XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X |
| | | X X X X |
| | | O X X X X | +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 21 O: 82 X-O: 0-0
Cube: 2, O own cube
X to play 21
---
Tim Chow
XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10
Compared to the previous bearoff problem, X has three more checkers
off, so his gammon chances are better, as are his winning chances if
he gets hit, especially since O's board is crunched, with an open 6pt.
XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
worth the risk. On the other hand, with an extra checker on the 1pt,
XG prefers the safe play.
On 9/5/2021 8:22 AM, Timothy Chow wrote:...
XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10I should have said that it's not just that with an extra checker, X's
Compared to the previous bearoff problem, X has three more checkers
off, so his gammon chances are better, as are his winning chances if
he gets hit, especially since O's board is crunched, with an open 6pt.
XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
worth the risk. On the other hand, with an extra checker on the 1pt,
XG prefers the safe play.
gammon chances go down. XG also prefers clearing the 4pt with one fewer checker on the 1pt (see below). There is an odd/even effect at play,
meaning that X's chances of saving a roll by bearing off a checker now
are low. And X still doesn't want to get hit, not because he's afraid
of losing the game, but because it will greatly reduce his chances of
winning a gammon.
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