Wiggins’s Boards, Blots, and Double Shots
Norm Wiggins’s excellent book
Boards, Blots, and Double Shots
is based on Jellyfish rollouts.
Jellyfish was the strongest backgammon program available at the time,
but since then, stronger programs have emerged
(though still based on the same neural net paradigm).
In 2007, Torsten Schoop ran a head-to-head
competition among several bots.
The results
of this “Big Bot Shoot-out” were that Jellyfish
was decidedly weaker than BGBlitz, Snowie, and GNU Backgammon,
with GNU doing the best.
In 2010, Michael Depreli organized a bot
comparison project to compare BGBlitz, Snowie, GNU, and
eXtreme Gammon (version 1). The strongest bot according to this
project was eXtreme Gammon.
It is therefore interesting to see whether eXtreme Gammon
disagrees with Jellyfish on any of the positions in the book.
I manually entered all the positions,
as well as some variants mentioned by Wiggins in his analysis,
into eXtreme Gammon version 1.21.
Where XG Roller+ indicated that there might be an issue of some sort,
I asked my friend Miller Maley, who owns eXtreme Gammon version 2.00,
to perform a full rollout.
The most interesting results of this study are presented below.
All rollouts below were done with eXtreme Gammon version 2.00.
The most dramatic disagreements between the two bots
occur in positions 3, 14, and 89.
Other notable disagreements include
positions 60, 72, 80, 92, 100, 102, 118.
I have also included a number of other rollouts
for reasons explained in more detail below.
Except where otherwise specified,
the rollouts below assume that the Jacoby rule is in effect.
Wiggins is not entirely clear about whether the Jacoby rule
is supposed to apply in all the positions in the book.
His comments on Positions 80 and 93 suggest that Jacoby should
be assumed to apply.
However, in Problem 114, he talks about being too good to double
with the cube in the center.
The question is somewhat moot because I believe it is very unlikely
that the Jacoby rule will affect which play comes out on top
in any of the positions in the book
(unless two or more plays are almost tied for top).
For a general explanation of why the Jacoby rule rarely makes
a difference when it comes to checker plays,
see this
article that I posted to rec.games.backgammon.
I should mention that for many of the positions in the book,
the absolute equity figures of XG
differ substantially from Jellyfish’s;
however, if the overall qualitative verdict
(i.e., which play is best, and by a large or a small margin)
remains the same, then I have usually not bothered to
include the rollout here.
NOTE: I have included rollout information only
and have not included diagrams of the positions.
This is intentional. I do not want to violate copyright,
and I do not want this website to act as a partial substitute
for Wiggins’s book. It is intended solely as a study tool
for those who have already purchased the book.
Position 3
One of the most dramatic results of this study. Jellyfish prefers 6/5*/2,
which XG thinks is a whopper.
| 1. | Rollout1 | 13/10 6/5* | eq: -0.070 |
| Player:
Opponent: |
42.58% (G:27.47% B:1.05%)
57.42% (G:30.12% B:3.79%) | Conf: ± 0.007 (-0.077...-0.063)
Duration: 16 minutes 00 second |
|
| 2. | Rollout1 | 6/5* 5/2 | eq: -0.194 (-0.124) |
| Player:
Opponent: |
42.53% (G:21.89% B:0.44%)
57.47% (G:20.47% B:0.85%) | Conf: ± 0.007 (-0.201...-0.187)
Duration: 31 minutes 32 seconds |
|
| 3. | Rollout1 | 13/10 11/10 | eq: -0.347 (-0.277) |
| Player:
Opponent: |
40.09% (G:14.64% B:0.23%)
59.91% (G:16.12% B:0.61%) | Conf: ± 0.007 (-0.354...-0.340)
Duration: 38 minutes 35 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Below is a rollout with the Jacoby rule turned off.
This is one of those rare positions where the Jacoby rule
makes a detectable difference.
With the Jacoby rule in force, 13/10 6/5* forces White
to double from the bar in order to reap the full benefit
of hitting back,
whereas without Jacoby, White can leave the cube in the center
and play on for a gammon when she hits back.
