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Mastering Backgammon (40)
2007-08-30
Bill Robertie
Bill Robertie
40. An Unusual Backgame
This position arose during a recent chouette. Black, in the box, doubled. After a lot of thought, all the team members took. Black fanned, and White's next two rolls were 3-2 and 5-5, winning easily. Was Back's double correct? How about White's take?
Position 1: Money game. Black on roll. Should he double? Should White take?
The argument for doubling is clear enough. White has very little chance of playing a successful back game. His front position is on the verge of crashing. If Black rolls a 3, White is just about sunk. Even if Black dances, White will collapse quickly unless he rolls a 5 or a 6-1 in
The taking question is much more difficult. From White's point of view, the game can go in one of four directions:
1. A collapsed back game. White rolls lots of 3s and 4s, and his board collapses. Black sweeps around the board. White hopes to hit a late shot to save the gammon.
2. A successful back game. Black enters quickly, hitting a blot or two. White dances, or else reenters and escapes. He preserves his timing until Black starts the bearoff.
3. A low anchor game. White releases some, but not all, of his back checkers. The checkers that remain (probably on the 3-point), form a well-timed low anchor game.
4. A forward game. Black doesn't enter quickly and White throws some aces, 5s, and 6s to escape some of his back men while preserving a strong board.
Variations (2) and (4) are good for White. The others are very bad. But how often do variations (2) and (4) arise?
In the actual game, the White players decided to take, an understandable decision. "When in doubt, take" is a very good general rule. At first glance, White's chances of going forward seem reasonably good, especially considering how his numbers play on the next turn. His 6s (except for 6-1 and 6-5) don't play, 5s escape, 3s cover, aces and deuces move in back. Only 4s are immediately useless. The fact that Black doesn't have a real 5-point prime, but a prime with a gap, is also a factor, facilitating White's escape. White can leap from either the 22-point or the 23-point, so Black's apparent strength might be a bit of an illusion.
Plausible arguments, but is it in fact a take? The answer is a solid "No". White has just a little too much difficulty getting his back men out quickly, and when his board collapses, he's in great danger of losing a gammon. Rollouts show that White can win the game a little less than 30% of the time, but he loses too many gammons to make a take worthwhile.
Interestingly, only a small change in White's position will give him a takeable game. Look at the next diagram:
Position 2: Money game. Black on roll. Should he double? Should White take?
Now Black again has a double, but White has a clear take. The addition of 6-2 and 6-4 as good numbers and 6-3 as a great number is enough to tip the balance from a pass to a take.
Another question that arises from this position is the following: Suppose Black doubles, White takes, and things then start to swing White's way. At what point does White have a redouble?
Let's start by considering Position 3:
Position 3: Money game. White on roll. Should he double? Should Black take?
Position 3 comes from Position 1 after Black doubles, White takes, Black fans, White rolls 3-1, Black fans again, White rolls 5-4 and runs, and Black fans a third time. Needless to say, it's a very good sequence for White. However, he still doesn't have a double, and Black has a very easy take. White has, however, become a favorite in the game. (About a 58-42 favorite, actually.)
Position 4: Money game. White on roll. Should he double? Should Black take?
Position 4 comes from the previous diagram after White rolls 6-4, running to the midpoint, and Black fans yet again. Now White finally has a double, and Black has an easy take. White's winning chances are now about 62%, but his gammon chances are pretty high – over 30%.
If White had rolled a 5-4 rather than a 6-4, so his back checkers were on both the 23-point and 22-point, his game would be much stronger, and the verdict would be double and pass.
