Classic Backgammon Dilemma

This is a money game position. The classic backgammon dilemma – to hit or not to hit? The two moves that need to be considered are (a) 20/15*/13 and (b) 13/8, 13/11.

This is a money game position. The classic backgammon dilemma – to hit or not to hit? The two moves that need to be considered are (a) 20/15*/13 and (b) 13/8, 13/11.

How we do go about analysing these two possibilities and then how do we make a decision?

First things first. Let’s look at the strengths and weaknesses of the two players and then decide how black is going to win this game? Here are the key points of the position:

• After the roll black will either be 8 pips behind, after play (b), or 7 pips ahead, after play (a). In a race of this length these are not big differences. The hit will improve black’s winning chances but not by a huge amount.

•  
• In terms of board strength white has the better home board  (4 points made to 2). White also has the better checker distribution. Black still has 5 checkers on his 6-pt which is a very inefficient use of his forces. After (b) he will have, in addition, 4 checkers on his 8-pt.
• Black already owns the doubling cube. This is a powerful asset but it also means that gammons are active - remember this is a money game.
• Before the roll the position was not particularly volatile. Mutual holding games, which is what this is, are quite often resolved when one side or the other rolls a big double.

Black’s only real winning plan is to win the race. Given the distribution of his checkers he is unlikely to be able to prime any of white’s checkers. So now the question is should he sit quietly with (b) and bide his time, or make a run for it and take the lead in the race with (a)If he plays (b) he will be a slight underdog but holding the cube chances will be nearly even. If he plays (a) he will take the lead in the race so from that perspective he will be better off but there is one potential downside to the play that we haven’t yet considered and that is without an anchor he will at risk of losing a gammon if one (or more) of his checkers gets hit.

After (a) White will return hits with 11 rolls (42, 24, 52, 25, 21, 12, 56, 65, 11, 44, 22). Were black then to fan (a), a 44% chance, then he will be in severe gammon danger.

The upshot of this is that black will gain a slight edge after (a) when thing go well, but when thing go badly he could find himself on the wrong end a gammon. There is an old saying in backgammon that you should never take a knife to a gunfight and that is the case here.

Blacks’ plan should be quite simply:

• Play safely
• Build a stronger home board.
• Hope for a big double to make a run for it

One of the key points is that holding the cube he doesn’t have to take huge risks – he can wait for a better time to break his anchor, for example when he has a stronger home board.
 

The rollouts support this approach – look how many gammons black loses with the risky play. Play (a) wins slightly more games but that doesn’t compensate for all the extra gammon losses.
 
Chris Bray
02/2007