Thus 13/10 6/5* is relatively less attractive without Jacoby,
but it still rolls out way ahead of the alternatives.
| 1. | Rollout1 | 13/10 6/5* | eq: -0.132 |
| Player:
Opponent: |
42.60% (G:27.47% B:1.05%)
57.40% (G:30.01% B:3.66%) | Conf: ± 0.004 (-0.136...-0.128)
Duration: 20 minutes 53 seconds |
|
| 2. | Rollout1 | 6/5* 5/2 | eq: -0.215 (-0.083) |
| Player:
Opponent: |
42.63% (G:22.00% B:0.41%)
57.37% (G:21.45% B:0.79%) | Conf: ± 0.007 (-0.222...-0.208)
Duration: 40 minutes 09 seconds |
|
| 3. | Rollout1 | 13/10 11/10 | eq: -0.346 (-0.214) |
| Player:
Opponent: |
40.13% (G:14.59% B:0.21%)
59.87% (G:16.44% B:0.58%) | Conf: ± 0.006 (-0.352...-0.340)
Duration: 38 minutes 54 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
For reference, here is a rollout of White’s cube decision from the
bar after 13/10 6/5* if the Jacoby rule is in force:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 57.17% (G: 28.34% B: 3.05%) |
| Opponent Winning Chances: | 42.83% (G: 27.04% B: 1.08%) |
| Double/Take |
| Player Winning Chances: | 57.43% (G: 30.26% B: 3.70%) |
| Opponent Winning Chances: | 42.57% (G: 27.53% B: 1.10%) |
| |
| Cubeless Equities |
| No Double: | +0.143 |
| Double: | +0.404 |
| |
| Cubeful Equities |
| No Double: | -0.010 (-0.079) |
| Double/Take: | +0.068 |
| Double/Drop: | +1.000 (+0.932) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
2592 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.004 (-0.014...-0.007) |
| Confidence Double: | ± 0.008 (+0.060...+0.077) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 11 minutes 31 seconds |
And here is a rollout of White’s cube decision from the bar
after 13/10 6/5* if the Jacoby rule is not in force:
| Analyzed in Rollout |
| No Double |
| Player Winning
Chances: | 57.44% (G: 30.13% B: 3.63%) |
| Opponent Winning
Chances: | 42.56% (G: 27.52% B: 1.10%) |
| Double/Take |
| Player Winning
Chances: | 57.43% (G: 30.27% B: 3.70%) |
| Opponent Winning
Chances: | 42.57% (G: 27.53% B: 1.10%) |
| |
| Cubeless
Equities |
| No
Double: | +0.200 |
| Double: | +0.404 |
| |
| Cubeful
Equities |
| No Double: | +0.137 |
|
Double/Take: | +0.068 (-0.069) |
|
Double/Drop: | +1.000 (+0.863) |
| |
| Best Cube action: No Double /
Take |
| |
| Rollout
details |
2592
Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG
Roller |
| |
| Confidence No Double: | ±
0.005 (+0.132...+0.142) |
| Confidence Double: |
± 0.008 (+0.060...+0.077) |
| |
| Double Decision confidence: |
100.0% |
| Take Decision
confidence: | 100.0% |
| |
| Duration: 16 minutes 24
seconds |
Position 4
My play here was 6/5 6/4, which Wiggins does not even
mention as a candidate. It comes in second place in the XG rollout.
| 1. | Rollout1 | 24/22 6/5 | eq: -0.312 |
| Player:
Opponent: |
42.23% (G:6.92% B:0.25%)
57.77% (G:11.90% B:0.30%) | Conf: ± 0.006 (-0.318...-0.306)
Duration: 1 hour 53 minutes |
|
| 2. | Rollout1 | 6/5 6/4 | eq: -0.328 (-0.017) |
| Player:
Opponent: |
42.01% (G:8.60% B:0.31%)
57.99% (G:13.78% B:0.43%) | Conf: ± 0.007 (-0.335...-0.321)
Duration: 1 hour 49 minutes |
|
| 3. | Rollout1 | 24/23 6/4 | eq: -0.351 (-0.039) |
| Player:
Opponent: |
41.22% (G:8.04% B:0.29%)
58.78% (G:13.61% B:0.40%) | Conf: ± 0.006 (-0.357...-0.345)
Duration: 1 hour 28 minutes |
|
| 4. | Rollout1 | 16/15 6/4 | eq: -0.358 (-0.047) |
| Player:
Opponent: |
41.09% (G:8.34% B:0.31%)
58.91% (G:13.65% B:0.40%) | Conf: ± 0.006 (-0.364...-0.352)
Duration: 1 hour 31 minutes |
|
| 5. | Rollout1 | 16/13 | eq: -0.362 (-0.050) |
| Player:
Opponent: |
40.93% (G:6.35% B:0.22%)
59.07% (G:11.60% B:0.23%) | Conf: ± 0.006 (-0.368...-0.356)
Duration: 1 hour 28 minutes |
|
| 6. | Rollout1 | 24/21 | eq: -0.376 (-0.064) |
| Player:
Opponent: |
40.75% (G:5.43% B:0.21%)
59.25% (G:12.42% B:0.31%) | Conf: ± 0.006 (-0.382...-0.370)
Duration: 2 hours 32 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 14
A dramatic disagreement: the top play by a clear margin in the XG rollout is
not even mentioned by Wiggins!
