If XG had all six checkers on the ace, it's a clear (clear in the
sense of everyone knows it) D/P.
However, XG's position is clearly worse than that, so it may not
be obvious that the position below is still a pass.
I think that for variantizations of 3 rolls vs 3 rolls to be a take,
the on-roll player needs to have an anti-joker. Here, XG doesn't
have any -- a 21 would not be as bad as a can't-import-module error
when you're trying to code in python.

So I was pretty confident about the pass, but not quite 100% confident.
But how does this position Axelise?
Here, we have to realise that mathematically, the position is exactly equivalent to what it would be if I had 6 checkers on my ace instead of 5. There are two equivalent representations of exactly the same position.
So it would be absurd to say that one of these postions is a pass and the
other is a take. Let's Axelise both and take the mean.
For the current position, the raw pip counts are 10 and 5.
XG's stack penalty is 2 and mine is 6.
14 - 11 = 3.
But there's another equally valid representation.
How would we Axelise if I had six checkers on my ace point?
Then my count would be 6, and my penalty would be 8 leading to
a score of 14-14 = 0.
Now take the average: (0 + 3)/2 = 1.5 which is the correct pass zone.

Paul




XGID=-E--------------------abc-:1:-1:-1:00:0:5:3:0:10
X:eXtremeGammon O:Daniel

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

Analyzed in 4-ply
Player Winning Chances: 76.58% (G:0.00% B:0.00%)
Opponent Winning Chances: 23.42% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.532, Double=+1.063

Cubeful Equities:
No redouble: +0.745 (-0.255)
Redouble/Take: +1.026 (+0.026)
Redouble/Pass: +1.000

Best Cube action: Redouble / Pass

eXtreme Gammon Version: 2.10

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