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Some thoughts about retrograde backgammon

Posted By: Nack Ballard
Date: Friday, 13 June 2014, at 5:06 a.m.

In Response To: Some thoughts about retrograde backgammon (Timothy Chow)

Here are some thoughts:

In backgammon problems (whether with a legally played, well-played or best played criterion), finding the shortest sequence is much more difficult to solve than it is when the exact number of rolls is announced. The latter is a huge hint. Moreover, for every legal-play solution in x rolls, there are usually many solutions in x+1 rolls, and a huge number of solutions in x+2 rolls, etc. This difference between chess and backgammon problems has much to do with the former having one set of legal moves possible each move, and the latter having in essence twenty-one sets of legal moves based on a range of 4 pips (double 1s) to 24 pips (double 6s).

Without necessarily comparing the degree of difficulty, if the backgammon roll sequence (without the plays) was supplied, then backgammon proof problems would be more similar to chess proof problems.

Note that in chess problems, a "move" is two ply (though it can mean one ply in other chess contexts). In backgammon problems, I try to remember to say "roll" (actually meaning roll+play), as "move" might be interpreted as either one ply or two ply unless there is clarification in context.

Bob's problem of reaching the opening 31P position in the fewest number of rolls that is greater than one, turns out to be a great proof problem, IMO.

"I am not the only one to have devised [the four-roll re-opening sequence], but I believe I was the first."

Did you come up with it before 1996? If not, then the famous Murat Kalinyaprak scooped you.

Definitely earlier. I no longer recall exactly, but I think I came up with it in the early 1980s.

BTW, I was unable to view either of the links in your post. Perhaps the problem is on my end or it is only temporary.

If you come up with puzzles that meet the kind of aesthetic criteria I mentioned, I can circulate them among the larger puzzle-solving community for feedback. Almost anything is fair game for this crowd except knowledge of good backgammon strategy.

Thanks. That's an interesting idea.

A few (three or four?) years ago, I posted a lot of puzzles that to solve required knowing nothing more than knowing the rules of backgammon. I'm not sure how to find those posts now, but if you or I do run across them, we could compare notes and see which would be best to share and I could double-check them for cooks. That would be a good place to start.

Nack

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