| 1. | Rollout1 | 13/7 9/8 | eq: +0.130 |
| Player:
Opponent: |
53.66% (G:18.10% B:1.17%)
46.34% (G:18.37% B:1.98%) | Conf: ± 0.009 (+0.121...+0.139)
Duration: 41 minutes 04 seconds |
|
| 2. | Rollout1 | 13/6 | eq: +0.091 (-0.039) |
| Player:
Opponent: |
51.77% (G:19.36% B:1.36%)
48.23% (G:16.47% B:1.21%) | Conf: ± 0.008 (+0.083...+0.099)
Duration: 37 minutes 19 seconds |
|
| 3. | Rollout1 | 24/18 10/9 | eq: +0.071 (-0.059) |
| Player:
Opponent: |
53.95% (G:20.30% B:2.11%)
46.05% (G:22.03% B:0.65%) | Conf: ± 0.008 (+0.063...+0.079)
Duration: 35 minutes 53 seconds |
|
| 4. | Rollout1 | 24/23 10/4 | eq: -0.007 (-0.136) |
| Player:
Opponent: |
50.65% (G:19.68% B:1.65%)
49.35% (G:22.28% B:1.11%) | Conf: ± 0.009 (-0.016...+0.002)
Duration: 35 minutes 07 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
The play 13/7 9/8 is volatile enough that I thought the Jacoby rule
might be relevant. However, the rollout below
with the Jacoby rule turned off indicates that the Jacoby rule makes no
difference.
| 1. | Rollout1 | 13/7 9/8 | eq: +0.127 |
| Player:
Opponent: |
53.79% (G:18.04% B:1.17%)
46.21% (G:18.41% B:2.06%) | Conf: ± 0.009 (+0.118...+0.136)
Duration: 44 minutes 17 seconds |
|
| 2. | Rollout1 | 13/6 | eq: +0.091 (-0.037) |
| Player:
Opponent: |
51.75% (G:19.47% B:1.36%)
48.25% (G:16.55% B:1.22%) | Conf: ± 0.007 (+0.084...+0.098)
Duration: 40 minutes 32 seconds |
|
| 3. | Rollout1 | 24/18 10/9 | eq: +0.072 (-0.056) |
| Player:
Opponent: |
53.90% (G:20.42% B:2.14%)
46.10% (G:23.01% B:0.61%) | Conf: ± 0.008 (+0.064...+0.080)
Duration: 43 minutes 29 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 16
Wiggins does not mention 21/18 8/7*;
the XG rollout says that it is a top contender.
| 1. | Rollout1 | 13/10 8/7* | eq: +0.271 |
| Player:
Opponent: |
56.67% (G:17.65% B:0.89%)
43.33% (G:13.51% B:0.95%) | Conf: ± 0.008 (+0.263...+0.279)
Duration: 1 hour 11 minutes |
|
| 2. | Rollout1 | 21/18 8/7* | eq: +0.266 (-0.005) |
| Player:
Opponent: |
56.69% (G:16.75% B:0.82%)
43.31% (G:13.58% B:0.75%) | Conf: ± 0.008 (+0.258...+0.274)
Duration: 1 hour 10 minutes |
|
| 3. | Rollout1 | 8/7* 7/4 | eq: +0.238 (-0.033) |
| Player:
Opponent: |
55.40% (G:17.82% B:0.82%)
44.60% (G:12.57% B:0.57%) | Conf: ± 0.009 (+0.229...+0.247)
Duration: 1 hour 11 minutes |
|
| 4. | Rollout1 | 8/5 8/7* | eq: +0.218 (-0.053) |
| Player:
Opponent: |
55.05% (G:16.62% B:0.73%)
44.95% (G:12.30% B:0.55%) | Conf: ± 0.008 (+0.210...+0.226)
Duration: 1 hour 07 minutes |
|
| 5. | Rollout1 | 21/18 5/4 | eq: +0.217 (-0.054) |
| Player:
Opponent: |
55.92% (G:15.08% B:0.65%)
44.08% (G:13.22% B:0.46%) | Conf: ± 0.008 (+0.209...+0.225)
Duration: 1 hour 04 minutes |
|
| 6. | Rollout1 | 23/22 21/18 | eq: +0.200 (-0.071) |
| Player:
Opponent: |
55.54% (G:15.53% B:0.70%)
44.46% (G:13.74% B:0.46%) | Conf: ± 0.007 (+0.193...+0.207)
Duration: 1 hour 04 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 23 (variant)
This is a rollout of the variant position, mentioned by Wiggins,
in which White owns her 2pt instead of her midpoint.
