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I’ve discovered that most players don’t know how to use the doubling cube very well. Without getting too technical, I’ll give you some rules for using the doubling cube that will make you superior to most Internet backgammon players.

When a game is doubled, it is being played for twice the original stake. A redoubled game is being played for four times the original stake, and so forth. After a player doubles, her opponent controls the doubling cube, and she may not redouble until her opponent redoubles.

Doubling is done for two reasons. One reason is to double the points you receive for winning a game. The other reason is to end a game the result of which is a foregone conclusion without having to play it out. In this case the person who is ahead doubles, and the person who is behind refuses to accept the double, ending the tedium of having to finish the game.

When should you accept a double? The general rule is to accept a double if you have at least a 25 percent chance of winning. This only applies if your opponent has no chance of gammoning you, because if she does that increases her expected winnings.

The math looks like this. If you decline a double you will lose 1 point. If you accept a double with a 25 percent chance of winning, your expected winnings are .5. The formula is .25 X 2 (the 2 points are what you receive for winning a doubled game). Your expected losses are 1.5. The formula is .75 X 2). The difference between your expected winnings and expected losses is 1, which is equal to your loss if you don’t accept the double. If you have greater than a 25 percent chance of winning, your expected winnings will increase and your expected losses will decrease.

How do you tell if you have a 25 percent chance of winning? One indicator is the number of pips you’re behind. In Internet backgammon the computer gives you a running total of the pip counts of you and your opponent, so you don’t have to estimate them. If you’re well behind in the pip count, your chances of winning are much diminished. The more you play the better the feel you will have for your chances of winning.

Late in the game, when both sides are bearing off, the pip count may have much less meaning. If your opponent has 15 checkers on his 1-point his pip count is 15. If you have 4 checkers on your 6-point your pip count is 24, but there’s little doubt you’re going to beat him. So the number of checkers left has to be taken into consideration as well as the pip count.

In Microsoft Internet Backgammon the first player to receive 5 points wins the match. If your opponent has 3 points and doubles you, you may want to think twice about accepting, even if you figure you have at least a 25 percent chance of winning, since he is doubling himself into winning the match. If you decline the double, at least you’ll get another crack at him. Don’t accept a double because of pride. He who fights and runs away will live to fight another day.

If your opponent doubles himself into winning the match, and you decide to accept the double, always redouble on your next turn. You have nothing to lose, and if you have 1 or more points, you will be doubling yourself into winning the match.

When else should you double? The general rule is to double if you have better than a 50 percent chance of winning. This is simplistic and comes with a lot of caveats.

The Microsoft Internet game doesn’t allow a double in the game following a game when one player reaches 4 points. During the game following this game, if your opponent has 4 points, you should always double, because you have nothing to lose. If you are the player with 4 points, never double.

If you double early in the game, your opponent has control of the doubling cube. If the odds swing in his favor, he can redouble, placing you in a position where you’ll either lose 2 points immediately or be playing for 4 points. Be cautious about doubling early in a game.

I recommend not doubling as long as you have a chance to gammon your opponent. A smart opponent will refuse a double if he thinks he might be gammoned. However, this doesn’t apply when you’re playing the Microsoft Computer Backgammon game, because it will always accept a double!

Some of the best doubles occur near the end of the game. Here’s an example. It’s your turn and you have 2 checkers left, both on your 2-point. Your opponent also has 2 checkers, both on his 1-point. Should you double?

Your chances of winning are 26/36 (26 out of 36). You’ll win unless you roll a 1 on just one of your dice. A double-1 is a winner. Of course you should double. Should your opponent accept? His chances of winning are 10/36 or better than 25 percent. Yes, he should accept the double.

Another example. It’s your turn. You have checkers on your 6, 2, and 1 points. Your opponent has 3 checkers on his 1-point. Should you double? You will win immediately with double-3 or greater. The chances are 1/9. If you don’t win immediately, your opponent will win with any double. His chances of winning are 8/9 X 1/6 or 8/54, which reduces to 4/27, and is less than 25 percent. If he doesn’t win on his turn, your chances of winning on your next turn are excellent. Your opponent still has a chance of winning, however slim. Even so, without going through all the math, I would say you should double and your opponent should refuse the double.

Don’t be afraid of using the doubling cube. It will add a new dimension to your game. It will also put you one-up on many of your opponents.