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Asymptotics

by Douglas Zare
1 January 2006

Douglas Zare

In several recent New England Backgammon Club tournament matches, players have come back from Crawford 9-away and similarly lopsided scores to win the match. These reversals are remarkable, not only because the trailer wins only a few percent of the time from the Crawford game, but also because it is rare for us to reach Crawford 9-away, since we rarely play matches of 11 or more points. Extreme Crawford and post-Crawford scores are more common in long matches, and it is worth reviewing them before playing in a tournament with long matches

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Subject: Re: Asymptotics

From: gammonvillage334455

Date: 02 Jan 2006 19:42 EST

hoping for a detailed article about the -2,-4 -3,-4 and -2,-3 scores which are the most important ones in 5 point and 7 point matches imo.

Subject: Re: Asymptotics

From: zare

Date: 04 Jan 2006 15:55 EST

For a detailed discussion of scores within the 5 point match, I recommend Kit Woolsey's article on the 5 point match in Gammonline. Much of the same material is also in his book, How to Play Tournament Backgammon, which also covers many other topics.

Douglas Zare

Subject: Re: Asymptotics

From: zare

Date: 07 Jan 2006 03:43 EST

I'll add that Woolsey's article is good, but much more could be written about particular scores. It would be nice to see a detailed discussion of the opening and doubling/taking reference positions, as well as a discussion of positions that are too good to double.

Chris Yep pointed out to me that my model underestimates the asymptotic value of the free drop since it underestimates the value of the most favorable sequences for the trailer. The main consequence is that the gammon price should be a bit lower at Crawford even-away and higher at Crawford odd-away. The increased value of the free drop also increases the racing take point on delayed doubles at pC odd-away.

Douglas Zare

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