Escape or close the board?

[Timothy Chow]

XGID=aCACBBC-aa-------b-ccbb-A-:1:-1:1:51:0:0:0:0:10

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 X | +---+
| O | | O O O O | | 2 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X X |
| | | 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: 74 O: 121 X-O: 0-0
Cube: 2, O own cube
X to play 51

---
Tim Chow

[peps...@gmail.com]

6/1 2/1 is correct.
The large number of gammons we get when we escape are a huge factor.
On a slow day for combinatorial game theory, I could easily imagine Tim
doing a ton of variantizing by lessening and increasing the gammonability
to change the play.

The escape play might seem correct as a gamble on your opponent not rolling a 2.
But your opponent's 2s will lose some gammons. There's a lot of value in taking away
all of your opponent's gammons by closing out.
After closing out, we win immediately with 51 and any 6 except 61.
This is 11/36. If we don't get such a roll we can hope to escape before the opponent enters.

Am I confident?

Recently, I went to spectate a tennis tournament which officially had no spectators. However,
there was a way of getting in which was to meet a competitor and ask to be on their guest list
to gain entrance as a competitor's guest.
I am as confident in my solution, as I was when asking players to sign me in as their guest.

Paul

[Timothy Chow]

On 8/12/2022 1:34 PM, peps...@gmail.com wrote:
> 6/1 2/1 is correct.
> The large number of gammons we get when we escape are a huge factor.
> On a slow day for combinatorial game theory, I could easily imagine Tim
> doing a ton of variantizing by lessening and increasing the gammonability
> to change the play.
>
> The escape play might seem correct as a gamble on your opponent not rolling a 2.
> But your opponent's 2s will lose some gammons. There's a lot of value in taking away
> all of your opponent's gammons by closing out.
> After closing out, we win immediately with 51 and any 6 except 61.
> This is 11/36. If we don't get such a roll we can hope to escape before the opponent enters.

Since you talk about closing out, I assume you meant to say
"6/1 3/2" and that "6/1 2/1" is a typo?

By the way, I don't know why you frequently mention combinatorial
game theory. I haven't ever published anything in combinatorial
game theory, and I don't even think about it much.

---
Tim Chow

[ah....Clem]

Sixes don't grow on trees and X is in danger of crunching. Escape!!!


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

[peps...@gmail.com]

Yes, I meant the closeout play.
Because backgammon isn't sufficiently interesting or stimulating (to me),
I have to mention stuff outside backgammon so that I don't suffer intensely
from extreme boredom.

I'll try to pick on stuff that I know you have researched, next time.


Paul

[Timothy Chow]

XGID=aCACBBC-aa-------b-ccbb-A-:1:-1:1:51:0:0:0:0:10

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 X | +---+
| O | | O O O O | | 2 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X X |
| | | 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: 74 O: 121 X-O: 0-0
Cube: 2, O own cube

X to play 51

Closing the board is in triple-whopper territory.

1. Rollout¹ 24/18 eq:+0.602
Player: 67.63% (G:42.86% B:0.55%)
Opponent: 32.37% (G:8.29% B:0.35%)
Confidence: ±0.005 (+0.597..+0.607) - [100.0%]

2. Rollout¹ 6/1 3/2 eq:+0.328 (-0.274)
Player: 60.95% (G:31.98% B:0.21%)
Opponent: 39.05% (G:3.06% B:0.08%)
Confidence: ±0.007 (+0.321..+0.335) - [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

[peps...@gmail.com]

Yes, I should have figured that. I like Walt's reasoning, brief though it was.

Paul

[Timothy Chow]

On 8/14/2022 2:41 PM, peps...@gmail.com wrote:
> Yes, I should have figured that. I like Walt's reasoning, brief though it was.

Here's another way to think about it. If we close the board,
what are we hoping for? A 6 or a 51; otherwise we're unhappy.
Chances of a 6 or a 51 are 13/36. If we run, what are we hoping
for? A dance; otherwise we're unhappy. Chances of a dance are
25/36.

We'd rather be in a situation where 25/36 rolls are good than in
a situation where 13/36 rolls are good.

---
Tim Chow