Anyone who solves this problem correctly will get a sandwich!

[peps...@gmail.com]

My title is almost certainly correct.
It seems extremely unlikely that someone will solve this problem and
then never eat a sandwich during the entire rest of their life.
I never suggested any causality.
On the other hand, there are wheat allergies...
I think the accuracy of my title is acceptable at p = 0.05 or so, which
is fine by rgb standards.

I find this an interesting checkerplay problem, which is deeper than I first
thought. Not that much equity at stake, but the choice isn't ultra-marginal
either.

Paul

XGID=--CB-a--------A-------cbc-:1:-1:1:21:0:1:3:0:10
X:Daniel O:eXtremeGammon

Score is X:0 O:1. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X |
| | | O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 26 O: 36 X-O: 0-1
Cube: 2, O own cube
X to play 21

[Axel Reichert]

"peps...@gmail.com" <peps...@gmail.com> writes:

> XGID=--CB-a--------A-------cbc-:1:-1:1:21:0:1:3:0:10
> X:Daniel O:eXtremeGammon
>
> Score is X:0 O:1. Unlimited Game, Jacoby Beaver
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X | | O O O | +---+
> | | | O O O | | 2 |
> | | | O O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X |
> | | | X X |
> | | | O X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 26 O: 36 X-O: 0-1
> Cube: 2, O own cube
> X to play 21

We are ahead in the race, so want to jump over the last opposing checker
as soon as possible. 14/11 gives a direct shot and thus is way too
risky. The partial moves 14/12 and 14/13 both give 6 indirect shots, but
14/12 is closer to safety. With it goes 2/1 which unstacks and fills a
gap (whereas 3/2 would stack and not fill a gap). 14/13 mandates 3/1,
which fills a gap, but does not unstack the heavy 2 point. Staying back
on point 14 is a two-edged sword with respect to getting/leaving
shots. No gammons are possible and we do not need to hit.

14/12 2/1

Axel

[ah...Clem]

On 9/18/2022 3:28 AM, peps...@gmail.com wrote:

> Score is X:0 O:1. Unlimited Game, Jacoby Beaver
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X | | O O O | +---+
> | | | O O O | | 2 |
> | | | O O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X |
> | | | X X |
> | | | O X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 26 O: 36 X-O: 0-1
> Cube: 2, O own cube
> X to play 21
>
>

X is far enough ahead in the race that avoiding being hit is priority
one. Staying on the fourteen exposes 5 shots, moving up to the 12 or 13
exposes 6 shots, and moving to the 11 exposes 17 shots.

But, the closer we get to our homeboard, the more rolls we have to run
past her straggler.

I'll risk the extra shot to have a better chance of breaking contact.
Then 2/1 seems like the obvius follow on. I probably won't want to hit
next roll even if I can, so no worries about leaving a blot in the
homeboard.

[peps...@gmail.com]

I wrongly made my acepoint.
1. Rollout¹ 3/1 2/1 eq:+0.583
Player: 81.96% (G:0.00% B:0.00%)
Opponent: 18.04% (G:0.00% B:0.00%)
Confidence: ±0.003 (+0.580..+0.585) - [100.0%]
Duration: 4.1 seconds

2. XG Roller+ 14/12 2/1 eq:+0.640 (+0.058)
Player: 84.44% (G:0.00% B:0.00%)
Opponent: 15.56% (G:0.00% B:0.00%)

3. 4-ply 14/12 3/2 eq:+0.579 (-0.004)
Player: 81.70% (G:0.00% B:0.00%)
Opponent: 18.30% (G:0.00% B:0.00%)

4. 4-ply 14/13 3/1 eq:+0.576 (-0.007)
Player: 81.64% (G:0.00% B:0.00%)
Opponent: 18.36% (G:0.00% B:0.00%)

5. 3-ply 3/2 3/1 eq:+0.544 (-0.039)
Player: 80.48% (G:0.00% B:0.00%)
Opponent: 19.52% (G:0.00% B:0.00%)


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


eXtreme Gammon Version: 2.10