Confession

by Gerry Tanseyttansey

I committed an act of thievery while playing backgammon in Peoria the other day.  I feel no remorse about it.  It was a crime of opportunity, and if I find myself in a similar situation in the future, I will surely steal again.  Even if you catch me red-handed, the dice gods may simply reward my wrongdoing.

It all started while I was trailing 3-2 in a 7-point match.  My opponent had to play a 61 in the following position as Black:

thief 1

Black cannot avoid leaving a direct shot with this roll.  The play 8/1 leaves White only 11 hitting numbers, but it has absolutely no positional upside.  Black is almost out of time, and even if she gets away with playing 8/1 for one roll, the stripped 13 and 15 points will likely disintegrate soon in a very unpleasant way.

My opponent played 15/8, giving White 16 hitting numbers (any 3, plus 21, 62 and 44).  If Black is not hit, she will have a decent chance to move the blot out of harm’s way.  Black will then have a few turns in which she will not be forced to leave a shot.  During this time, White will probably be forced to clear the midpoint, and Black could seal the game on her own with a set of clearing doubles.

However, even though 15/8 is a much better play than 8/1, it is still a blunder.  The best play, by far, is to leave two blots with 15/14 15/9.

thief 1

1. Rollout1 15/14 15/9 eq: -0.053
Player:
Opponent:
46.96% (G:3.27% B:0.11%)
53.04% (G:14.59% B:0.51%)
2. Rollout1 15/8 eq: -0.154 (-0.102)
Player:
Opponent:
41.62% (G:3.22% B:0.10%)
58.38% (G:11.07% B:0.34%)
3. Rollout1 8/1 eq: -0.526 (-0.473)
Player:
Opponent:
38.77% (G:4.67% B:0.22%)
61.23% (G:19.39% B:0.77%)

This play duplicates White’s hitting 2s, and the only additional hitting number is 43 (61 does not hit).  Thus, Black gains a lot of flexibility while leaving only 13 shots.  I think that players who see this play will make it.  The trouble is, a lot of us are overcome by “two-blot terror” and fail to even consider such a move.

And now we come to my crime.  My opponent showed clear (and understandable) signs of worry about leaving that blot on her 15-point.  A hit is usually a winner for me in this position.  So I started counting shots.  Out loud.  Slowly.  Then I doubled confidently, but without any excessive fanfare.

Thief2

There are two important things I did not do.  First, I did not count the race.  I knew just by looking at the position that I was behind in the pip count by a wide margin, and I did not want to draw attention to this fact.  Second, I let my opponent tell her own story about the position.  Some players will try to oversell a pass here by describing the parade of horribles that will befall their opponent after a hit in excruciating detail.  Backgammon players tend to be intelligent, creative people, and my opponent was no exception.  I let my opponent imagine her lonely checker trapped behind a prime, the additional blots being exposed and swept up, the demoralizing closeout, the inevitable gammon loss, the Crawford game, and the post-match handshake.  And after my opponent realized she could avoid all of this by simply setting up the checkers for the next game, she passed.

Thief2

Analyzed in Rollout No double Double/Take
 Player Winning Chances: 58.33% (G:11.06% B:0.35%) 58.82% (G:11.14% B:0.37%)
 Opponent Winning Chances: 41.67% (G:3.26% B:0.08%) 41.18% (G:3.41% B:0.08%)
 Cubeless Equities +0.235 +0.469
Cubeful Equities
No double: +0.152 (-0.011) ±0.004 (+0.148..+0.157)
Double/Take: +0.163 ±0.008 (+0.155..+0.171)
Double/Pass: +1.000 (+0.837)
Best Cube action: Double / Take

But Black’s fears could have been cured with a dose of cold mathematical reality.  Sure, White hits with 16 numbers, but on the 20 misses, Black is favored to win the game.  White is not even guaranteed to win after a hit, and a lot has to happen before White can lay claim to a gammon.  After a 5184-trial rollout, XG finally decided that White does have a proper, razor-thin double in this position.  In practice, I wouldn’t normally think of cubing this position unless I thought the double had some bluff value against my opponent.  Passing here is among the largest errors you will see in backgammon outside of flagrant oversights.  But rather than dwell on my opponent’s error, I prefer to believe I stole that point, fair and square.

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