You Play to Win the Game

Previously (Putanumonit): Player of Games

Original Words of Wisdom:

Quite right, sir. Quite right.

By far the most important house rule I have for playing games is exactly that: You Play to Win the Game.

That doesn’t mean you always have to take exactly the path that maximizes your probability of winning. Style points can be a thing. Experimentation can be a thing. But in the end, you play to win the game. If you don’t think it matters, do as Herm Edwards implores us: Retire.

It’s easy to forget, sometimes, what ‘the game’ actually is, in context.

The most common and important mistake is to maximize expected points or point differential, at the cost of win probability. Alpha Go brought us many innovations, but perhaps its most impressive is its willingness to sacrifice territory it doesn’t need to minimize the chances that something will go wrong. Thus it often wins by the narrowest of point margins, but in ways that are very secure.

The larger-context version of this error is to maximize winning or points in the round rather than chance of winning the event.

In any context where points are added up over the course of an event, the game that matters is the entire event. You do play to win each round, to win each point, but strategically. You’re there to hoist the trophy.

Thus, when we face a game theory experiment like Jacob faced in Player of Games, we have to understand that we’ll face a variety of opponents with a variety of goals and methods. We’ll play a prisoner’s dilemma with them, or an iterated prisoner’s dilemma, or a guess-the-average game.

To win, one must outscore every other player. Our goal is to win the game.

Unless or until it isn’t. Jacob explicitly wasn’t trying to win at least one of the games by scoring the most points, instead choosing to win the greater game of life itself, or at least a larger subgame. This became especially clear once winning was beyond his reach. At that point, the game becomes something odd – you’re scoring points that don’t matter. It’s not much of a contest, and it doesn’t teach you much about game theory or decision theory.

It teaches you other things about human nature, instead.

A key insight is what happens when a prize is offered for the most successful player of one-shot prisoner’s dilemmas, or a series of iterated prisoner’s dilemmas.

If you cooperate, you cannot win. Period. Someone else will defect while their opponents cooperate. Maybe they’ll collude with their significant other. Maybe they’ll lie convincingly. Maybe they’ll bribe with out-of-game currency. Maybe they’ll just get lucky and face several variations on ‘cooperate bot’. Regardless of how legitimate you think those tactics are, with enough opponents, one of them will happen.

That means the only way to win is to defect and convince opponents to cooperate. Playing any other way means playing a different game.

When scoring points, make sure the points matter.

These issues will also be key to the next post as well, where we will analyze a trading board game proposed by Robin Hanson.


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20 Responses to You Play to Win the Game

  1. benquo says:

    Sonetimes you’re playing an open-ended game and “winning” isn’t really a thing. This was Jacob’s position.

    • benquo says:

      I think this is more like the original meaning of “play” anyhow – exploration in action-space.

      • TheZvi says:

        I thought I explicitly noted that? Clearly he realized that the game as designed wasn’t interesting and chose to do something else rather than try to win it – which to me also means he wasn’t playing it, either. Which I think he’d agree with.

      • benquo says:

        No, the title of your post explicitly advises playing to “win.” You say that there might be a more important concealed game with a different win condition, but that’s not the same as a concealed game without a well-defined “win” position, or things that aren’t fully games at all. If you don’t want me to believe the title (& the first few paragraphs of the post) you should say so more explicitly in the post.

      • Benquo says:

        What I think is going on here is that I’m responding to a bit of your frame – which is part of the literal explicit text of your post, but you’re used to thinking of as a neutral carrier for your message (e.g. using “winning” to stand in for all desirable outcomes).

      • Ah, I see. I did note tat Jacob chose to play a different game slash not care about winning the prize, but I definitely also take the stance that when participants in an explicit game are indifferent to winning, or primarily aiming at a different target, it usually means something has gone horribly wrong. I do think that applies in this case – bad design of the rules caused the goal to not be interesting.

      • Benquo says:

        It seems to me like this implies that most socializing through the casual playing of games has gone “horribly wrong,” and that’s pretty surprising. What am I missing?

      • Ah, I see the confusion. I’m not saying that if we choose to get together and chat while playing chess, and we mostly value that we’re chatting and hanging out and put 75% of our optimization pressure on that, that anything is bad. That’s fine.

        What I’m saying is, if I start making chess moves that are not aimed at winning the game (or exploring or learning about a variation, or other such goals), that something is going wrong. I shouldn’t be trying to prove that I’m the type of person who plays the Sicilian Defense and thus has proper revolutionary thought, or letting someone else win to stroke their ego, or what not.

  2. Kniffler says:

    How do you make sure points matter? Any game can have its reward/penalty distributions overwhelmed by reward/penalty incentives from the broader “game”.

    • What you can do is make sure that people care about winning the game, by creating a culture that makes that automatic and intrinsic.

      What you can also do is avoid playing games where broader issues threaten to interfere, and designing around this concern, and make as explicit and large as possible the penalties for trying to use such issues.

      What you can’t do, is get rid of them entirely or wish them away. It will always be a struggle. Wish I had a better answer.

  3. Magister Ludi says:

    I really can’t overstate how much I enjoy your discussions of game theory. Thank you! I’m looking forward to your take on Whodunit wagers.

    Maybe one day you can be persuaded to give the Darwin Game a second look.

  4. michealvassar says:

    If I was going to frivilously make a wish for a game analysis it would be of ‘the beer game’, which I only recently heard about (probably on SSC)

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  7. Doug S. says:

    When you “play to win the game”, if there are more than two people playing, do you care about the difference between second and last? If you had a choice between guaranteed second place or a one percent chance of first and a 99% chance of fifth place (out of five players), which are you supposed to take?

    • That’s less clear. Certainly if there is a points system, such that second place gives a substantial prize on its own, there’s nothing wrong with locking in second there, because there’s a larger game at stake.

      But in a game where second place doesn’t actually matter, I think taking a path that locks in a loss over a path that might win is always incorrect. For example, take a game of Risk. Often one can ignore the leader and attack other players, in a way that ensures his victory, and that makes it likely or almost certain that you’ll be in second place. But that’s terrible, and if I saw someone do that, I would not invite them back to play again. They’re ruining the game.

      In games where you’re not hurting the chances of third players, it’s less bad, but it’s still bad form and I would strongly discourage it.

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