Hit and then...?

[Timothy Chow]

XGID=--ABBDBB--b-a-----Bbbbbbb-:0:0:1:61:0:0:0:0:10

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-+
| X | | O O O O O O |
| X | | O O O O O O |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| O X | | X X X X |
| O O X | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 98 O: 85 X-O: 0-0
Cube: 1
X to play 61

---
Tim Chow

[badgolferman]

I feel like your quiz title is trying to lead us into the wrong answer.
Perhaps the bot won't hit but I will. 18/12* 5/4. It seems my only
chance is to hope O enters and stays on the 1-point thus running out of
plays before crunching his board.

[peps...@gmail.com]

Tim can be a bit tricky with his titles but not this time.
We were extremely lucky to get a hitting number and we absolutely must hit.
But the decision of how to play the ace does really matter (hence the quiz).
This time, Tim really did mean what he said.
The natural way to play these positions is 2/1 so that, even if we get hit, the
opponent is rather trapped.
18/12* 2/1 for me.

Paul

[Timothy Chow]

The cube location makes a big difference here. With cube access,
X is looking to cash next turn. 5/4 is a higher-variance play;
it makes the good sequences better and the bad sequences worse,
and in particular if O rolls a 2 then she will be too good. X just
needs his good sequences to be good enough to cash, and 2/1
accomplishes that, while avoiding giving O rolls that leave her
too good.

With the cube turned (or at DMP), the more aggressive 5/4 is XG's
preference.

Note also that if the Jacoby rule were in force, then X wouldn't
have to worry about O being too good, and XG favors the somewhat
unusual-looking 18/12*/11. I haven't tried to figure out why XG
prefers this over 18/12* 5/4.

1. Rollout¹ 18/12* 2/1 eq:+0.260
Player: 60.28% (G:12.29% B:0.13%)
Opponent: 39.72% (G:19.99% B:0.89%)
Confidence: ±0.003 (+0.257..+0.263) - [100.0%]

2. Rollout¹ 18/12* 5/4 eq:+0.178 (-0.082)
Player: 62.47% (G:16.78% B:0.41%)
Opponent: 37.53% (G:25.37% B:1.29%)
Confidence: ±0.005 (+0.172..+0.183) - [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

--------------------
With the cube turned
--------------------

XGID=--ABBDBB--b-a-----Bbbbbbb-:1:-1:1:61:0:0:0:0:10

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-+

| X | | O O O O O O | +---+
| X | | O O O O O O | | 2 |
| | | | +---+

| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| O X | | X X X X |
| O O X | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 98 O: 85 X-O: 0-0

Cube: 2, O own cube
X to play 61

1. Rollout¹ 18/12* 5/4 eq:+0.130
Player: 63.28% (G:16.16% B:0.37%)
Opponent: 36.72% (G:25.20% B:1.30%)
Confidence: ±0.006 (+0.125..+0.136) - [100.0%]

2. Rollout¹ 18/17 18/12* eq:+0.032 (-0.098)
Player: 60.22% (G:14.74% B:0.37%)
Opponent: 39.78% (G:26.65% B:1.35%)
Confidence: ±0.006 (+0.027..+0.038) - [0.0%]

3. Rollout¹ 18/12* 12/11 eq:+0.012 (-0.119)
Player: 59.39% (G:14.31% B:0.33%)
Opponent: 40.61% (G:26.58% B:1.29%)
Confidence: ±0.006 (+0.006..+0.018) - [0.0%]

4. Rollout¹ 18/12* 2/1 eq:+0.009 (-0.121)
Player: 60.71% (G:11.50% B:0.12%)
Opponent: 39.29% (G:20.13% B:0.88%)
Confidence: ±0.005 (+0.004..+0.014) - [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

------
Jacoby
------

XGID=--ABBDBB--b-a-----Bbbbbbb-:0:0:1:16:0:0:1:0:10

X:Player 1 O:Player 2

Score is X:0 O:0. Unlimited Game, Jacoby

+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O O O O O O |
| X | | O O O O O O |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| O X | | X X X X |
| O O X | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 98 O: 85 X-O: 0-0
Cube: 1

X to play 16

1. Rollout¹ 18/12* 12/11 eq:+0.373
Player: 58.28% (G:14.99% B:0.34%)
Opponent: 41.72% (G:27.02% B:1.19%)
Confidence: ±0.005 (+0.367..+0.378) - [100.0%]

2. Rollout¹ 18/12* 5/4 eq:+0.333 (-0.039)
Player: 62.79% (G:15.02% B:0.32%)
Opponent: 37.21% (G:24.15% B:1.09%)
Confidence: ±0.000 (+0.333..+0.333) - [0.0%]

3. Rollout¹ 18/17 18/12* eq:+0.333 (-0.039)
Player: 59.16% (G:14.07% B:0.36%)
Opponent: 40.84% (G:26.12% B:1.09%)
Confidence: ±0.000 (+0.333..+0.333) - [0.0%]

4. Rollout¹ 18/12* 2/1 eq:+0.287 (-0.085)
Player: 59.85% (G:11.77% B:0.14%)
Opponent: 40.15% (G:19.68% B:0.77%)
Confidence: ±0.002 (+0.285..+0.289) - [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