In this variant, Wiggins recommends bar/24 13/10,
but XG prefers bar/24 6/3.
| 1. | Rollout1 | Bar/24 6/3 | eq: -0.251 |
| Player:
Opponent: |
45.07% (G:5.51% B:0.20%)
54.93% (G:15.00% B:0.23%) | Conf: ± 0.006 (-0.257...-0.245)
Duration: 40 minutes 44 seconds |
|
| 2. | Rollout1 | Bar/24 13/10 | eq: -0.324 (-0.073) |
| Player:
Opponent: |
43.32% (G:6.02% B:0.23%)
56.68% (G:18.42% B:0.26%) | Conf: ± 0.006 (-0.330...-0.318)
Duration: 36 minutes 48 seconds |
|
| 3. | Rollout1 | Bar/21 | eq: -0.365 (-0.114) |
| Player:
Opponent: |
42.32% (G:6.51% B:0.26%)
57.68% (G:21.38% B:0.20%) | Conf: ± 0.005 (-0.370...-0.360)
Duration: 30 minutes 20 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 24 (subsequent cube action)
This is a rollout of White’s doubling decision after
Black runs with 20/14. Wiggins implies that White does not
have a double, but XG says that it would be a whopper
for White not to double here.
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 70.15% (G: 10.83% B: 0.39%) |
| Opponent Winning Chances: | 29.85% (G: 3.31% B: 0.03%) |
| Double/Take |
| Player Winning Chances: | 70.67% (G: 11.80% B: 0.39%) |
| Opponent Winning Chances: | 29.33% (G: 3.81% B: 0.04%) |
| |
| Cubeless Equities |
| No Redouble: | +0.482 |
| Redouble: | +0.993 |
| |
| Cubeful Equities |
| No Redouble: | +0.766 (-0.121) |
| Redouble/Take: | +0.887 |
| Redouble/Drop: | +1.000 (+0.113) |
| |
| Best Cube action: Redouble / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Redouble: | ± 0.003 (+0.763...+0.769) |
| Confidence Redouble: | ± 0.005 (+0.882...+0.892) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 30 minutes 12 seconds |
Position 32
The only comment here is that 24/23 6/4* is a plausible candidate
not mentioned by Wiggins.
| 1. | Rollout1 | 11/10 6/4* | eq: +0.350 |
| Player:
Opponent: | 62.66% (G:28.96% B:3.61%)
37.34%
(G:7.37% B:0.34%) | Conf.:
± 0.006 (+0.344...+0.356) - [100.0%]
Duration: 4 hours 04
minutes |
|
| 2. | Rollout1 | 24/23 6/4* | eq: +0.328 (-0.022) |
| Player:
Opponent: | 62.49% (G:27.80% B:3.36%)
37.51%
(G:7.57% B:0.35%) | Conf.:
± 0.006 (+0.322...+0.334) - [0.0%]
Duration: 2 hours 39
minutes |
|
| 3. | Rollout1 | 6/4* 4/3 | eq: +0.306 (-0.043) |
| Player:
Opponent: | 60.85% (G:29.15% B:3.93%)
39.15%
(G:7.26% B:0.33%) | Conf.:
± 0.006 (+0.300...+0.313) - [0.0%]
Duration: 2 hours 37
minutes |
|
| |
1 5184 Games
rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG
Roller
|
Position 33
Contrary to what Wiggins says, XG thinks that 8/2* 4/2 is indeed
Black’s second-best play.
| 1. | Rollout1 | 24/16 | eq: -0.334 |
| Player:
Opponent: | 37.17% (G:9.45% B:0.51%)
62.83%
(G:31.20% B:0.87%) | Conf.:
± 0.004 (-0.338...-0.329) - [100.0%]
Duration: 26 minutes 58
seconds |
|
| 2. | Rollout1 | 8/2* 4/2 | eq: -0.390 (-0.056) |
| Player:
Opponent: | 32.99% (G:6.97% B:0.20%)
67.01%
(G:22.89% B:1.16%) | Conf.:
± 0.004 (-0.394...-0.386) - [0.0%]
Duration: 23 minutes 41
seconds |
|
| 3. | Rollout1 | 24/18 4/2* | eq: -0.413 (-0.080) |
| Player:
Opponent: | 35.61% (G:6.94% B:0.31%)
64.39%
(G:32.17% B:1.42%) | Conf.:
± 0.004 (-0.417...-0.409) - [0.0%]
Duration: 27 minutes 20
seconds |
|
| |
1 5184 Games
rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG
Roller
|
Position 35
No real disagreement here but a long rollout indicates
that XG thinks the top two plays are even closer than
Jellyfish thinks.
