For the record, the original position in Gammon 64 was from a match, side on roll leading 7a/9a, and centered cube. The prop position that Karsten and Mary wrote about, and that I played, was money game and centered cube.
Anyway, Stick's opinion is consonant with the one with which Karsten Nielsen ended his Gammon 65 article:
"In theory no double/easy take. In practice strong double/take-drop. As a prop: easy take."
And for what it's worth, I always played it as a take. Similar to Karsten's informal survey, most folks I showed it to thought it was a drop. Some others thought it might be a take but didn't want to play the take side.
(1) In theory no double because not much is happening on the next exchange. (2) In practice a strong double because many strong players would drop -- Karsten said over 90% of the strong players he showed the position to would have passed -- and take/drop because it's easy to make huge checker play and cube errors without a good feel for containment and for the unusual cube decisions coming up. (3) An easy take in a prop because, well, because it's a take ;-
In his article, Karsten said that after playing it a lot, and using his bot(s), he had no idea of the positions exact equity. Having played it hundreds of times, neither did I. I only know that I was a winner taking a point to take the cube.
However, I do think the take is much closer than Stick's short XG rollout and a Gnubg rollout and a JF rollout say. A short Gnubg rollout roughly agrees with Stick's short XG rollout on W/G/BG percentages. Also, a JF level 6 rollout found cubeless equity of 0.563 -- compare to Stick's XG cubeless equity of 0.563 (±0.100 or so -- the rollout doesn't say).
If I had XG, I'd watch it play and see how it does with both checker play and cube. I did that a lot years ago with whichever bot I was using then. I think Gnubg plays the fill-in-the-board part of the containment game well. I'm less confident in its movement of the back checkers. Here, for example:
| White | 169 |
|---|---|
| |
| Blue | 65 |
Position ID: +D4AILCZCYBoAw Match ID: AQEJAAAAAAAA | |
Gnubg gives up the ace point with 24/22 19/15 8/6. I'd play 19/13 8/6. Giving up the acepoint looks blunderful.
Here's another checker play that caught my eye:
| White | 126 |
|---|---|
| |
| Blue | 20 |
Position ID: rAEAwNY2AAENAA Match ID: AQENAAAAAAAA | |
Gnubg plays 23/21*/18. I'd play 24/21* 16/14.
More important, the equity of the position depends greatly on correct cube action for both sides. I have no confidence in Gnubg's cube action.
Just now, I let Gnubg play the position out once, and it reached this cube action:
| White | 67 |
|---|---|
| |
| Blue | 57 |
Position ID: uAcAgLbdhgIAAA Match ID: AQEAAAAAAAAA | |
2-ply evaluation says Double/Take +0.745, No Double +0.743, with White cubeless wins 73%. Actually, this is a huge 1.150 pass. White wins about 81.5% cubeless. I believe the correct time to redouble was 4 rolls earlier in this position:
| White | 106 |
|---|---|
| |
| Blue | 57 |
Position ID: uAcAgLa2UQBgAA Match ID: AQEAAAAAAAAA | |
Here, Gnubg thinks White wins 65% cubeless. Actually White wins 72% cubeless. White has 21 immediate cover numbers and will be big favorite to cover after the sequence no cover ... fan. I'm not sure that White should redouble now, instead of covering and cashing. But I think so. A rollout will say No Double. But rolling out the No Double is pointless, since Gnubg will double and take after closing the board.
Here's another cube action the bot reached:
| White | 63 |
|---|---|
| |
| Blue | 53 |
Position ID: +AMAgLbtDgEAAA Match ID: AQEAAAAAAAAA | |
Gnubg says double/take. No way. White wins about 81%. Gnubg seems to have trouble evaluating Blue's winning chances with X checkers off and the rest stacked on the 3, 4 and 5 points. I imagine many human players would, too.
Here's one more Gnubg cube action:
| White | 124 |
|---|---|
| |
| Blue | 89 |
Position ID: +B0AALY1CwVEAg Match ID: AQEAAAAAAAAA | |
Gnubg 2-ply doubles and takes, with about 79% wins. But it's a huge pass. White wins about 86%. The position the roll before:
| White | 144 |
|---|---|
| |
| Blue | 86 |
Position ID: +B0AQLSZhQKiAg Match ID: AQEAAAAAAAAA | |
Gnubg says No double, with 64% winning chances. A rollout says double/take -- and that's in comparison to a very inflated No Double equity -- with White winning about 76%.