The Half-Crossover Pipcount

by Douglas Zare
14 June 2000

The Half-Crossover Pipcount

by Douglas Zare

"And you do Addition?" the White Queen asked.
"What's one and one and one and one and one and one and one and one and one and one?"



"I don't know," said Alice. "I lost count."



Lewis Carroll, Through the Looking Glass.

Perhaps I have gotten a bit rusty at mental arithmetic. I had difficulty computing a pipcount in Backgammon, which I found a bit embarrassing. It is a straightforward calculation, but the difficulty was doing it accurately with no pencil and paper while an opponent rattles the dice.



The approximate pipcount is vital to correct backgammon play: "When ahead in the race, race. When behind in the race, don't race." Some times one needs more. The exact pipcount is extremely useful to guide one's doubling strategy in some situations. For example, in a race of more than 70 pips, if you are on roll a good rule of thumb is that if you lead by at least than 8% then you probably have a correct double, and if your lead is at most 12% then your opponent probably has a correct take. It arises in many other situations as well. Since the pipcount is important, there have been a wide variety of methods developed to compute it over the board. See Mark Driver's article, "A Beginner's Guide to Counting Pips" for one method and references to more. There is some related discussion in the Pip Counting section of the rec.games.backgammon archive
 

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