This is a game at 2-away, 2-away. From now on I will call the player who won the opening roll Player A and the other one Player B.
1) 31: 8/5 6/5
33: 24/18(2)
2) 66: 24/18(2) 8/2(2)
55: 13/3(2)
3) 44: 18/14(2) 13/9(2)
55: 18/8(2)
4) 55: 13/8(2) 13/3
66: 13/7(3) 8/2
5) 66: 14/8 14/2 9/3
66: 8/2(2) 7/1(2)
6) 66: 9/3 8/2(3)
66: 8/2(2) 7/1 6/Off
7) 66: 6/Off(4)
66: 6/Off(4)
8) 66: 5/Off(2) 3/Off(2)
33: 3/Off(2) 2/Off(2)
9) 55: 3/Off 2/Off(3)
66: 2/Off(3) 1/Off
10) 22: 2/Off(3)
Wins a Single Game 1pt.
Neither player touches the cube the whole game. XG gives Player B a 0.00PR and Player A a 0.56PR for one 0.11 failure to cube error.
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| XGID=--B--BD--B--cCB--e-e--b---:0:0:1:00:0:0:0:2:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 43.43% (G:0.08% B:0.00%) | 43.49% (G:0.06% B:0.00%) |
| Opponent Winning Chances: | 56.57% (G:0.11% B:0.01%) | 56.51% (G:0.11% B:0.01%) |
| Cubeless Equities | -0.132 | -0.367 |
| Cubeful Equities | ||
| No double: | -0.378 (-0.011) | ±0.007 (-0.385..-0.372) |
| Double/Take: | -0.367 | ±0.007 (-0.373..-0.360) |
| Double/Pass: | +1.000 (+1.367) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 99.1% | |
| Take Decision confidence: | 100.0% | |
| Duration: 5 minutes 34 seconds | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Player A is 43% to win the game, but has market losers. If Player A rolls a 21, Player B does not lose his market, so this is a small technical double. All other cube decisions in this game are either "No double" or "Optional double".
2-away, 2-away doubling theory is based on the fact that at some point in a game with that score, one player or the other will always have a correct double that is a take. Since the cube should always end up at 2 anyway, it is not a mistake to double even if you have no market losers. This game is interesting to me because it dances on the edge of disproving that "one player or the other will always have a correct double that is a take" without actually getting there.
I do wish that I could make this post more clear. I will email the XG file of this game to anyone who wants it. If you want a post that will actually help you win backgammon matches, this is not the post for you.