I Told You That Story So I Could Tell You This One

by Gerry Tansey

In my last post, I went through the proper cube actions for a 2-roll position versus a 2-checker position in the bearoff.  I’d like to use a little bit of what we learned to examine a position that could occur one roll earlier.  What is the proper cube action for money in the following position?  What about at 2-2 in a 5-point match?

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In a money game, if White redoubles to 4 and Black takes, White will immediately hate his life upon rolling 21, since he must then pass Black’s redouble to 8.  Unpleasant but takeable recubes also arise when White rolls 31 and 11.  Rolls of 32 and 41 lead to the fun scenario in my last article, usually ending with a 16-cube in play.  But White shouldn’t be too afraid of these rolls, since Black’s redouble is just barely correct in that case.

On the plus side, White wins immediately with three rolls: 44, 55, and 66.  Further, White wins barring Black’s rolling a set on 65, 64, 54, and 33, or seven additional rolls.  We must also consider the five numbers 63, 53, and 22 to be really good numbers for White, as they lose the market by a mile provided Black does not roll doubles.  White is usually pretty happy with 43, 52, and 62 as well.

For the rest of White’s numbers, he is indifferent about whether or not he doubled, provided that Black does not roll a set.  That is because he would be redoubling – and Black would be taking – after these sequences anyway.  For instance, if White holds onto the cube and rolls 42, and Black fails to roll a doublet, then White would redouble and Black would take.  The end result is usually going to be the same in these cases regardless of whether White redoubled before his first roll or not.

A better player than me might be able to calculate all of this precisely over the board.  But what I would glean from this examination of the numbers is that a lot more could go right for White than go wrong, and so I would redouble as White.  Hopefully you can see that Black has a trivial take in this position.  Black wins immediately on 2 of White’s numbers, and practically speaking we can count the 31 and 11 rolls as 3 wins for Black, since he gets to give such a nice recube in these variations.  It is not hard to find 4 more wins for Black out of White’s remaining 28 non-winning rolls to give him the requisite 9 wins out of 36 for a take.  Here is what XG has to say

Analyzed in XG Roller++No redouble	Redouble/Take   Player Winning Chances:	64.66% (G:0.00% B:0.00%)	64.66% (G:0.00% B:0.00%)   Opponent Winning Chances:	35.34% (G:0.00% B:0.00%)	35.34% (G:0.00% B:0.00%)   Cubeless Equities	+0.293	+0.586 Cubeful Equities No redouble:	+0.399 (-0.072)	 Redouble/Take:	+0.470	 Redouble/Pass:	+1.000 (+0.530)   Best Cube action: Redouble / Take eXtreme Gammon Version: 2.10

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 64.66% (G:0.00% B:0.00%) 64.66% (G:0.00% B:0.00%)
Opponent Winning Chances: 35.34% (G:0.00% B:0.00%) 35.34% (G:0.00% B:0.00%)
Cubeless Equities +0.293 +0.586
Cubeful Equities
No redouble: +0.399 (-0.072)
Redouble/Take: +0.470
Redouble/Pass: +1.000 (+0.530)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10

It is indeed a sizable double and a monster take for money.  Now, what if this is a 5-point match and the score is 2-2?  How does this change things?

Well, Black’s take is still trivial, since his take point is 25 percent at the score, and he has over a 35 percent chance to win this game.  However, White should be even more willing to redouble in this scenario than for money.  Remember that White is a favorite in a highly volatile position.  Often times this turn will be White’s last chance to use the cube he owns.  For money, the main deterring factor for White’s recube is Black’s ability to shove it back down White’s throat on a poor roll.  But in this match scenario, White is giving Black a dead cube when he redoubles.  White’s recube is all ice cream and no spinach, and failing to ship the cube would be a massive blunder for White.

Analyzed in 4-plyNo redouble	Redouble/Take   Player Winning Chances:	64.66% (G:0.00% B:0.00%)	64.66% (G:0.00% B:0.00%)   Opponent Winning Chances:	35.34% (G:0.00% B:0.00%)	35.34% (G:0.00% B:0.00%)   Cubeless Equities	+0.293	+0.585 Cubeful Equities No redouble:	+0.398 (-0.186)	 Redouble/Take:	+0.585	 Redouble/Pass:	+1.000 (+0.415)   Best Cube action: Redouble / Take eXtreme Gammon Version: 2.10, MET: Kazaross XG2

Analyzed in 4-ply No redouble Redouble/Take
Player Winning Chances: 64.66% (G:0.00% B:0.00%) 64.66% (G:0.00% B:0.00%)
Opponent Winning Chances: 35.34% (G:0.00% B:0.00%) 35.34% (G:0.00% B:0.00%)
Cubeless Equities +0.293 +0.585
Cubeful Equities
No redouble: +0.398 (-0.186)
Redouble/Take: +0.585
Redouble/Pass: +1.000 (+0.415)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10, MET: Kazaross XG2

The above scenario actually arose in the first match I ever played against one of the Giants of backgammon.  The Giant was White, and he failed to redouble me after a long think.  He was probably relieved when he rolled 31, but after I failed to roll a set, he was able to bear off his checkers.  And then I won the next two games to win the match.  This was the only major mistake the Giant made in our match, but it cost him dearly (Unfortunately, I still played a bit worse than he did).  This position taught me that the Giants are human, and beatable.  If you find yourself playing a Giant, just fight as best as you can.  Sometimes they will give you a gift.

 

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