“To see what is in front of one’s nose needs a constant struggle.” – George Orwell

by Gerry Tansey

(Quick note-I’ve made the positions as large as I can, but if you would like to see it a bit bigger, click on the picture and it will open in a separate window.)

I have a feeling that a lot of my posts are going to arise because someone screwed up while playing backgammon.  Alas, the “someone” in question will usually be me.  Here is a position that arose during an online match the other night.  I was White, and while I was leading the match to 7 by the score of 5 to 1, I was white-knuckling it in this position while holding a 2-cube.  I had to play a 65.

65-1

You can skip this next paragraph if you are not interested in a little mathematical discussion.  The score matters here, but not as much as many may think.  Of course, I can’t use the cube or win a gammon.  But shouldn’t I be super-cautious to avoid losing a gammon?  Well, not really.  Losing a single game gives me roughly a 67% chance to win the match, while losing a gammon puts me at 50%, a difference of 17% match-winning chances.  But if I win the game, I win the match, so the difference in match equity between winning the game and losing a single game is 100% – 67%, or 33%.  Thus the gammon price, in this case the ratio 17/33, is almost exactly the value of 0.5 that it is for money.  In more plain English, I should be willing to make a play that trades 5% more wins for 10% extra gammon losses, just like in a money game.

Now, how do I play this 65?  Well, first I have to decide what to do with the 6.  We’ve all heard the expression “Sixes don’t grow on trees.”  (If you haven’t, you have now).  And indeed, it is often right to take some risks to get one’s checkers free from a blockade, particularly if the forward position will collapse otherwise.  The trouble is that after the play 24/13, Black has 13 shots, after which he wins many gammons.  This is simply too many, considering that the game is not won even after a miss.

So I covered, playing 11/5, 7/2, leaving just 61 and 62 as hitters from the bar, while hoping to extricate my straggler later.  But I didn’t even consider the best play, and when that happens, I usually make a big blunder.  This occasion is no exception.

The trouble with my play is that have to deal with my 18-point anchor sooner, rather than later.  If I don’t roll a 6 immediately, I will have to break the anchor, potentially in a disastrous fashion.  Even if I do get a quick 6, it is extremely unlikely that Black will stay on the bar long enough for me to break contact and bring all of my checkers around.  I am likely going to have to break that anchor at an inconvenient time.  Also, breaking the 7-point to bury a checker is just generally an awful idea.  I should start the process of disengaging now while Black is on the bar by playing 18/13, 11/5.  Although this play leaves 3 blots, there are only 5 immediate hitting numbers for Black.  If Black misses, I could escape my back checker, make the midpoint, or bring down builders for the 6-point, depending on what I roll.  But mainly I’m breaking the 18-point (which I will have to do eventually anyway) on my own terms, when it is relatively safe to do so.  The plays are not close.  Each play is about .150 better than the next best play.

1.Rollout118/13 11/5	eq: -0.212 	Player: Opponent:	48.25% (G:5.05% B:0.02%) 51.75% (G:15.20% B:0.75%)	Conf.: ± 0.004 (-0.216...-0.209) - [100.0%] Duration: 1 minute 37 seconds 2.	Rollout1	11/5 7/2	eq: -0.361 (-0.149) 	Player: Opponent:	41.55% (G:4.52% B:0.01%) 58.45% (G:16.85% B:0.69%)	Conf.: ± 0.004 (-0.366...-0.357) - [0.0%] Duration: 1 minute 40 seconds 3.	Rollout1	24/13	eq: -0.514 (-0.302) 	Player: Opponent:	41.56% (G:3.82% B:0.01%) 58.44% (G:30.32% B:1.20%)	Conf.: ± 0.004 (-0.518...-0.510) - [0.0%] Duration: 1 minute 49 seconds   1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller eXtreme Gammon Version: 2.10, MET: Kazaross XG2

1. Rollout1 18/13 11/5 eq: -0.212
Player:
Opponent: 48.25% (G:5.05% B:0.02%)
51.75% (G:15.20% B:0.75%) Conf.: ± 0.004 (-0.216…-0.209) – [100.0%]
Duration: 1 minute 37 seconds
2. Rollout1 11/5 7/2 eq: -0.361 (-0.149)
Player:
Opponent: 41.55% (G:4.52% B:0.01%)
58.45% (G:16.85% B:0.69%) Conf.: ± 0.004 (-0.366…-0.357) – [0.0%]
Duration: 1 minute 40 seconds
3. Rollout1 24/13 eq: -0.514 (-0.302)
Player:
Opponent: 41.56% (G:3.82% B:0.01%)
58.44% (G:30.32% B:1.20%) Conf.: ± 0.004 (-0.518…-0.510) – [0.0%]
Duration: 1 minute 49 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.10, MET: Kazaross XG2

I guess I should be glad that I merely played a whopper with cheese rather than a triple whopper.  But I was so concerned about choosing between play A and play B that I didn’t grasp the whole position.  I never even thought about play C, which looks superficially risky, but, as the rollout shows, loses the fewest gammons of all the plays.  It also wins a ton more games.

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