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First goer problem

Posted By: Ray Kershaw
Date: Monday, 27 March 2017, at 5:44 p.m.

In his Cleveland lecture, Art Benjamin shows how easy it is to solve the First Goer problem. Usually this asks what is the probability that A who goes first tosses a head or throws a 6 etc before B.

Art shows a case where A and B have different objectives, specifically A has to come in from the bar against a 5 point board and B has to come in from the bar against a 4 point board. B is the favourite.

I wondered whether there are different objectives with a backgammon interpretation where A and B are equally likely to win. Here is an example. A, the first goer, has the objective of failing to bear off a checker from his 6pt (9/36) before B hits a blot two pips distant (12/36). Checkers are not moved if you fail.