XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 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 Sunday, January 29, 2023 at 4:08:19 PM UTC-5, Tim Chow wrote:

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

This may be the most straight forward cube action problem ever posted that's not a reference position or reference position like. The only way it could be even more so would be to center the cube.

Stick

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

On 1/29/2023 4:08 PM, Timothy Chow wrote:

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
 |             O    |   | O  O  O  O  O  O |
 |                  |   | O  O  O  O  O  O |
 |                  |   |             O    |
 |                  |   |                  |
 |                  |   |                  |
 |                  |BAR|                  |
 |                  |   |                8 |
 |                  |   |             X  X |
 |                  |   |             X  X | +---+
 |          X       |   |             X  X | | 2 |
 |          X       |   |    O  X     X  X | +---+
 +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 38  O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

If X manages to not be hit he's basically gin. 65, 55, and 33 "win" immediately. 21, 31, 11, and 22 make it very difficult for O to
prevail. The other 26 rolls cough up a direct shot, but O still has to
hit it. Assuming the ten good rolls win and the 26 others give O a
shot, and that O is 1/3 to hit I arrive at about a 24% GWC for O with
few gammons. Assuming that a hit for O is a win for O, which isn't
exactly true.

So, D/T. Definitely a practical double since some will pass.

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

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

On Sunday, January 29, 2023 at 9:08:19 PM UTC, Tim Chow wrote:

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

This is kind of a semi-Walt.
I've read Stick's post, but I haven't seen anything else.
I agree that the problem looks straightforward, but I don't know
the action yet. I'll reason through it in real time.
I'll assume that the opponent wins if she hits but loses otherwise.
The probability of getting hit can be estimated somewhat accurately,
I think, and this will hopefully be a guide to the cube action.
BTW, I'm not using any calculation aid (other than writing numbers down)
and that might explain my somewhat laborious computations.

First let's look at the one-ply hits. We blot and then get immediately hit.
64 gets hit 75% of the time.
63 gets hit 11/36 of the time.
62 -> 1/3
61 -> 7/18
54 -> 13/36
53 -> 11/36
52 -> 1/3
51 -> 7/18
44 -> 13/36
43 -> 4/9
42 -> 1/2
41 -> 5/36

5/12

22 -> 13/36

This combined probability of getting immediately hit is:
1/24 + 1/9 * 11/36 + 1/9 * 1/3 + 1/9 * 7/18 + 1/9 * 13/36
+ 2/81 + 1/36 + 5/648 + 5/216 =

(54 + 44 + 48 + 56 + 52 + 32 + 36 + 10 + 30)/1296 = 362/1296 = 181/648 > 25%.

So the opponent has a very clear take. Note that we've underestimated
the opponent's equity for two reasons. 1) There are sequences which give
the opponent more than one blot to shoot at, so we have gammon losses.
[Note 64 in particular].
2) If we roll small, we preserve the status quo and the risk repeats.

So the take is even clearer than indicated by the 349/1296 estimate.
But is it such a clear take that we should even hold the cube?

Well no. The factors 1 and 2 above are somewhat small. In particular,
there aren't that many rolls which hold the position -- only 31 and 21 with 11 being
an intermediate case. Clear double, clear take.

The chances of being hit are around 28% which isn't that far from 25% so I don't think
this is an easy problem OTB where players can't do this type of computation.
It wouldn't be surprising to see a drop OTB (and I'm sceptical of the claim that a drop
is inconceivable for a world-class player).

Paul

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

On Monday, January 30, 2023 at 1:12:41 AM UTC, ah....Clem wrote:

On 1/29/2023 4:08 PM, Timothy Chow wrote:

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

If X manages to not be hit he's basically gin. 65, 55, and 33 "win" immediately. 21, 31, 11, and 22 make it very difficult for O to
prevail. The other 26 rolls cough up a direct shot, but O still has to
hit it. Assuming the ten good rolls win and the 26 others give O a
shot, and that O is 1/3 to hit I arrive at about a 24% GWC for O with
few gammons. Assuming that a hit for O is a win for O, which isn't
exactly true.

