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A problem with Turing’s run-around-the-house chess game?

Alan Turing is said to have invented a game that combines chess and middle-distance running. It goes like this: You make your move, then you run around the house, and the other player has to make his or her move before you return to your seat. I’ve never played the game but it sounds like fun. I’ve always thought, though, that the chess part has got to be much more important than the running part: the difference in time between a sprint and a slow jog is small enough that I’d think it would always make sense just to do the jog and save one’s energy for the chess game.

But when I was speaking last week at the University of London, Turing’s chess/running game came up somehow in conversation, and somebody made a point which I’d never thought of before, that I think completely destroys the game. I’d always assumed that it makes sense to run as fast as possible, but what if you want the time to think about a move? Then you can just run halfway around the house and sit for as long as you want.

It goes like this. You’re in a tough spot and want some time to think. So you make a move where the opponent’s move is pretty much obvious, then you go outside and sit on the stoop for an hour or two to ponder. Your opponent makes the obvious move and then has to sit and wait for you to come back in. Sure, he or she can plan ahead, but with less effectiveness than you because of not knowing what you’re going to do when you come back in.

So . . . I don’t know if anyone has actually played Turing’s running chess game, but I think it would need another rule or two to really work.

13 Comments

  1. ben farrer says:

    i always thought this hybrid seemed like more fun

    http://en.wikipedia.org/wiki/Chess_boxing

    or maybe after you make a move you should play tag around the house, and the length of time you last running away from your opponent is the length of time you get to think about your next move or something? the 'pawn to run' variant.

  2. LemmusLemmus says:

    As someone's bound to bring it up anyway, I might as well say that chessboxing appears not to suffer from similar problems.

  3. LemmusLemmus says:

    Hah! What did I say?

  4. David R. says:

    Well, I think it's not trivial that if you're in a tough position you'll have an obvious play… this will just mean that you're probably postponing (or making it worse) the problem.

    But to solve all of this probably the best way is to do as in regular chess: use a clock. Every player has, let's say, 1h in his clock… and in that 1h he has to win the game with the conditional of going around the house every play made. Then the runs will be quick.

  5. Mike says:

    Why does the opponent have to wait for you to get back? Once the opponent makes the obvious move, then the opponent should start running too. That means you can't sit around as long as you like, but instead need to get back as quickly as possible to maximize your time to play.

  6. Andrew Gelman says:

    Mike:

    Good point. But then this suggests another way of beating the game: if you're the faster of the two players, just make your move immediately after your opponent, then start running, catch up to him or her as you're going around the house and get back to your seat before your opponent has had a chance to move. This gives you an automatic win or at least a free move (depending on one's interpretation of the rules), which doesn't sound quite right either.

    David:

    Sure, the clock would work, but that seems to me to violate the self-regulating aspect of Turing's game (as I first perceived it). I have a similar reaction to the chessboxing. It's amusing but the rules seem artificial. In contrast, the rules for Turing's game seem so natural.

  7. Amit says:

    Weird… I always thought the chess to be secondary part of the game. Running around the house 40 or more times seems to me to be more difficult than winning a chess game. Think about an endgame in which you might spend 10-20 (or more) easy moves just to get the opponent's king to the right spot on the board. I think I'd rather lose the chess game than running these extra rounds.

  8. Andrew Gelman says:

    Amit: It would be tough to run 40 times around a McMansion, but the houses were pretty small in 1940s England. You do make a good point, however, about the interaction between the running and endgame strategy. Still, it's ultimately the chess skill that will do it for you. If you have a winning position, it doesn't matter how slowly you crawl around the house, you'll still win, right?

  9. conchis says:

    "you go outside and sit on the stoop for an hour or two to ponder."

    Maybe I just have poor spatial memory, but not being able to see the board from the stoop would make such pondering pretty much worthless for me.

  10. dsquared says:

    Moves aren't necessarily sequential in Turing's game – if you have made your move, run around the house and come back and your opponent is still thinking, you're allowed to make another move. So in your situation, the opponent makes his move, does his run, then comes back and moves again, runs again, moves again, more or less destroying you while you sit thinking

  11. Andrew Gelman says:

    Dsquared: That makes sense, but then does it give too much of an advantage to the faster player, especially in the opening stages, because he can make really quick moves and outrun the other?

    For example, suppose the faster player is Black. Consider the following sequence:

    White: P-Q4. Run.
    Black (immediately!): P-Q4. Run.
    Black then catches up to White and gets another move!
    Black: P-QB4. Run.
    Now Black has caught up. If he can ever make White think long enough that he (Black) has time to run around the house, he can repeat the trick and get another free move.

    Hmm. Now that I think about it, I guess it's ok. If the slower runner is a good enough chess player and can play fast enough and throw out enough complications, he can keep the faster runner at bay–probably. But if the two players are close in chess ability, then the faster player might get in a few free moves and win. If the faster player is Black, he or she will always get two moves in a row at the beginning, but I assume that's not such an advantage?

    So I guess the game is all right (or should that be "alright"? I'm not quite sure how they write that in England) after all. I think it isn't usually described so clearly, though. I've always been under the impression that two-moves-in-succession would only occur if someone wasn't paying attention. As I see it, though, the game involves a lot more running than usually supposed. If you're the slower one, you can't just sit there thinking about your move while the other player is running; you really have to slap something down and get off your butt right away!

    P.S. Yes, I realize that my use of descriptive notation reveals my advanced age.

  12. Phil says:

    I think the point of the whole, um, exercise is to have a sport that credits both mental and physical skill. Different rules can lead to different weightings of these two parameters. Andrew, you seem to think of this as a way to somewhat modify a chess game so that speed comes into it a bit, so you're uncomfortable with the idea that a really fast guy should be able to win even if he's a terrible chess player. You'd like to see a weighting that makes the sport mostly about chess, with the running being a not-too-huge modification. And that was probably Turing's idea, too.

    But I could imagine doing it the other way, emphasizing the running instead. For instance, you and your opponent play at the track instead of at a house. Each player has to make a move every 2 minutes, but must do a lap between moves. Don't make it? You lose. To start the game, player A moves at time 0 and must move every 2 minutes thereafter; player B moves at 1 minute, and every two minutes thereafter. If you're really fast, you finish your lap in 1:30 and get 30 seconds to ponder (and recover) before setting off again. If you're slow, you're taking 1:55 to do the lap and it's pretty much speed chess for you. (In either case, if you're struggling on the first few laps, you will be in real trouble by lap 5 or 10).

    I guess my point is, we're probably creative enough to come up with many possible sets of rules that would work OK. The harder question is, what are you trying to achieve? Do you want a super-fast runner who is bad at chess to be able to beat a slug-like grandmaster, or a slug-like average player, or only a slug-like bad player?

  13. Andrew Gelman says:

    Phil: I agree that there's some balance between the chess and the running. Somehow based on the description, I've always thought of round-the-house chess as a chess variant rather than a track-and-field event. The other thing that's key, I think, is the beautiful simplicity of Turing's rule–no clocks!