Checkers is Strongly Solved Through 7 Pieces

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Checkers is Strongly Solved Through 7 Pieces

Postby Ed Trice on Tue Dec 20, 2016 7:16 am

My computer has reported that today it finished solving all of the 6x1 slices with "perfect play," down to the last one, 6 checkers against 1 checker. With white to move with the 6 checkers, the position with the longest win requires 29-ply to complete.

I seem to recall Gil Dodgen's birthday was somewhere around December 20th. What a nice tribute to my friend and former colleague if this happened serendipitously on what would have been his 66th birthday.

White checkers: 29,16,14,13,10,9
Red checker: 8

White to move.

Whoever sets this position up first will be only the second person on planet earth to have seen it :)
Ed Trice
 
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Re: Checkers is Strongly Solved Through 7 Pieces

Postby Bill Salot on Thu Dec 22, 2016 4:57 pm

6 against 1 doesn't seem like checkers.
I once composed a problem with 13 pieces of each color. It got the same reaction.
Checker players are weird. It's not us, is it?
Bill Salot
 
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Joined: Sat Dec 15, 2007 10:57 am

Re: Checkers is Strongly Solved Through 7 Pieces

Postby Ed Trice on Fri Dec 23, 2016 10:16 pm

Well, the 4x3 set has been solved with perfect play since 2001, but the claim could not yet be made that all 7-piece endings were "strongly solved." Gil Dodgen and I decided to skip the 5x2 and 6x1 set, since, as you alluded to, it's not really that interesting.

Since I'm doing db8 4x4 right now, I decided to give the unused 2 processors on my computer the task of completing the 7-piece endings. Even chess has all 7-piece endgames strongly solved, requiring 140 Terabytes of storage. Checkers was behind chess before December 20, 2016!

Not anymore :)
Ed Trice
 
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Joined: Wed Aug 10, 2016 9:16 pm


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