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When to Double (To D or not to D)?
In backgammon, the decision of when to offer a double is always more difficult than the decision of whether to accept or refuse. The problem is volatility. Your situation in the game may change considerably from one chance to double to the next.
The best time to double is at the top of your market, when it would be correct for your opponent to either accept or refuse. But such an opportunity almost never arises. You have to either double early (when your opponent should accept), or late (when your opponent should refuse).
Any time you are very close to the top of the market window, it is almost certainly correct to double. And, of course, if you are beyond the opponent's drop point, you should definitely double and take the sure point (unless there is a significant chance of a gammon). But what about before the opponent's drop point, while the opponent still has a clear takes?
One way to view the doubling decision is that there is a cost associated with any double which is not made at exactly the top of the market window. When you double early, you give the opponent the cube at a time when he still has a good chance of using it against you. When you double late, you are not getting the maximum possible leverage out of your double.
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