XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51
---
Tim Chow
On Friday, November 4, 2022 at 1:47:44 PM UTC, Tim Chow wrote:
XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game +13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51
---This one _looks_ very easy. But note the emphasis on "looks".
Tim Chow
With O's board being very strong, any indirect shot giving 5.5% hits
would have to be very well motivated to be correct.
There is only one legal play here which is safe in the sense that
that none of O's possible next-rolls enable a legal blot hit.
I see absolutely no reason not to make this safe play, particularly
since it doesn't seem to introduce any weaknesses whatsoever.
Solution:
1. Find the unique play which is completely safe.
2. Make that play.
Note on Solution:
If it happens to be the case that the number of completely safe plays
is different to 1 (and, after all, I could have made a mistake),
then simply mark my solution as wrong. (And, of course, I'm also
wrong if we should play unsafely.)
Paul
On Friday, November 4, 2022 at 11:09:01 AM UTC-4, peps...@gmail.com wrote:have a killer board and what will you have? A mess you just created by dumping a checker so low. (and a slightly harder time with containment in the outfield since you stacked your checkers up so inflexibly)
On Friday, November 4, 2022 at 1:47:44 PM UTC, Tim Chow wrote:
XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game +13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51
---This one _looks_ very easy. But note the emphasis on "looks".
Tim Chow
With O's board being very strong, any indirect shot giving 5.5% hits
would have to be very well motivated to be correct.
There is only one legal play here which is safe in the sense that
that none of O's possible next-rolls enable a legal blot hit.
I see absolutely no reason not to make this safe play, particularly
since it doesn't seem to introduce any weaknesses whatsoever.
Solution:
1. Find the unique play which is completely safe.
2. Make that play.
Note on Solution:
If it happens to be the case that the number of completely safe plays
is different to 1 (and, after all, I could have made a mistake),
then simply mark my solution as wrong. (And, of course, I'm also
wrong if we should play unsafely.)
PaulThe weakness this play introduces is you have to play the rest of the game out. How is the rest of the game going to pan out? Your opponent is going to have to run off his anchor and he's going to have to do it very soon. When he does so he'll still
XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51
I called this a "holding game," but who's holding whom? X is the one
who is well behind in the pip count, so it's X who wants to get and hit
a shot. So he wants to arrange his checkers for containment purposes,
but he also has to be wary of leaving too many shots because O's board
is rather strong.
The safest play is 16/15 6/1, but it leaves a blot in X's board. Does
O's blot in her own board allow X to play more boldly than that?
According to the rollout below, yes. I tried 13/7, trying for more
diversity in the outfield at the cost of 2 extra immediate shots and
some additional blotting danger in the future; XG says that's too bold.
The equity differences are big, showing how delicate this decision is.
See also the variant, in which O's board is perfect.
1. Rollout¹ 16/15 13/8 eq:-0.288
Player: 40.20% (G:4.50% B:0.17%)
Opponent: 59.80% (G:14.93% B:0.19%)
Confidence: ±0.015 (-0.303..-0.273) - [100.0%]
2. Rollout¹ 16/15 6/1 eq:-0.426 (-0.139)
Player: 38.59% (G:4.37% B:0.13%)
Opponent: 61.41% (G:15.67% B:0.24%)
Confidence: ±0.013 (-0.439..-0.414) - [0.0%]
3. Rollout¹ 13/7 eq:-0.442 (-0.154)
Player: 39.00% (G:4.66% B:0.17%)
Opponent: 61.00% (G:19.40% B:0.30%)
Confidence: ±0.016 (-0.458..-0.426) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.211.pre-release
-------
Variant
-------
XGID=---B-bDBB----B-BA-bcbbbb--:0:0:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 100 X-O: 0-0
Cube: 1
X to play 51
1. Rollout¹ 16/15 13/8 eq:-0.478
Player: 37.41% (G:3.65% B:0.12%)
Opponent: 62.59% (G:16.88% B:0.18%)
Confidence: ±0.014 (-0.492..-0.464) - [68.1%]
2. Rollout¹ 16/15 6/1 eq:-0.483 (-0.005)
Player: 37.20% (G:4.08% B:0.11%)
Opponent: 62.80% (G:16.24% B:0.31%)
Confidence: ±0.013 (-0.496..-0.469) - [31.9%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.211.pre-release
On Sunday, November 6, 2022 at 12:43:19 PM UTC, Tim Chow wrote:
XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game +13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51
I called this a "holding game," but who's holding whom? X is the one
who is well behind in the pip count, so it's X who wants to get and hit
a shot. So he wants to arrange his checkers for containment purposes,
but he also has to be wary of leaving too many shots because O's board
is rather strong.
The safest play is 16/15 6/1, but it leaves a blot in X's board. Does
O's blot in her own board allow X to play more boldly than that?
According to the rollout below, yes. I tried 13/7, trying for more diversity in the outfield at the cost of 2 extra immediate shots and
some additional blotting danger in the future; XG says that's too bold. The equity differences are big, showing how delicate this decision is.
See also the variant, in which O's board is perfect.
1. Rollout¹ 16/15 13/8 eq:-0.288
Player: 40.20% (G:4.50% B:0.17%)
Opponent: 59.80% (G:14.93% B:0.19%)
Confidence: ±0.015 (-0.303..-0.273) - [100.0%]
2. Rollout¹ 16/15 6/1 eq:-0.426 (-0.139)
Player: 38.59% (G:4.37% B:0.13%)
Opponent: 61.41% (G:15.67% B:0.24%)
Confidence: ±0.013 (-0.439..-0.414) - [0.0%]
3. Rollout¹ 13/7 eq:-0.442 (-0.154)
Player: 39.00% (G:4.66% B:0.17%)
Opponent: 61.00% (G:19.40% B:0.30%)
Confidence: ±0.016 (-0.458..-0.426) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.211.pre-release
-------
Variant
-------
XGID=---B-bDBB----B-BA-bcbbbb--:0:0:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game +13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 100 X-O: 0-0
Cube: 1
X to play 51
1. Rollout¹ 16/15 13/8 eq:-0.478
Player: 37.41% (G:3.65% B:0.12%)
Opponent: 62.59% (G:16.88% B:0.18%)
Confidence: ±0.014 (-0.492..-0.464) - [68.1%]
2. Rollout¹ 16/15 6/1 eq:-0.483 (-0.005)
Player: 37.20% (G:4.08% B:0.11%)
Opponent: 62.80% (G:16.24% B:0.31%)
Confidence: ±0.013 (-0.496..-0.469) - [31.9%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.211.pre-releaseThe fact that you can so effortlessly variantize to make my
play optimal (or at least quite possibly optimal) tells me that
Stick's argument is too crude -- it applies just as well to your variantization
where, if we believe the equities, the conclusion of the argument is false.
Paul
The fact that you can so effortlessly variantize to make my
play optimal (or at least quite possibly optimal) tells me that
Stick's argument is too crude -- it applies just as well to your variantization
where, if we believe the equities, the conclusion of the argument is false.
On 11/7/2022 4:09 PM, peps...@gmail.com wrote:
The fact that you can so effortlessly variantize to make myActually, if you take what Stick wrote at face value, without
play optimal (or at least quite possibly optimal) tells me that
Stick's argument is too crude -- it applies just as well to your variantization
where, if we believe the equities, the conclusion of the argument is false.
reading between the lines, all he did was to point out the
weaknesses of your play. He did not explicitly draw the
conclusion that your play was wrong, let alone explicitly
say that your play was wrong *because* of the features he
mentioned.
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