In the below position, 21/17 is mandatory to save the backgammon. Furthermore, there is no reason to concede the gammon -- gammon-saving
is unlikely (to put it mildly) but far from impossible.
Another conclusion (they don't call me "Oracle" for nothing) is that
the gammon-saving probability is small enough that any reasonable
play is unlikely to lose much PR.
But they also don't call me "Stickler for nothing" (they just call me a "stickler" (Tim does anyway)) so I am keen to play this roll correctly.
XG says that 10/9 is better than the alternatives.
Is this another incident of XG's roundomania where it comes to
bizarre conclusions through rounding errors? Or is 10/9 really
the uniquely optimal play?
Thank You,
Paul
XGID=-ABCBBB--AA----------Aaab-:1:-1:1:41:1:5:3:0:10
X:Daniel O:eXtremeGammon
Score is X:1 O:5. Unlimited Game, Jacoby Beaver +13-14-15-16-17-18------19-20-21-22-23-24-+
| | | X O O O | +---+
| | | O | | 2 |
| | | | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X 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: 84 O: 7 X-O: 1-5
Cube: 2, O own cube
X to play 41
1. 4-ply 21/17 10/9 eq:-1.999
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:99.95% B:0.00%)
2. 4-ply 21/17 9/8 eq:-2.000
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:99.95% B:0.00%)
3. 4-ply 21/16 eq:-2.000
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:99.95% B:0.00%)
4. 4-ply 10/9 6/2 eq:-2.111 (-0.111)
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:99.97% B:11.11%)
5. 3-ply 21/17 2/1 eq:-1.999 (+0.001)
Player: 0.02% (G:0.00% B:0.00%)
Opponent: 99.98% (G:99.91% B:0.00%)
eXtreme Gammon Version: 2.10
I believe XG is correct for in the scenarios where your opponent rolls back to back [21]s on our second roll with various numbers we'll be able to get off with [33] or better instead of [44] or better.
On 5/22/2022 7:52 PM, Stick Rice wrote:Oh wow! Thanks to Tim and Stick.
I believe XG is correct for in the scenarios where your opponent rolls back to back [21]s on our second roll with various numbers we'll be able to get off with [33] or better instead of [44] or better.Sounds plausible. I just did an XG rollout with 2 million trials.
Number of trials in which X saved the gammon:
21/7 10/9: 1043
21/7 9/8: 990
21/16: 987
---
Tim Chow
On Monday, May 23, 2022 at 2:08:14 PM UTC+1, Tim Chow wrote:
On 5/22/2022 7:52 PM, Stick Rice wrote:Oh wow! Thanks to Tim and Stick.
I believe XG is correct for in the scenarios where your opponent rolls back to back [21]s on our second roll with various numbers we'll be able to get off with [33] or better instead of [44] or better.Sounds plausible. I just did an XG rollout with 2 million trials.
Number of trials in which X saved the gammon:
21/7 10/9: 1043
21/7 9/8: 990
21/16: 987
---
Tim Chow
A one in two thousand parlay is something that could quite easily happen.
On 5/23/2022 4:12 PM, peps...@gmail.com wrote:
On Monday, May 23, 2022 at 2:08:14 PM UTC+1, Tim Chow wrote:Do you mean a one in forty thousand parlay? The difference
On 5/22/2022 7:52 PM, Stick Rice wrote:Oh wow! Thanks to Tim and Stick.
I believe XG is correct for in the scenarios where your opponent rolls back to back [21]s on our second roll with various numbers we'll be able to get off with [33] or better instead of [44] or better.Sounds plausible. I just did an XG rollout with 2 million trials.
Number of trials in which X saved the gammon:
21/7 10/9: 1043
21/7 9/8: 990
21/16: 987
---
Tim Chow
A one in two thousand parlay is something that could quite easily happen.
between 21/7 10/9 and 21/7 9/8 is only about 50 in 2 million
according to the rollout.
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 307 |
Nodes: | 16 (2 / 14) |
Uptime: | 109:12:20 |
Calls: | 6,852 |
Calls today: | 3 |
Files: | 12,355 |
Messages: | 5,416,159 |