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Retrograde Backgammon � Three Puzzles, partial spoiler

Posted By: Nack Ballard
Date: Wednesday, 4 November 2015, at 3:31 a.m.

In Response To: Retrograde Backgammon – Three Puzzles (Taper_Mike)

Great retro-puzzles, Mike.

Puzzle 1: Technically, there are two solutions, but they are very similar.

Puzzle 2: Technically, there are three solutions, but they are very similar.

In case you want there to be a unique solution for each of the above, you could add the condition that neither player fans in the sequence. (I'm not saying that would necessarily improve the problems; it's a tradeoff.)

[If a different roll is used to make an identical play, I do not count that as a separate solution. Also, by "fan," I mean completely. Entering one checker is not fanning.]

Puzzle 3: The shortest sequence I found adhering to XGR++ is eight rolls. However, the shortest sequence that is perfectly played according to ROLLOUTS is SEVEN rolls (though still pending).

I think it's important to state how "perfectly played" is judged: Some of the many possibilities are: (a) Purely by XGR++, (b) Roll out all close plays, (c) XGR++ plus selective rollouts, (d) XGR++ but within .02 on opening play, .00 thereafter, (e) within .02 on opener, .01 on second-roll plays, .00 thereafter.

Nack

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