Hit or cover?

[Timothy Chow]

XGID=aAABBBBaA----A-b-bcb-Cbb--:1:-1:1:63:0:0:0:0:10

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 X O O | +---+
| O O O | | O X O O | | 2 |
| O | | X | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | |
| | | X X X X |
| X O | | X X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 122 X-O: 0-0
Cube: 2, O own cube
X to play 63

---
Tim Chow

[badgolferman]

I will hit. There are three points open for me to reenter.

13/7*, 8/5

[Timothy Chow]

It's often better to cover a home-board blot than to hit another
checker. Here, 8/2 gives O 25 dancing rolls instead of 16. But
X also has to consider his back checkers, which are somewhat hemmed
in by O's broken prime. For X, getting hit back is less of a disaster
than being forced to crunch his board. Hitting with 13/7* is not
just an attacking play; it's a priming play, sending O's outfield
checker behind X's prime in case the game evolves into a priming
battle.

In the variant, I have shuffled X's back checkers around a bit to
get a position where XG favors 8/2 over 13/7*.

1. Rollout¹ 13/7* 7/4 eq:+0.225
Player: 59.95% (G:31.21% B:0.69%)
Opponent: 40.05% (G:13.48% B:0.62%)
Confidence: ±0.011 (+0.214..+0.236) - [99.7%]

2. Rollout¹ 13/7* 8/5 eq:+0.203 (-0.022)
Player: 59.16% (G:31.50% B:0.65%)
Opponent: 40.84% (G:13.83% B:0.63%)
Confidence: ±0.011 (+0.192..+0.215) - [0.3%]

3. Rollout¹ 13/10 8/2 eq:+0.141 (-0.085)
Player: 56.57% (G:29.95% B:0.53%)
Opponent: 43.43% (G:10.57% B:0.41%)
Confidence: ±0.010 (+0.131..+0.151) - [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
-------

XGID=aAABBBBaA----A-b-bcbB-bbA-:1:-1:1:63:0:0:0:0:10

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 X O O X | +---+

| O O O | | O X O O | | 2 |

| O | | | +---+

| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | |
| | | X X X X |
| X O | | X X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pip count X: 124 O: 122 X-O: 0-0

Cube: 2, O own cube
X to play 63

1. Rollout¹ 24/21 8/2 eq:+0.571
Player: 68.60% (G:41.09% B:0.73%)
Opponent: 31.40% (G:8.98% B:0.44%)
Confidence: ±0.008 (+0.563..+0.580) - [100.0%]

2. Rollout¹ 24/21 13/7* eq:+0.508 (-0.063)
Player: 68.06% (G:38.50% B:0.71%)
Opponent: 31.94% (G:12.75% B:0.97%)
Confidence: ±0.010 (+0.498..+0.518) - [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

[badgolferman]

Timothy Chow wrote:

> 1. Rollout¹ 13/7* 7/4 eq:+0.225
> Player: 59.95% (G:31.21% B:0.69%)
> Opponent: 40.05% (G:13.48% B:0.62%)
> Confidence: ±0.011 (+0.214..+0.236) - [99.7%]
>
> 2. Rollout¹ 13/7* 8/5 eq:+0.203 (-0.022)
> Player: 59.16% (G:31.50% B:0.65%)
> Opponent: 40.84% (G:13.83% B:0.63%)
> Confidence: ±0.011 (+0.192..+0.215) - [0.3%]

Please give me a compelling reason why 7/4 is preferred over 8/5.

[peps...@gmail.com]

But it's only 0.022 better so you wouldn't expect a compelling reason to exist.
When two plays look to be "about as good as each other", they don't usually differ in equity by less than 0.022.

Paul

[J R]

It allows your 6s and 5s to play better.

Stick