Puzzles

Forum Archive : Puzzles

 Worst symmetric bearoff of 8 checkers

 From: Gregg Cattanach Address: none Date: 6 January 2004 Subject: semi-useless puzzle Forum: GammOnLine

```This came up in my forum: What symmetrical orientation of 8 checkers for
each player in the home board gives the roller the least chance to win
the game (cubeless).

And why?

Gregg C.
```

 Kit Woolsey  writes: ```The obvious answer would be everybody on the six point, since this is the longest race and the shorter the race the better it is for the leader. Also, there is plenty of chance for subsequent wastage (for both sides, of course), and that has to favor the trailer. I checked out a few other possibilities and everybody on the six point was the lowest of the ones I checked, although everybody on the five point was a close second. Perhaps there is some trick position I didn't consider. Kit ```

 Ian Dunstan  writes: ```I haven't looked too hard and there might be something better, but [000035] vs [000035] seems to win less for player-on-roll than everybody on the 6pt (62.5% vs 63.2%, cubeless rollout). The length of the race is certainly the main consideration, but doesn't the player-not-on-roll also want a low wastage position as well, making the most of his good catch up numbers (6's, 5's, high doubles)? ```

 Jordan Lampe  writes: ```A quick perusal of Ye Olde Two Sided Databafe reveals that Ian's [000035] is the correct answer. I don't have a good intuition as to why that pattern is any better than any others. Perhaps the goal is to simply look for the highest variance?? ```

 Dean Gay  writes: ```I think you are right about looking for the highest variance. As to why 000035 is the answer, perhaps part of the reason is because 4s play poorly, going to the one point, which could tend to leave checkers on odd-numbered points, thus making even numbers continue to play poorly. This has the effect of lengthening the race, which tends to help the trailer. That's one thought, anyway. ```

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