| 1. | Rollout1 | 24/21 6/4* | eq: +0.130 |
| Player:
Opponent: |
53.42% (G:16.01% B:0.85%)
46.58% (G:14.78% B:0.85%) | Conf: ± 0.004 (+0.126...+0.134)
Duration: 5 hours 31 minutes |
|
| 2. | Rollout1 | 13/10 6/4* | eq: +0.118 (-0.012) |
| Player:
Opponent: |
53.14% (G:17.15% B:0.91%)
46.86% (G:15.66% B:1.18%) | Conf: ± 0.005 (+0.113...+0.123)
Duration: 5 hours 22 minutes |
|
| 3. | Rollout2 | 6/4* 4/1* | eq: +0.051 (-0.079) |
| Player:
Opponent: |
50.73% (G:17.22% B:0.69%)
49.27% (G:14.83% B:0.82%) | Conf: ± 0.008 (+0.043...+0.059)
Duration: 1 hour 19 minutes |
|
| |
1 20736 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 40
Though XG does favor 5/2 3/2 over 10/6*, it is by a much smaller margin,
and its estimated cubeless statistics differ quite a bit from
Jellyfish’s.
| 1. | Rollout1 | 5/2 3/2 | eq: -0.400 |
| Player:
Opponent: | 40.18% (G:5.53% B:0.06%)
59.82%
(G:13.73% B:0.36%) | Conf.:
± 0.005 (-0.405...-0.395) - [100.0%]
Duration: 25 minutes 35
seconds |
|
| 2. | Rollout1 | 10/6* | eq: -0.424 (-0.024) |
| Player:
Opponent: | 41.49% (G:9.62% B:0.13%)
58.51%
(G:30.19% B:0.78%) | Conf.:
± 0.007 (-0.431...-0.417) - [0.0%]
Duration: 15 minutes 48
seconds |
|
| |
1 5184 Games
rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG
Roller
|
Position 42 (variant)
This is a rollout of the variant position mentioned by Wiggins,
in which we shift White’s 9pt forwards to the 8pt to make
a solid five-prime. Wiggins says that the decision whether to
hit “would be truly close…too close for comfort.”
However, the XG rollout below says that hitting would still be
very clear.
| 1. | Rollout1 | 11/5 4/3* | eq: +0.618 |
| Player:
Opponent: |
64.70% (G:43.98% B:8.27%)
35.30% (G:3.76% B:0.18%) | Conf: ± 0.005 (+0.613...+0.623)
Duration: 33 minutes 19 seconds |
|
| 2. | Rollout1 | 13/7 4/3* | eq: +0.582 (-0.036) |
| Player:
Opponent: |
64.02% (G:43.48% B:8.13%)
35.98% (G:4.99% B:0.38%) | Conf: ± 0.005 (+0.577...+0.587)
Duration: 30 minutes 08 seconds |
|
| 3. | Rollout1 | 10/3* | eq: +0.553 (-0.065) |
| Player:
Opponent: |
62.96% (G:42.40% B:8.00%)
37.04% (G:4.34% B:0.20%) | Conf: ± 0.005 (+0.548...+0.558)
Duration: 31 minutes 33 seconds |
|
| 4. | Rollout1 | 13/12 11/5 | eq: +0.513 (-0.105) |
| Player:
Opponent: |
62.28% (G:38.25% B:6.65%)
37.72% (G:1.34% B:0.05%) | Conf: ± 0.005 (+0.508...+0.518)
Duration: 32 minutes 55 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 45 (variant)
If we move two of White’s checkers from her 8pt to her 7pt,
then Wiggins says that 14/4 should be the top play.
XG concurs, but just barely.
| 1. | Rollout1 | 14/4 | eq: +0.922 |
| Player:
Opponent: | 81.60% (G:37.53% B:0.67%)
18.40%
(G:2.60% B:0.10%) | Conf.:
± 0.003 (+0.918...+0.925) - [96.6%]
Duration: 24 minutes 20
seconds |
|
| 2. | Rollout1 | 14/8 6/2* | eq: +0.917 (-0.005) |
| Player:
Opponent: | 76.93% (G:51.76% B:1.00%)
23.07%
(G:5.97% B:0.29%) | Conf.:
± 0.004 (+0.913...+0.921) - [3.4%]
Duration: 24 minutes 02
seconds |
|
| |
1 5184 Games
rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG
Roller
|
Position 46
The main point here is that the XG rollout says that bar/22 6/4
is second best, but Wiggins does not mention it as a candidate.
