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.