XGID=abbBCBDBB----------bbbbb--:1:-1:1:23:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X X |
| X X | | X X X X O O |
| X X | | X X X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 82 O: 159 X-O: 0-0
Cube: 2, O own cube
X to play 23

---
Tim Chow

XGID=abbBCBDBB----------bbbbb--:1:-1:1:23:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X X |
| X X | | X X X X O O |
| X X | | X X X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 82 O: 159 X-O: 0-0
Cube: 2, O own cube
X to play 23

The chapter on "Backgame Bear-In" in Trice's "Backgammon Boot Camp"
has a remark that has long been a source of confusion for me. Trice
writes, "Against a single anchor, it is usually right to 'clear from
the rear and don't ask questions,' as Kit Woolsey puts in. In
backgames there is a common exception: Clear the tough points when
you can." He then goes on to argue for clearing the next-to-the-last
point because it is opposed by two anchors, so that if you leave a
shot there then your opponent will have a double shot, whereas the
rearmost point is opposed by only one anchor.

The confusing point is that this principle applies more often to
13-backgames and 23-backgames than to 12-backgames. In the
aforementioned chapter, Trice discusses 4 positions, 3 of which
are 12-backgames, and one of which is a 23-backgame. It's the
23-backgame position where Snowie clears the next-to-the-last point.
Against a 12-backgame, clearing from the rear kills your large
numbers, whereas against a 13-backgame (respectively, a 23-backgame)
you have to worry about being forced to play a checker awkwardly to
your 2pt (respectively, your 1pt).

The position above may look like a contrived reference position but it
actually arose OTB for me. I played 7/5 7/4, but see the rollout below
and the two variants.

1. Rollout¹ 8/6 8/5 eq:+0.843
Player: 74.22% (G:40.70% B:6.80%)
Opponent: 25.78% (G:0.51% B:0.02%)
Confidence: ±0.010 (+0.833..+0.853) - [100.0%]

2. Rollout¹ 8/5 6/4 eq:+0.809 (-0.034)
Player: 73.57% (G:39.47% B:6.66%)
Opponent: 26.43% (G:1.13% B:0.04%)
Confidence: ±0.010 (+0.798..+0.819) - [0.0%]

3. Rollout¹ 6/4 6/3 eq:+0.786 (-0.056)
Player: 73.18% (G:38.86% B:6.10%)
Opponent: 26.82% (G:0.94% B:0.04%)
Confidence: ±0.011 (+0.776..+0.797) - [0.0%]

4. Rollout¹ 8/3 eq:+0.784 (-0.058)
Player: 72.96% (G:38.69% B:6.38%)
Opponent: 27.04% (G:1.09% B:0.04%)
Confidence: ±0.011 (+0.774..+0.795) - [0.0%]

5. Rollout¹ 7/5 7/4 eq:+0.735 (-0.108)
Player: 70.17% (G:39.67% B:7.73%)
Opponent: 29.83% (G:0.47% B:0.01%)
Confidence: ±0.013 (+0.722..+0.748) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---------
Variant 1
---------

XGID=abBbCBDBB----------bbbbb--:1:-1:1:23:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X X |
| X X | | X X X O X O |
| X X | | X X X O X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 80 O: 157 X-O: 0-0
Cube: 2, O own cube
X to play 23

1. Rollout¹ 7/5 7/4 eq:+0.469
Player: 62.42% (G:33.94% B:5.36%)
Opponent: 37.58% (G:0.55% B:0.02%)
Confidence: ±0.010 (+0.458..+0.479) - [100.0%]

2. Rollout¹ 8/6 8/5 eq:+0.413 (-0.056)
Player: 61.23% (G:32.20% B:4.62%)
Opponent: 38.77% (G:1.32% B:0.04%)
Confidence: ±0.009 (+0.403..+0.422) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---------
Variant 2
---------

XGID=aBbbCBDBB----------bbbbb--:1:-1:1:23:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X X |
| X X | | X X X O O X |
| X X | | X X X O O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 78 O: 155 X-O: 0-0
Cube: 2, O own cube
X to play 23

1. Rollout¹ 7/5 7/4 eq:+0.377
Player: 60.57% (G:33.55% B:1.90%)
Opponent: 39.43% (G:2.39% B:0.08%)
Confidence: ±0.010 (+0.367..+0.387) - [100.0%]

2. Rollout¹ 8/6 8/5 eq:+0.309 (-0.068)
Player: 58.21% (G:32.58% B:1.66%)
Opponent: 41.79% (G:2.57% B:0.09%)
Confidence: ±0.011 (+0.298..+0.320) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow