Pay now or pay later #4352 in a series

[ah....Clem]

XGID=--AB-bD-D---cB---Bbcbba---:0:0:1:64:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X O | | O O O O |
| X X O | | O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| X | | X |
| O X | | X |
| O X | | X O X |
| O X | | X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 124 O: 132 X-O: 0-0
Cube: 1
X to play 64



--
Ah....Clem
The future is fun, the future is fair.

[Timothy Chow]

On 7/26/2023 7:37 PM, ah....Clem wrote:
> XGID=--AB-bD-D---cB---Bbcbba---:0:0:1:64:0:0:3:0:10
>
> X:Player 1   O:Player 2
> Score is X:0 O:0. Unlimited Game, Jacoby Beaver
>  +13-14-15-16-17-18------19-20-21-22-23-24-+
>  | X           X  O |   | O  O  O  O       |
>  | X           X  O |   | O  O  O          |
>  |                  |   | O                |
>  |                  |   |                  |
>  |                  |   |                  |
>  |                  |BAR|                  |
>  |                  |   |                  |
>  |             X    |   | X                |
>  | O           X    |   | X                |
>  | O           X    |   | X  O     X       |
>  | O           X    |   | X  O     X  X    |
>  +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count  X: 124  O: 132 X-O: 0-0
> Cube: 1
> X to play 64

The pay-later move is 8/4 8/2 (or possibly 8/2 6/2 but that stack
on the 2pt looks ugly). The argument for paying now is that the
pay-later move totally strips our outfield points, and O's board
rates to get stronger next turn. On the other hand, paying now
with 17/13 17/11 gives O 17 shots, and if we get into a blot-hitting
contest then our weak board means we might get a second checker
sent back. We could also pay now with 17/13 8/2 which I think is
better---we cover our home-board blot and give O 16 shots. Not sure
but I'll go for 17/13 8/2.

---
Tim Chow

[ah....Clem]

On 7/26/2023 7:37 PM, ah....Clem wrote:

This came up in the online match, with the vote overwhelmingly tilted
towards paying now by clearing the 17 point. Only NeilKaz and I opted
to pay later, and as Tim observes, stacking the deuce point is clearly
inferior to slotting the four point.


After a 10368 trial rollout those two plays are within .002 of each other.

I didn't consider the hybrid play of 17/13 8/2, and there are good
arguments to be made for it, but XGR++ doesn't like it very much.

XGID=--AB-bD-D---cB---Bbcbba---:0:0:1:64:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X O | | O O O O |
| X X O | | O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| X | | X |
| O X | | X |
| O X | | X O X |
| O X | | X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 124 O: 132 X-O: 0-0
Cube: 1
X to play 64

1. Rollout¹ 17/13 17/11 eq:+0.015
Player: 50.75% (G:4.78% B:0.20%)
Opponent: 49.25% (G:10.80% B:0.23%)
Confidence: ±0.004 (+0.012..+0.019) - [73.8%]
Duration: 1 hour 06 minutes

2. Rollout¹ 8/4 8/2 eq:+0.014 (-0.002)
Player: 50.82% (G:5.91% B:0.17%)
Opponent: 49.18% (G:10.71% B:0.28%)
Confidence: ±0.004 (+0.010..+0.018) - [26.2%]
Duration: 58 minutes 06 seconds

3. XG Roller++ 8/2 6/2 eq:-0.055 (-0.070)
Player: 49.33% (G:4.81% B:0.10%)
Opponent: 50.67% (G:11.23% B:0.22%)

4. XG Roller++ 17/13 8/2 eq:-0.131 (-0.147)
Player: 46.94% (G:4.31% B:0.11%)
Opponent: 53.06% (G:11.91% B:0.23%)

5. 2-ply 13/3 eq:-0.277 (-0.292)
Player: 43.09% (G:5.39% B:0.11%)
Opponent: 56.91% (G:14.51% B:0.41%)


¹ 10368 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller


eXtreme Gammon Version: 2.10

[Timothy Chow]

On 7/28/2023 10:24 AM, ah....Clem wrote:
> I didn't consider the hybrid play of 17/13 8/2, and there are good
> arguments to be made for it, but XGR++ doesn't like it very much.

In retrospect, I should have realized that this play can't be better
than 17/13 17/11. 17/11 forces O to give up her anchor to hit. This
is a lot more important than covering our blot on our 2pt.

---
Tim Chow

[Stick Rice]

I would have argued strongly for paying later too.

Stick

[Stick Rice]

I feel like it's more about getting our guy to safety when missed than where the opponent hits from that makes coming around the corner so right. We get to safety when missed 35/36 times with the best play. With your hybrid there are 13! rolls that don't get it to safety (quick count) and some other numbers that just play ugly and worse.

Stick