interaction this is one of the strategies that you can use.

Now suppose that you’re dealing with an opponent who’s not sophisticated, you are smarter than they are, there it depends very much on: how smart are they? Can you outthink them? And what’s the individual interaction that you’re engaged in? So to return it to the example of poker players, poker players will engage in interactions where they’re trying to think, “Well does my opponent think I’m going to bluff here, yes or no? And maybe I’ll do the opposite.” But that’s going to depend on how smart is your opponent? What are they thinking about, and the individual interaction that you’re engaged in. Game theorists have actually proven—although it’s not very helpful—but game theorists have actually proven that there is no the one size fits all strategy in a situation where you’re dealing with an opponent who is not very sophisticated.