An ode to a doubling cube

I’ve been playing backgammon quite a lot recently, mostly against a computer opponent, but also against friends. I think the game has many merits and it’s much more interesting than I thought it was after just playing once or twice. However, the most interesting part of the game is the doubling cube.

doubling_cubeSince you don’t really need to know the rules in backgammon to understand the doubling cube, I won’t bother with teaching you the game (check Wikipedia if you want to learn how to play). What you need to know is that each round is fairly short and that a game typically consists of many rounds. Each round can be won in three ways: a normal win (1 point), a gammon (2 points) and a backgammon (3 points).

Enter: The doubling cube

The doubling cube is a normal die with the numbers 2, 4, 8, 16, 32 and 64 inscribed on its sides. At the beginning of the game, the die is not active. During the game, a player can use the doubling cube to raise the stakes. If the opponent accepts, the winner of that round will win the normal amount of points multiplied by the number on the doubling cube. The first time it’s used, the stakes are doubled (2), next time they are doubled again (4) and so on. If the opponent doesn’t accept, he loses that round automatically with as many points as the doubling cube shows.

Why do I write an article about this, you might ask? I think the doubling cube is brilliant. It’s one of the simplest and coolest game mechanism I’ve seen in quite a while. It deserves to be explained, praised and spread.

Here’s why the doubling cube is awesome:

  1. It shortens games with a predictable outcome. In most games, there are times when both players know who’s most likely to win. It doesn’t mean that they are absolutely sure who will win, but they definitely have a clear idea. In backgammon, many of these games end because the player who is slightly ahead proposes a double. His opponent, being behind, will not accept the doubling and therefore concedes the round and gives one point to the opponent, rather than risking losing two or more if he continues playing.
  2. It adds an extra dimension of strategy which is not directly related to the game (and which is therefore possible to transfer to other games). It’s not easy to Know when to double, when to accept a double or when to pass. It requires knowledge of the game and the ability to assess the current state of the game (i.e. determining if someone is ahead or not, and if someone is, by how much). Making correct cube decisions is very hard.
  3. It makes it possible to catch up even if you’ve fallen far behind. By playing correctly and using the doubling cube, you can increase the stakes and therefore also the variance of the game, making it possible to catch up with someone far ahead of you. If you’re ahead yourself, you need to balance playing safely to maintain your lead against the risk of being bullied by the other player, who can double more often because he has less to lose.

Beyond backgammon

This kind of mechanism could be introduced in any kind of game which is played with more than one round (which includes games where the players have a ranking or care about the meta-game). It also works for games where it matters by how much you win (such as any game where you play for money). I’m not sure what I want to use this for personally, but I definitely feel that it would be an excellent ingredient in rules for duels in role-playing games.

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