On Friday, May 6, 2022 at 2:07:35 PM UTC+1, Tim Chow wrote:
On 5/6/2022 7:51 AM, BlueDice wrote:
XGID=-EDb-BB-a---------acbbbaa-:1:-1:1:63:0:0:3:0:10
X:Daniel O:eXtremeGammon
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 | | 2 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | X |
| | | X X |
| | | X X |
| | | X X O X X |
| O | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 35 O: 113 X-O: 0-0
Cube: 2, O own cube
X to play 63
eXtreme Gammon Version: 2.10
X has a huge advantage, I'm guessing 70%/80% GWC and 25%/35% gammons, equity ~ 0.9
Maybe you misunderstood the question? Paul means, what's X's
equity after he makes the only legal play, 6/off 5/2?
It's a nice question. X has three checkers off already and has
decent gammon chances. O has just 21 rolls to hit, and the win
isn't guaranteed after a hit. I suspect that X is still the
equity favorite but I'm not sure.
XG's 3-ply evaluation is:
1. 3-ply 6/Off 5/2 eq:-0.103
Player: 43.33% (G:15.54% B:0.04%)
Opponent: 56.67% (G:0.00% B:0.00%)
Like Tim, I was also surprised by how low this is.
I think the reason that Tim and I overestimate X is that
we weren't taking enough consideration of the cube.
We can variantize to obtain cube symmetry in any of the following
three variantizations:
A) The checker position is kept the same. However, instead of
giving O the cube, use a 50/50 coin toss to determine whether O or X has cube ownership.
B) My grandma rolls a fair die separately in another room. If she
rolls <=2, X has cube ownership; if she rolls >=5, O has cube ownership; otherwise, the cube goes to the middle.
C) The game continues cubelessly but gammons and backgammons are scored as usual.
I suspect that X is an equity favourite in all these three variantizations.
So, I do think it's fair to say that the checker position itself is favourable to X.
But please try not to minimise the importance of cube ownership.
Paul
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