| 1. | Rollout1 | Bar/23 24/21 | eq: +0.238 |
| Player:
Opponent: |
55.28% (G:17.06% B:0.73%)
44.72% (G:10.47% B:0.48%) | Conf: ± 0.008 (+0.230...+0.246)
Duration: 1 hour 24 minutes |
|
| 2. | Rollout1 | Bar/22 6/4 | eq: +0.220 (-0.018) |
| Player:
Opponent: |
55.10% (G:16.14% B:0.68%)
44.90% (G:10.40% B:0.46%) | Conf: ± 0.008 (+0.212...+0.228)
Duration: 1 hour 19 minutes |
|
| 3. | Rollout1 | Bar/20 | eq: +0.210 (-0.027) |
| Player:
Opponent: |
54.76% (G:15.94% B:0.67%)
45.24% (G:10.84% B:0.50%) | Conf: ± 0.009 (+0.201...+0.219)
Duration: 1 hour 21 minutes |
|
| 4. | Rollout1 | Bar/22 8/6 | eq: +0.192 (-0.046) |
| Player:
Opponent: |
54.38% (G:15.31% B:0.63%)
45.62% (G:10.22% B:0.43%) | Conf: ± 0.008 (+0.184...+0.200)
Duration: 1 hour 16 minutes |
|
| 5. | Rollout1 | Bar/23 7/4 | eq: +0.189 (-0.049) |
| Player:
Opponent: |
54.19% (G:16.77% B:0.82%)
45.81% (G:12.00% B:0.65%) | Conf: ± 0.008 (+0.181...+0.197)
Duration: 1 hour 30 minutes |
|
| 6. | Rollout1 | Bar/22 7/5 | eq: +0.173 (-0.065) |
| Player:
Opponent: |
53.87% (G:15.08% B:0.63%)
46.13% (G:10.45% B:0.45%) | Conf: ± 0.008 (+0.165...+0.181)
Duration: 1 hour 30 minutes |
|
| 7. | Rollout1 | Bar/22 24/22 | eq: +0.171 (-0.067) |
| Player:
Opponent: |
53.95% (G:14.45% B:0.62%)
46.05% (G:10.17% B:0.38%) | Conf: ± 0.008 (+0.163...+0.179)
Duration: 1 hour 28 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 52 (subsequent cube action)
Wiggins implies that if White comes in with just one checker on the 3pt,
White can take Black’s double. However, the XG rollout says that
it is a drop:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 68.13% (G: 34.84% B: 0.61%) |
| Opponent Winning Chances: | 31.87% (G: 8.61% B: 0.33%) |
| Double/Take |
| Player Winning Chances: | 68.21% (G: 37.68% B: 0.60%) |
| Opponent Winning Chances: | 31.79% (G: 9.23% B: 0.43%) |
| |
| Cubeless Equities |
| No Double: | +0.363 |
| Double: | +1.301 |
| |
| Cubeful Equities |
| No Double: | +0.678 (-0.322) |
| Double/Take: | +1.061 (+0.061) |
| Double/Drop: | +1.000 |
| |
| Best Cube action: Double / Drop |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.005 (+0.674...+0.683) |
| Confidence Double: | ± 0.008 (+1.053...+1.069) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 26 minutes 52 seconds |
Similarly, Wiggins implies that if White rolls 5-3 and enters both
checkers, then Black does not have a double.
However, the XG rollout says that Black does have a double:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 61.56% (G: 26.03% B: 0.53%) |
| Opponent Winning Chances: | 38.44% (G: 10.85% B: 0.41%) |
| Double/Take |
| Player Winning Chances: | 61.76% (G: 27.64% B: 0.53%) |
| Opponent Winning Chances: | 38.24% (G: 11.46% B: 0.53%) |
| |
| Cubeless Equities |
| No Double: | +0.231 |
| Double: | +0.794 |
| |
| Cubeful Equities |
| No Double: | +0.460 (-0.052) |
| Double/Take: | +0.512 |
| Double/Drop: | +1.000 (+0.488) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.006 (+0.453...+0.466) |
| Confidence Double: | ± 0.009 (+0.503...+0.521) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 35 minutes |
Position 55
Slotting with 6/5 comes in second place in the XG rollout
but Wiggins does not mention it as a candidate.
| 1. | Rollout1 | Bar/20 24/23 | eq: -0.215 |
| Player:
Opponent: |
45.19% (G:11.43% B:0.51%)
54.81% (G:16.18% B:0.73%) | Conf: ± 0.008 (-0.223...-0.207)
Duration: 2 hours 22 minutes |
|
| 2. | Rollout1 | Bar/20 6/5 | eq: -0.240 (-0.025) |
| Player:
Opponent: |
45.62% (G:11.91% B:0.64%)
54.38% (G:19.26% B:1.22%) | Conf: ± 0.009 (-0.249...-0.231)
Duration: 1 hour 49 minutes |
|
| 3. | Rollout1 | Bar/20 11/10 | eq: -0.252 (-0.037) |
| Player:
Opponent: |
44.37% (G:11.32% B:0.55%)
55.63% (G:16.82% B:0.85%) | Conf: ± 0.008 (-0.260...-0.244)
Duration: 2 hours 25 minutes |
|
| 4. | Rollout1 | Bar/24 13/8 | eq: -0.291 (-0.076) |
| Player:
Opponent: |
43.13% (G:12.18% B:0.57%)
56.87% (G:17.18% B:1.00%) | Conf: ± 0.008 (-0.299...-0.283)
Duration: 3 hours 13 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 59 (variant)
This is a rollout of the variant position in which
White’s 6pt spare has been moved forward one pip
to make her 5pt. Wiggins says that in this variant,
10/6 8/3* would be correct, but XG still prefers the double hit.
