You may or may not have found this specific problem easy, but certainly this class of problems—breaking anchor to hit when your opponent has no checkers back and you have one or more blots in your board—is a very difficult one to master, and I'm surprised that I haven't seen more examples of it discussed in books and articles. The difference in wins and gammons between the candidate plays can be enormous, making the tradeoff difficult to evaluate even for money, let alone at some funny match score. Many variations can arise that are not easily captured in a simple rule or a small set of reference positions. The best I can do at the moment is to collect several examples and offer a few observations.
In the position at hand, since Blue is somewhat ahead in the race, the safe play of advancing the anchor is definitely worth considering. The pseudocubeless numbers suggest, however, that hitting not only wins somewhat more games, but wins a lot more gammons.
| | White is Player 2
score: 0 pip: 133 | Unlimited Game | pip: 134 score: 0
Blue is Player 1 | |
XGID=-B-AB-C-BabacB---b-bBA-bb-:0:0:1:65:0:0:0:0:10 |
Blue to play 65 |
1. | Rollout1 | 20/9* | eq: +0.385 |
| Player: Opponent: | 58.09% (G:29.79% B:0.79%) 41.91% (G:14.01% B:0.76%) | Conf.: ± 0.013 (+0.372...+0.398) - [100.0%] Duration: 12 minutes 45 seconds |
|
2. | Rollout1 | 21/15 20/15 | eq: +0.262 (-0.123) |
| Player: Opponent: | 56.96% (G:15.56% B:0.36%) 43.04% (G:8.96% B:0.26%) | Conf.: ± 0.015 (+0.247...+0.276) - [0.0%] Duration: 15 minutes 33 seconds |
|
|
1 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10
Here's another example with a similar flavor that arose in a different game of mine. The race is even and both sides have a three-point board, with Blue having a blot in his board. This time, though, Blue's alternative isn't as appealing, and the pseudocubeless numbers indicate that the advantage of hitting comes from the extra games won, not the gammons.
| | White is Player 2
score: 0 pip: 113 | Unlimited Game | pip: 117 score: 0
Blue is Player 1 | |
XGID=-B-CA-B-C-b-bB--ab-cBc--b-:0:0:1:54:0:0:0:0:10 |
Blue to play 54 |
1. | Rollout1 | 20/16* 16/11 | eq: -0.089 |
| Player: Opponent: | 47.50% (G:18.15% B:0.55%) 52.50% (G:21.30% B:0.80%) | Conf.: ± 0.012 (-0.101...-0.076) - [100.0%] Duration: 10 minutes 35 seconds |
|
2. | Rollout1 | 13/9 13/8 | eq: -0.236 (-0.147) |
| Player: Opponent: | 43.83% (G:3.94% B:0.09%) 56.17% (G:4.23% B:0.28%) | Conf.: ± 0.009 (-0.245...-0.228) - [0.0%] Duration: 9 minutes 29 seconds |
|
|
1 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10
As I mentioned over on rec.games.backgammon when this topic came up recently, a more dramatic example of this type of decision was posted here on BGO Mislav Kovacic a few years ago. I'm reproducing the position below for convenience; click here for the rollout.
Here's another one from one of my old "Checkerplay Challenges" where Blue is far behind in the race; click here for the rollout (see Problem 3).
Lest you think that it's always right to hit in such situations, in the aforementioned discussion on rec.games.backgammon, smcrtorchs posted an interesting example from Mochy–Phipps (San Antonio 2014) where the computer dings Mochy's choice to hit. (Though strictly speaking this position doesn't quite fit the description I gave above because White has an anchor; that does make a difference.)