I decided to do a strict algorithmic Axelisation in the position below,
rather than using intuition to adjust.
I ended up wrongly passing, but it's not such a bad error and my PR
for this game was superb (approx 2.3 or something if I remember rightly).
The Axelisation (as I see it) adds 2 to my score for my extra crossovers
to get 86. Then 75 + 75/6 = 87.5. 87.5 - 86 < 2.

I wonder whether there's a way to intuitively and correctly take.
One consideration is that the other algos I know 8/9/12 and 10% + 2
correctly take.
But a more relevant point is that my crossovers are being overly penalised.
We can see that they won't bear off that inefficiently.

Does anyone have any thoughts about how to correctly assess this
position?

Thank you,

Paul

XGID=---BBCFA----A------egab---:0:0:-1:00:10:0:3:0:10
X:eXtremeGammon O:Daniel

Score is X:0 O:10. 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 |
| | | 6 |
| |BAR| |
| | | X 7 |
| | | X X |
| | | X X |
| | | X X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 75 O: 84 X-O: 0-10
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 77.07% (G:0.00% B:0.00%)
Opponent Winning Chances: 22.93% (G:0.00% B:0.00%)
Double/Take
Player Winning Chances: 77.05% (G:0.00% B:0.00%)
Opponent Winning Chances: 22.95% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.541, Double=+1.082

Cubeful Equities:
No double: +0.831 (-0.112)
Double/Take: +0.943
Double/Pass: +1.000 (+0.057)

Best Cube action: Double / Take

Rollout:
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.002 (+0.829..+0.834)
Confidence Double: ± 0.003 (+0.940..+0.947)

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

Duration: 4 minutes 32 seconds

eXtreme Gammon Version: 2.10

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"peps...@gmail.com" <pepstein5@gmail.com> writes:

my crossovers are being overly penalised

Maybe, or XG's thin 4 point is underpenalised.

Best regards

Axel

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On Sunday, June 19, 2022 at 11:45:06 AM UTC+1, Axel Reichert wrote:

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

my crossovers are being overly penalised

Maybe, or XG's thin 4 point is underpenalised.

Best regards

Axel

I don't agree. The thin 4 point is not a problem here at all because aces and twos can be played to the four point.
Here, your algo does actually work very well, producing an error of only approx 0.05 in a difficult and not very standard
position. I think where your algo could be tricked is if we variantize to get similar positions where XG has no
checkers on the 4 point, but where the +1 penalty is inappropriate because the 4 point will get filled with any ace or two.

Maybe, it's not possible for any human to play all these positions correctly. After all, I got a PR of about 2.3 on that game, which matches the best humans. I did feel it was a take, then I Axelised it, hoping that that would validate the take, but it didn't, so I passed.
Maybe I should have given more weight to my intuition.

Paul

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