Black – Pips 132 (-25)
(a) Black on roll. Cube action?
Black – Pips 132 (-26)
(b) Black on roll. Cube action?
The argument for doubling is clear enough. White has practically no chance of playing a successful back game. His front position is on the verge of crashing, and if Black rolls a 3, White is just about sunk. Even if Black dances, White will collapse quickly unless he rolls a 5 or 6-1 in the next couple of turns.
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 threes and fours, and his board falls apart. 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, fives, and sixes 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 an excellent general rule. At first glance, White’s chances of going forward seem reasonable, especially considering how his numbers play on the next turn. His sixes (except for 6-1 and 6-5) don’t play, fives escape, threes cover, and aces and deuces move in back; only fours are immediately useless. The fact that Black doesn’t have a real 5-point prime, but instead 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.)
These are plausible arguments, but the position still isn’t a take. 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 with few winning chances to balance out. Rollouts show that White can win the game a bit less than 30% of the time, but he loses too many gammons to make a take worthwhile.
Interestingly, only a tiny change in White’s position is sufficient to take. In (B), Black again has a double, but now 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.
