by Mary Hickey
2 May 2012
Knowing when to double is one of the hardest aspects of backgammon to learn. Some positions demand a cube with only a slight pull in your favor, but others call for waiting with a much larger advantage. The difference when match score is not an issue is often "volatility", the likelihood of a game-changing swing on the next sequence. That is also true in another very difficult class of backgammon problems--where you have to decide whether to play on rather than double or redouble.
I'll start with a mention of the "2 to 1 rule", which states that in a money game, the value of an incremental gammon you might win is approximately half as important as an incremental game you might lose. In other words, a risky play must give you approximately twice as many added gammons as it loses additional games. This rule can be profitably applied to some play-on cube decisions, but a great deal of the time, the best thing to do with this rule is forget you ever heard of it! Other factors, such as your ability to keep the (re)double/drop in hand while trying for the gammon, are often much more important.
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Mary, I'm confused by the first example. The analysis shows that your opponent wins 2.1% and you only win 3.8% gammons, which is less than twice as much. Why then is it too good to double? I would think that doubling would bring your equity from .987 to 1.
That .987 equity, and his 2.61 wins, are the cubeless numbers, so they would only apply if you not only didn't double here, but never doubled at all no matter what went down. The rollout assumes you will double later if your gammon equity has faded, and/or his winning chances have improved, to the point that it's best to pull the plug. A trivial example occurs when you roll a 21 and take off only one checker, and he rolls a 66. Time to make him go away in case he has more where those came from, thus ensuring that another of those 2.61 wins doesn't happen on your watch!
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