The below position looked to me like such an obvious double that I
doubled without even bothering to count.
However, XG's rollout says it's too close to call.
XG's first thought from its analysis is that it is a redouble.

I really should have Axelised with it being this close, so what does
the Axelisation say?
Raw pip counts are 52 to 51.
For me, add 2 for my acepoint stack to get 54.
For XG, add 2 for the acepoint stack and 2 for the twopoint stack.
and 1 for the extra crossover to get 56.
Add 1/6 to 54 and subtract from 56 to get 7 which is a hold.
With the action being ultra-marginal, there is nothing at all wrong
with this result.
I should have Axelised and held, even though this may have been the
wrong decision, and even though I won this game.

Paul

XGID=-CBAEBB------a-----aabcdc-:4:1:1:00:0:3:3:0:10
X:Daniel O:eXtremeGammon


Score is X:0 O:3. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O O |
| | | O O O O |
| | | O O O |
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X X | +---+
| | | X X X X X | | 16|
| | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 52 O: 51 X-O: 0-3
Cube: 16, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 72.29% (G:0.00% B:0.00%)
Opponent Winning Chances: 27.71% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 72.29% (G:0.00% B:0.00%)
Opponent Winning Chances: 27.71% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.446, Double=+0.891

Cubeful Equities:
No redouble: +0.722 (-0.003)
Redouble/Take: +0.725
Redouble/Pass: +1.000 (+0.275)

Best Cube action: Redouble / Take

Rollout:
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.003 (+0.719..+0.725)
Confidence Double: ± 0.004 (+0.721..+0.730)

Double Decision confidence: 84.7%
Take Decision confidence: 100.0%

Duration: 2 minutes 20 seconds

eXtreme Gammon Version: 2.10

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 8/28/2022 4:14 AM, peps...@gmail.com wrote:

However, XG's rollout says it's too close to call.
XG's first thought from its analysis is that it is a redouble.

Depending on what you mean by "too close to call," the longer
rollout below (with stronger settings) may be callable.

I assume that you're distinguishing between "ultra-marginal,"
which I take to mean that the true equities of ND and D/T are
extremely close, and "too close to call," which I take to mean
that there is too much room for error for you to feel
comfortable declaring that D/T is game-theoretically optimal.

There are two sources of error here: (pseudo)random statistical
error, and systematic error from misplays. XG declares that it
is 98% confident about doubling, which is high enough for most
people to feel comfortable "calling." Systematic error is harder
to estimate, but by choosing XGR+/XGR+/Huge settings, I tried to
minimize it. My guess is that the systematic error is negligible.

Note that because this is a non-contact position, we don't have
to worry about whether "game-theoretically optimal" and "misplay"
are well-defined terms.

XGID=-CBAEBB------a-----aabcdc-:4:1:1:00:0:0:3:0:10

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-+
| O | | O O O O O O |
| | | O O O O |
| | | O O O |
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X X | +---+
| | | X X X X X | | 16|
| | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 52 O: 51 X-O: 0-0
Cube: 16, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 72.31% (G:0.00% B:0.00%)
Opponent Winning Chances: 27.69% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 72.29% (G:0.00% B:0.00%)
Opponent Winning Chances: 27.71% (G:0.00% B:0.00%)

Cubeful Equities:
No redouble: +0.721 (-0.002)
Redouble/Take: +0.723
Redouble/Pass: +1.000 (+0.277)

Best Cube action: Redouble / Take

Rollout:
5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Huge
Confidence No Double: ± 0.001 (+0.720..+0.722)
Confidence Double: ± 0.002 (+0.721..+0.725)

Double Decision confidence: 98.1%
Take Decision confidence: 100.0%

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)