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

--- SoupGate-Win32 v1.05
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On Sunday, May 22, 2022 at 4:20:22 PM UTC-4, peps...@gmail.com wrote:

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.

Stick

--- SoupGate-Win32 v1.05
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On 5/22/2022 7:52 PM, Stick Rice wrote:

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

--- SoupGate-Win32 v1.05
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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:

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

Oh wow! Thanks to Tim and Stick.
A one in two thousand parlay is something that could quite easily happen. Experienced players will have received quite a few parlays like that.
I thought the gammon-saving chances were worse.
Shame on me for missing the optimal play.

Paul

--- SoupGate-Win32 v1.05
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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:

On 5/22/2022 7:52 PM, Stick Rice wrote:

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

Oh wow! Thanks to Tim and Stick.
A one in two thousand parlay is something that could quite easily happen.

Do you mean a one in forty thousand parlay? The difference
between 21/7 10/9 and 21/7 9/8 is only about 50 in 2 million
according to the rollout.

---
Tim Chow

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

On Wednesday, May 25, 2022 at 1:40:07 PM UTC+1, Tim Chow wrote:

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:

On 5/22/2022 7:52 PM, Stick Rice wrote:

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

Oh wow! Thanks to Tim and Stick.
A one in two thousand parlay is something that could quite easily happen.

Do you mean a one in forty thousand parlay? The difference
between 21/7 10/9 and 21/7 9/8 is only about 50 in 2 million
according to the rollout.

No, I meant what I said.
I was arguing against a common line of reasoning that says
"I'll lose a gammon whatever happens, so I don't really care."
And I was making the point (or trying to) that the loss of the gammon
actually doesn't always happens but only approx 99.95% of the time.

Paul

--- SoupGate-Win32 v1.05
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