| 1. | Rollout1 | 8/3* 5/1* | eq: +0.368 |
| Player:
Opponent: |
61.74% (G:38.94% B:1.72%)
38.26% (G:10.21% B:0.59%) | Conf: ± 0.007 (+0.361...+0.375)
Duration: 1 hour 07 minutes |
|
| 2. | Rollout1 | 22/18 8/3* | eq: +0.339 (-0.029) |
| Player:
Opponent: |
60.69% (G:35.59% B:2.51%)
39.31% (G:7.83% B:0.39%) | Conf: ± 0.006 (+0.333...+0.345)
Duration: 1 hour 02 minutes |
|
| 3. | Rollout1 | 22/13 | eq: +0.337 (-0.031) |
| Player:
Opponent: |
61.06% (G:32.84% B:1.80%)
38.94% (G:6.11% B:0.24%) | Conf: ± 0.006 (+0.331...+0.343)
Duration: 1 hour 08 minutes |
|
| 4. | Rollout1 | 10/1* | eq: +0.335 (-0.033) |
| Player:
Opponent: |
60.67% (G:36.21% B:1.40%)
39.33% (G:8.36% B:0.37%) | Conf: ± 0.006 (+0.329...+0.341)
Duration: 1 hour 04 minutes |
|
| 5. | Rollout1 | 10/6 8/3* | eq: +0.332 (-0.036) |
| Player:
Opponent: |
59.85% (G:37.30% B:2.66%)
40.15% (G:8.28% B:0.43%) | Conf: ± 0.006 (+0.326...+0.338)
Duration: 57 minutes 29 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 60
The XG rollout seems to slightly favor hitting over anchoring.
| 1. | Rollout1 | 24/21 8/7* | eq: -0.077 |
| Player:
Opponent: |
46.35% (G:19.21% B:0.87%)
53.65% (G:16.31% B:1.21%) | Conf: ± 0.008 (-0.085...-0.069)
Duration: 55 minutes 32 seconds |
|
| 2. | Rollout1 | 24/21 22/21 | eq: -0.092 (-0.014) |
| Player:
Opponent: |
46.40% (G:13.11% B:0.31%)
53.60% (G:9.05% B:0.39%) | Conf: ± 0.007 (-0.099...-0.085)
Duration: 1 hour 05 minutes |
|
| 3. | Rollout1 | 8/7* 7/4 | eq: -0.144 (-0.067) |
| Player:
Opponent: |
44.22% (G:20.04% B:0.82%)
55.78% (G:15.99% B:1.00%) | Conf: ± 0.008 (-0.152...-0.136)
Duration: 54 minutes 10 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 72
XG prefers making the 5pt to the pick-and-pass play.
| 1. | Rollout1 | 9/5 8/5 | eq: -0.339 |
| Player:
Opponent: |
40.54% (G:6.90% B:0.21%)
59.46% (G:9.11% B:0.34%) | Conf: ± 0.006 (-0.345...-0.333)
Duration: 1 hour 22 minutes |
|
| 2. | Rollout1 | 18/15* 15/11 | eq: -0.367 (-0.028) |
| Player:
Opponent: |
41.69% (G:10.39% B:0.47%)
58.31% (G:17.42% B:0.94%) | Conf: ± 0.008 (-0.375...-0.359)
Duration: 1 hour 32 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 80
XG demotes Jellyfish’s choice to third place,
and thinks the non-hitting 24/18 10/6 is a top contender.
| 1. | Rollout1 | 18/14 18/12* | eq: +0.598 |
| Player:
Opponent: |
64.06% (G:19.87% B:0.82%)
35.94% (G:9.21% B:0.72%) | Conf: ± 0.007 (+0.591...+0.605)
Duration: 36 minutes 37 seconds |
|
| 2. | Rollout1 | 24/18 10/6 | eq: +0.594 (-0.004) |
| Player:
Opponent: |
65.85% (G:9.67% B:0.28%)
34.15% (G:6.27% B:0.23%) | Conf: ± 0.006 (+0.588...+0.600)
Duration: 44 minutes 27 seconds |
|
| 3. | Rollout1 | 24/20 18/12* | eq: +0.560 (-0.038) |
| Player:
Opponent: |
62.82% (G:20.95% B:1.01%)
37.18% (G:11.88% B:1.12%) | Conf: ± 0.007 (+0.553...+0.567)
Duration: 29 minutes 49 seconds |
|
| 4. | Rollout2 | 18/12* 10/6 | eq: +0.468 (-0.130) |
| Player:
Opponent: |
60.92% (G:20.80% B:0.94%)
39.08% (G:10.28% B:0.60%) | Conf: ± 0.014 (+0.454...+0.482)
Duration: 8 minutes 39 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
2 1296 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 84
XG agrees that 24/22 24/21 and 24/22 8/5 and 24/21 9/7 are close,
but it has a definite preference for 24/22 24/21.