So, D/T. Definitely a practical double since some will pass.

I handled the problem a similar way, but did more precise computations.
[Not saying my approach was better, because although it's more accurate,
it isn't practical OTB.] A few of your errors are:
In the immediate wins, you left out 66. However, you balanced this error
by wrongly including 22 which in fact blots.
21, 31 and 22 are not particularly good rolls. 22 blots (as above) and
21 and 31 preserve the status quo and risk blotting later.
O being 1/3 to hit turns out to be a significant underestimate but I'm not
sure that would have been clear to me if I didn't do such a detailed analysis.

Paul

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

On Monday, January 30, 2023 at 1:12:41 AM UTC, ah....Clem wrote:

On 1/29/2023 4:08 PM, Timothy Chow wrote:

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

If X manages to not be hit he's basically gin. 65, 55, and 33 "win" immediately. 21, 31, 11, and 22 make it very difficult for O to
prevail. The other 26 rolls cough up a direct shot, but O still has to
hit it. Assuming the ten good rolls win and the 26 others give O a
shot, and that O is 1/3 to hit I arrive at about a 24% GWC for O with
few gammons. Assuming that a hit for O is a win for O, which isn't
exactly true.

So, D/T. Definitely a practical double since some will pass.

The assumption that a hit is a single win for O actually understates
O's equity. O's gammon equity more than compensates for the possibility
that O hits and loses -- 64 leaves three blots and the probability of getting a gammon with only one checker closed out is significant (but small).

Paul

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

On Monday, January 30, 2023 at 9:30:44 AM UTC, peps...@gmail.com wrote:

On Sunday, January 29, 2023 at 9:08:19 PM UTC, Tim Chow wrote:

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

This is kind of a semi-Walt.
I've read Stick's post, but I haven't seen anything else.
I agree that the problem looks straightforward, but I don't know
the action yet. I'll reason through it in real time.
I'll assume that the opponent wins if she hits but loses otherwise.
The probability of getting hit can be estimated somewhat accurately,
I think, and this will hopefully be a guide to the cube action.
BTW, I'm not using any calculation aid (other than writing numbers down)
and that might explain my somewhat laborious computations.

First let's look at the one-ply hits. We blot and then get immediately hit. 64 gets hit 75% of the time.
63 gets hit 11/36 of the time.
62 -> 1/3
61 -> 7/18
54 -> 13/36
53 -> 11/36
52 -> 1/3
51 -> 7/18
44 -> 13/36
43 -> 4/9
42 -> 1/2
41 -> 5/36

5/12

22 -> 13/36

43 and 42 are wildly wrong because I made idiotic misplays.
But I'm sure these errors aren't enough to shift the D/T verdict.

Paul

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

On Monday, January 30, 2023 at 9:30:44 AM UTC, peps...@gmail.com wrote:

On Sunday, January 29, 2023 at 9:08:19 PM UTC, Tim Chow wrote:

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

This is kind of a semi-Walt.
I've read Stick's post, but I haven't seen anything else.
I agree that the problem looks straightforward, but I don't know
the action yet. I'll reason through it in real time.
I'll assume that the opponent wins if she hits but loses otherwise.
The probability of getting hit can be estimated somewhat accurately,
I think, and this will hopefully be a guide to the cube action.
BTW, I'm not using any calculation aid (other than writing numbers down)
and that might explain my somewhat laborious computations.

First let's look at the one-ply hits. We blot and then get immediately hit. 64 gets hit 75% of the time.
63 gets hit 11/36 of the time.
62 -> 1/3
61 -> 7/18
54 -> 13/36
53 -> 11/36
52 -> 1/3
51 -> 7/18
44 -> 13/36
43 -> 4/9
42 -> 1/2
41 -> 5/36

5/12

22 -> 13/36

This combined probability of getting immediately hit is:
1/24 + 1/9 * 11/36 + 1/9 * 1/3 + 1/9 * 7/18 + 1/9 * 13/36
+ 2/81 + 1/36 + 5/648 + 5/216 =

(54 + 44 + 48 + 56 + 52 + 32 + 36 + 10 + 30)/1296 = 362/1296 = 181/648 > 25%.

