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Breakeven for hitting

Posted By: Nack Ballard
Date: Wednesday, 27 September 2023, at 8:38 p.m.

In Response To: Position of the day 9-25-23 (Stick)





White is Player 2

score: 0
pip: 119
Unlimited Game
Jacoby Beaver
pip: 185
score: 0

Blue is Player 1
XGID=-----AC-C-bBaB--abcbbbBB--:1:1:1:61:0:0:3:0:10
Trail by 66 pips: Don't Hit

1.XG Roller++11/5 8/7eq: -0.331
Player:
Opponent:
35.75% (G:4.33% B:0.14%)
64.25% (G:22.95% B:1.04%)
2.XG Roller++22/16* 6/5eq: -0.533 (-0.203)
Player:
Opponent:
30.55% (G:5.27% B:0.23%)
69.45% (G:29.14% B:2.02%)

These are only ++ evaluations, but they give a sense of what's going on. In the original position above, Black trails by 66 pips, and the eval prefers not hitting by .203 (roughly the same margin as in Stick's very short rollout).

I'll quote Tim quoting the book Backgammon Masterclass:"...the minimum pip deficit required to take a 2-3 backgame is 48 pips."

FWIW, the positions shown below, where Blue trails by 48, are passes by about .040 according to the eval. I did an (admittedly weak 3-ply) 5k rollout on the first, resulting in a pass by .077. (This does not necessarily contradict the book, which refers to a minimum.)

The take/pass cusp is a different issue than whether one should try to break out of a backgame, given that there are many factors to weigh. But it does happen that 48 is a pretty fair cusp for this situation.

In the first position below, according to ++ eval, Black should not hit (by .022). In the second position below, Black should hit (by .071). Smoothness is a sensitive factor.

Nack





White is Player 2

score: 0
pip: 127
Unlimited Game
Jacoby Beaver
pip: 175
score: 0

Blue is Player 1
XGID=-----ADC-Ac-aB--abbbbbBB--:1:1:1:61:0:0:3:0:10
Trail by 48 pips: Don't Hit, but close

1.XG Roller++9/3 6/5eq: -0.656
Player:
Opponent:
23.69% (G:2.27% B:0.09%)
76.31% (G:24.05% B:0.93%)
2.XG Roller++22/16* 6/5eq: -0.678 (-0.022)
Player:
Opponent:
25.09% (G:4.49% B:0.19%)
74.91% (G:29.96% B:2.00%)





White is Player 2

score: 0
pip: 127
Unlimited Game
Jacoby Beaver
pip: 175
score: 0

Blue is Player 1
XGID=-----ADBB-c-aB--abbbbbBB--:1:1:1:61:0:0:3:0:10
Trail by 48 pips, but smooth: Hit

1.XG Roller++22/16* 6/5eq: -0.588
Player:
Opponent:
27.45% (G:5.48% B:0.24%)
72.55% (G:27.70% B:1.78%)
2.XG Roller++8/2 6/5eq: -0.659 (-0.071)
Player:
Opponent:
23.60% (G:2.25% B:0.08%)
76.40% (G:24.08% B:0.93%)

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