Cube Insights by John O'Hagan


In the position below, Red leads 3away/4away, holds a 2-cube and is on roll.  Cube action?






Let's start out with a little test of honesty here first.  Unless this was presented as a problem, would you even give the slighted thought to doubling here?   It sure surprised me when ExtremeGammon doubled me in this position, and of course, being surprised, I took the cube and won the match. 

.  I wondered why the bot was redoubling so early when it was leading in a short  match and I had such an easy take (my 4-cube takepoint is just my MWC at Crawford - 4a, about 18%).  So I took and subsequently won the game and the match.  I don't often see XG make huge blunders, so I took a lot longer look at this double after the match.


I had XG roll out the position to see if the redouble was correct.  To my surprise, the answer was yes.  The leader is supposed to redouble this position at this score even though the opponent would have a beaver in a money game!  There certainly aren't many positions where the leader in a short match is supposed to redouble a position where the opponent would beaver for money, but this is one of them.

 

So why is the redouble correct?  First of all, most of your losses figure to be gammons which will cost you the match even if you don't recube.  Secondly, 5s are big market losers.  D5 and 51 make a full prime, 52 prepares to next time, while 53 and 54 hit.  65 isn't quite as strong but still leaves blonde with a big advantage.  Thirdly, redoubling makes your checker play decisions less difficult.  Redoubling makes it DMP so your only criteria will be to find the play that maximizes your winning chances.  If you keep the cube on 2, you'll have to also take into account gammon wins and losses along with blending your checker play with your future cube action.    Say that blonde fans for example and that brunette then rolls a 51 (13/8 24/23).  If blonde then responds with a 52, what's the right play?  If he's at DMP, it looks clear to me to keep the prime slotted and play the 2 13/11.  If he owns a 2-cube, he has to make the more difficult decision of whether or not the extra wins from 13/11 outweigh the extra gammons losses from having an extra blot.

 

If you look at the rollout results you can see that about 78% of blonde's losses are gammons and that about 20% of his wins are gammons.  These gammon fractions have a big effect on the leader's redoubling window at this score.  The only gain or loss from redoubling occurs when one side or the other wins a single game since a gammon wins the match for either side regardless if the cube is on 2 or 4.  A single loss with the cube on 2 gives the trailer around 41% MWC so the loss from redoubling is about 9% (41%*22%).  The gain occurs when blonde wins  a single game.  A single win with the cube on 2 gives blonde a 4-1 Crawford lead with about 82% MWC while a win with the cube on 4 wins the match with 100% MWC.  The gain from recubing is therefore 80% of 18%, ~ 14.4%.

 

The redoubling window therefore opens at around 38% (9/9 + 14.4) and closes at 82%.  Per the rollout, blonde is around 56% and has a redouble even though he's 26% away from an efficient redouble.  Waiting and hoping to creep up closer to a more efficient redouble is not correct here.  This isn't a position where you gradually improve your winning chances and then offer an efficient recube.  It's a volatile position where you either lose your market by a lot or dance and probably lose a gammon and the match anyway. 


The XG rollout is below


Analyzed in Rollout
No Double
Player Winning Chances: 55.61% (G: 11.22% B: 1.09%)
Opponent Winning Chances: 44.39% (G: 34.78% B: 9.39%)
Double/Take
Player Winning Chances: 56.20% (G: 12.63% B: 1.18%)
Opponent Winning Chances: 43.80% (G: 34.00% B: 3.20%)

Cubeless Equities
No Redouble:-0.462
Redouble:-0.220

Cubeful Equities
No Redouble:-0.285 (-0.065)
Redouble/Take:-0.220
Redouble/Drop:+1.000 (+1.220)

Best Cube action: Redouble / Take

Rollout details
648 Games rolled with Variance Reduction.
Dice Seed: 62357220
Moves and cube decisions: 3 ply

Confidence No Redouble: ± 0.021 (-0.306...-0.264)
Confidence Redouble: ± 0.025 (-0.245...-0.195)

Double Decision confidence: 100.0%
Take Decision confidence: 100.0%

Duration: 5 minutes 39 seconds






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