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Racing puzzle/ additional question
Posted By: Timothy Chow
Date: Tuesday, 21 October 2014, at 3:16 p.m.
In Response To: Racing puzzle/ additional question (Bob Koca)
Great stuff! Are these examples backed up by twosided cubeful bearoff databases? A mathematical proof is more definitive than a rollout for noncontact positions.
For the benefit of BGO readers, let me mention that this thread started offline when a friend of mine asked if 21 was always the worst racing roll. I didn't immediately see the answer in Backgammon Funfair, so I emailed Ray Kershaw, Bob Koca, and Nack Ballard. Bob responded first with a simple counterexample, and this led to a discussion of how far the counterexample could be pushed.
One remaining open question I have is whether 61 or 62 can be worse than 21 in a straight race. You might think that if 66 can be worse than 61 or 62 can be too, but it's not immediately clear to me.

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