So the opponent has a very clear take. Note that we've underestimated
the opponent's equity for two reasons. 1) There are sequences which give
the opponent more than one blot to shoot at, so we have gammon losses.
[Note 64 in particular].
2) If we roll small, we preserve the status quo and the risk repeats.

So the take is even clearer than indicated by the 59/216 estimate.
But is it such a clear take that we should even hold the cube?

Well no. The factors 1 and 2 above are somewhat small. In particular,
there aren't that many rolls which hold the position -- only 31 and 21 with 11 being
an intermediate case. Clear double, clear take.

The chances of being hit are around 28% which isn't that far from 25% so I don't think
this is an easy problem OTB where players can't do this type of computation. It wouldn't be surprising to see a drop OTB (and I'm sceptical of the claim that a drop
is inconceivable for a world-class player).

I can't resist correcting this. 43 and 42 both give 5/12 so I need to subtract (1/18 * 1/36 + 1/18 * 1/12)
So I need to subtract 1/162. So my revised estimate is 59/216 which again > 25%.

Paul

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

XGID=-HD-Aa---B-------a-bbbbcb-: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-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X | +---+
| X | | X X | | 2 |
| X | | O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

This is an anti-QF problem...it looks like D/T, and it is D/T,
according to the rollout.

There were psychological issues at play when I faced this position
OTB. I was leading 3a5a with a centered cube. On the preceding
turn, I had rolled 44, which I had played 13/9(2) 6/2(2), and then
O rolled 32, which was played 13/8. I had been reminding myself
throughout the game to be somewhat cautious about doubling because
of the score, and then when I played 6/2(2), I felt that I was
wrecking my position. But of course, 44 was an excellent roll.

The cube action is still a clear D/T at 3a5a with a centered cube,
though if you change it to 3a8a with a centered cube, XG does not
double (see below).

Analyzed in Rollout
No redouble
Player Winning Chances: 65.32% (G:0.04% B:0.00%)
Opponent Winning Chances: 34.68% (G:1.97% B:0.06%)
Redouble/Take
Player Winning Chances: 65.59% (G:0.03% B:0.00%)
Opponent Winning Chances: 34.41% (G:2.26% B:0.08%)

Cubeful Equities:
No redouble: +0.384 (-0.090)
Redouble/Take: +0.475
Redouble/Pass: +1.000 (+0.525)

Best Cube action: Redouble / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 4-ply, cube decisions: XG Roller+
Search interval: Large
Confidence No Double: ± 0.002 (+0.383..+0.386)
Confidence Double: ± 0.004 (+0.471..+0.478)

eXtreme Gammon Version: 2.19.211.pre-release

----
3a8a
----

XGID=-HD-Aa---B-------a-bbbbcb-:0:0:1:00:5:0:0:8:10

Score is X:5 O:0 8 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O O |
| | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X X |
| | | X X |
| X | | X X |
| X | | O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 72 X-O: 5-0/8
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 65.65% (G:0.05% B:0.00%)
Opponent Winning Chances: 34.35% (G:2.25% B:0.07%)
Double/Take
Player Winning Chances: 65.67% (G:0.06% B:0.00%)
Opponent Winning Chances: 34.33% (G:2.28% B:0.08%)

Cubeful Equities:
No double: +0.339
Double/Take: +0.282 (-0.057)
Double/Pass: +1.000 (+0.661)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 8.0%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.002 (+0.337..+0.341)
Confidence Double: ± 0.006 (+0.276..+0.287)

eXtreme Gammon Version: 2.19.211.pre-release, MET: Kazaross XG2

---
Tim Chow

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