XGID=aBABABCB----bA---bAbbdb---:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O X | | O O O O |
| O | | O O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X | +---+
| O X | | X X X X | | 2 |
| O X | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 87 O: 111 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

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

XGID=aBABABCB----bA---bAbbdb---:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O X | | O O O O |
| O | | O O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X | +---+
| O X | | X X X X | | 2 |
| O X | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 87 O: 111 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

In general, I still have a tendency to cash when XG says I should
play on, and I have been trying to correct that tendency. Here I
was inclined to cash, but decided that it was such a big pass that
I should try playing on. XG says that was a huge mistake. But as
you can see from the variants, changing the position by a pip or two
can make a huge difference. In particular, if X has not made the
1pt already, then he retains priming potential even if O enters on
the 1pt.

Analyzed in Rollout
No redouble
Player Winning Chances: 76.35% (G:23.68% B:0.10%)
Opponent Winning Chances: 23.65% (G:4.96% B:0.18%)
Redouble/Take
Player Winning Chances: 76.58% (G:23.76% B:0.10%)
Opponent Winning Chances: 23.42% (G:5.07% B:0.20%)

Cubeful Equities:
No redouble: +0.802 (-0.198)
Redouble/Take: +1.277 (+0.277)
Redouble/Pass: +1.000

Best Cube action: Redouble / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.004 (+0.798..+0.806)
Confidence Double: ± 0.009 (+1.268..+1.287)

eXtreme Gammon Version: 2.19.211.pre-release

---------
Variant 1
---------

XGID=aABBABCB----bA---bAbbdb---:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O X | | O O O O |
| O | | O O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X | +---+
| O X | | X X X X | | 2 |
| O X | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 88 O: 111 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 82.16% (G:27.27% B:0.15%)
Opponent Winning Chances: 17.84% (G:3.18% B:0.19%)
Redouble/Take
Player Winning Chances: 82.65% (G:27.79% B:0.15%)
Opponent Winning Chances: 17.35% (G:4.00% B:0.31%)

Cubeful Equities:
No redouble: +0.969 (-0.031)
Redouble/Take: +1.672 (+0.672)
Redouble/Pass: +1.000

Best Cube action: Redouble / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.004 (+0.965..+0.974)
Confidence Double: ± 0.010 (+1.662..+1.681)

eXtreme Gammon Version: 2.19.211.pre-release

---------
Variant 2
---------

XGID=aABABBCB----bA---bAbbdb---:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O X | | O O O O |
| O | | O O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X | +---+
| O X | | X X X X | | 2 |
| O X | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 89 O: 111 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 84.13% (G:28.40% B:0.16%)
Opponent Winning Chances: 15.87% (G:2.97% B:0.17%)
Redouble/Take
Player Winning Chances: 84.66% (G:28.66% B:0.16%)
Opponent Winning Chances: 15.34% (G:3.58% B:0.31%)

Cubeful Equities:
No redouble: +1.028
Redouble/Take: +1.784 (+0.755)
Redouble/Pass: +1.000 (-0.028)

Best Cube action: Too good to redouble / Pass
Percentage of wrong take needed to make the double decision right: 3.6%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.004 (+1.024..+1.032)
Confidence Double: ± 0.009 (+1.774..+1.793)

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

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

XGID=aB-BaBC-A-------BA-ccBacc-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X | | O O X O O O |
| X | | O O X O O |
| | | O O O O |
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X | +---+
| | | X X X X | | 2 |
| X | | X X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 135 O: 91 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

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

On 8/27/2023 9:52 AM, Timothy Chow wrote:

XGID=aB-BaBC-A-------BA-ccBacc-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
 +13-14-15-16-17-18------19-20-21-22-23-
 |          X  X    |   | O  O  X  O  O  O |
 |          X       |   | O  O  X     O  O |
 |                  |   | O  O        O  O |
 |                  |   |                  |
 |                  |   |                  |
 |                  |BAR|                  |
 |                  | O |                  |
 |                  |   |                  |
 |                  |   | X                | +---+
 |                  |   | X  X     X     X | | 2 |
 |             X    |   | X  X  O  X     X | +---+
 +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 135  O: 91 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

O's 16 dancing rolls seem like market losers, but X still has work to do
to bring this one home and if O anchors she's right back in the game,
maybe ahead.

So, I'll ship it, and O probably has to eat this one. R/T.

--
Ah....Clem
The future is fun, the future is fair.

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

XGID=aB-BaBC-A-------BA-ccBacc-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X | | O O X O O O |
| X | | O O X O O |
| | | O O O O |
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X | +---+
| | | X X X X | | 2 |
| X | | X X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 135 O: 91 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

It's going to take X a while to get more ammunition around the board
to complete a closeout, so I thought O had a take here. But XG says
it's a big pass. Again, I have a tendency to underestimate how bad
dead checkers are; see the variant below.

Analyzed in Rollout
No redouble
Player Winning Chances: 71.75% (G:26.42% B:0.91%)
Opponent Winning Chances: 28.25% (G:10.51% B:0.25%)
Redouble/Take
Player Winning Chances: 72.59% (G:27.37% B:1.06%)
Opponent Winning Chances: 27.41% (G:11.32% B:0.45%)

Cubeful Equities:
No redouble: +0.836 (-0.164)
Redouble/Take: +1.085 (+0.085)
Redouble/Pass: +1.000

Best Cube action: Redouble / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.007 (+0.829..+0.843)
Confidence Double: ± 0.016 (+1.069..+1.101)

eXtreme Gammon Version: 2.19.211.pre-release

-------
Variant
-------

XGID=aB-BaBC-A-------BA-dcBacb-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X | | O O X O O O |
| X | | O O X O O |
| | | O O O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X | +---+
| | | X X X X | | 2 |
| X | | X X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 135 O: 96 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 69.69% (G:25.05% B:0.85%)
Opponent Winning Chances: 30.31% (G:10.85% B:0.29%)
Redouble/Take
Player Winning Chances: 70.75% (G:26.52% B:0.98%)
Opponent Winning Chances: 29.25% (G:11.98% B:0.50%)

Cubeful Equities:
No redouble: +0.797 (-0.182)
Redouble/Take: +0.978
Redouble/Pass: +1.000 (+0.022)

Best Cube action: Redouble / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.008 (+0.789..+0.804)
Confidence Double: ± 0.015 (+0.963..+0.993)

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

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

On September 12, 2023 at 7:22:11 AM UTC-6, Timothy Chow wrote:

XGID=aB-BaBC-A-------BA-ccBacc-:1:1:1:00:0:0:0:0:10
X on roll, cube action
It's going to take X a while to get more...
Best Cube action: Redouble / Pass

The incorrect but best play here is No-redouble.

Ex-Gee is using 32-bit Mersenne Twister RNG and
applies modulo 6 to produce dice rolls.

I've used your "given math" "21^7 < 2^32 < 21^8" to
deduce the seed after 8-9 rolls and saw that Ex will
roll a 22 for you next, with subsequent rolls giving
you a gammon. So, play on... ;)

MK

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