2010-08-15 Match Cube/Answer

Comments by John O'Hagan:

This bizarre position actually came up in a match between Brent Cohen (Pa) and Sean Garber (In) at the recent Michigan Summer Backgammon Championships.  Cohen (Black) doubled and Garber accepted.  Was this the correct cube action?


We showed this position to a variety of open level players and nearly everyone thought Black should double and they were roughly split down the middle on whether White should take or not.  Everyone we showed this to thought the take/pass decision was close.  After all, the 13 immediate hits are mostly game winners for Black (with some gammon chances) and more shots will almost certainly be coming if this one is missed.  The takers thought White had just enough chances for a close take and the passers thought he was a bit short.    


Sean Garber was the only one who analyzed it correctly and he did it over the board.  He thought it was an easy take and he was 100% correct.  A 5184 game Extreme Gammon rollout confirmed that this is just barely a double and an extremely easy take.  Black only won 58% of the games in the rollout and only won 3% more gammons than White. 


So why did so many expert players misevaluate this position?  It seems that everyone but Sean overestimated the future shot danger from White's awkward position.  If you look at White's upcoming 36 rolls (assuming this shot is missed), you'll see that his chances aren't really that bad.  The blot on the 8-point becomes a builder so eleven numbers will now make the 2,4, or 5-point (64,61,44,42,31,22,11 plus 41 if Black moves from the 18-point which he will do if he rolls one of the 4 high doubles), 9 more play safely (65,62,55,53,32), and everything else leaves a single direct shot.  White will be a clear favorite if he rolls a point-maker, and probably a slight dog in the other 2 categories. 


This position is a reminder for us to never forget that backgammon is basically a race.  White leads here by 48 pips so he'll win (despite his awkward position) if he doesn't get hit and he might win even if he does.


Technically this position is therefore a small double and easy take but practically it's a mandatory double since you'll get lots of incorrect passes.