| 1. | Rollout1 | 24/22 24/21 | eq: +0.179 |
| Player:
Opponent: | 62.02% (G:19.14% B:1.18%)
37.98%
(G:11.55% B:0.51%) | Conf.:
± 0.005 (+0.174...+0.184) - [100.0%]
Duration: 47 minutes 10
seconds |
|
| 2. | Rollout1 | 24/22 8/5 | eq: +0.163 (-0.016) |
| Player:
Opponent: | 61.43% (G:19.02% B:1.11%)
38.57%
(G:11.34% B:0.48%) | Conf.:
± 0.005 (+0.158...+0.168) - [0.0%]
Duration: 44 minutes 12
seconds |
|
| 3. | Rollout1 | 24/21 9/7 | eq: +0.162 (-0.016) |
| Player:
Opponent: | 61.18% (G:19.94% B:1.19%)
38.82%
(G:11.66% B:0.56%) | Conf.:
± 0.005 (+0.157...+0.168) - [0.0%]
Duration: 46 minutes 17
seconds |
|
| 4. | Rollout1 | 24/22 9/6 | eq: +0.142 (-0.037) |
| Player:
Opponent: | 60.85% (G:18.03% B:1.03%)
39.15%
(G:11.15% B:0.40%) | Conf.:
± 0.005 (+0.137...+0.147) - [0.0%]
Duration: 38 minutes 04
seconds |
|
| 5. | Rollout1 | 24/21 6/4 | eq: +0.139 (-0.040) |
| Player:
Opponent: | 60.85% (G:20.47% B:1.29%)
39.15%
(G:13.37% B:0.92%) | Conf.:
± 0.006 (+0.133...+0.145) - [0.0%]
Duration: 48 minutes 31
seconds |
|
| 6. | Rollout1 | 24/21 8/6 | eq: +0.118 (-0.061) |
| Player:
Opponent: | 59.91% (G:18.95% B:1.10%)
40.09%
(G:12.06% B:0.51%) | Conf.:
± 0.005 (+0.113...+0.123) - [0.0%]
Duration: 43 minutes 23
seconds |
|
| 7. | Rollout1 | 9/4 | eq: +0.095 (-0.084) |
| Player:
Opponent: | 59.18% (G:18.40% B:1.01%)
40.82%
(G:11.90% B:0.59%) | Conf.:
± 0.006 (+0.090...+0.101) - [0.0%]
Duration: 41 minutes 26
seconds |
|
| 8. | Rollout1 | 24/22 13/10 | eq: +0.088 (-0.090) |
| Player:
Opponent: | 59.03% (G:19.54% B:1.32%)
40.97%
(G:13.26% B:1.07%) | Conf.:
± 0.005 (+0.083...+0.093) - [0.0%]
Duration: 44 minutes 25
seconds |
|
| |
1 5184 Games
rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG
Roller
|
Position 85
After Black closes his board, he has an immediate redouble,
which Wiggins says White can take.
The XG rollout says that White’s decision is right on the
take/drop borderline.
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 71.68% (G: 18.63% B: 0.04%) |
| Opponent Winning Chances: | 28.32% (G: 3.32% B: 0.12%) |
| Double/Take |
| Player Winning Chances: | 71.92% (G: 19.79% B: 0.04%) |
| Opponent Winning Chances: | 28.08% (G: 3.47% B: 0.12%) |
| |
| Cubeless Equities |
| No Redouble: | +0.586 |
| Redouble: | +1.202 |
| |
| Cubeful Equities |
| No Redouble: | +0.819 (-0.174) |
| Redouble/Take: | +0.993 |
| Redouble/Drop: | +1.000 (+0.007) |
| |
| Best Cube action: Redouble / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Redouble: | ± 0.002 (+0.817...+0.822) |
| Confidence Redouble: | ± 0.005 (+0.987...+0.998) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 99.5% |
| |
| Duration: 15 minutes 23 seconds |
Position 86
To trick XG into rolling this position out, I put Black’s two
rearmost checkers on the bar, moved White’s checker on the bar
to Black’s 17pt, and gave Black a roll of 4-4.
XG thinks that 13/9 is only slightly better, and not
“much better,” than 21/17.
| 1. | Rollout1 | Bar/21 Bar/17* 13/9 | eq: +0.557 |
| Player:
Opponent: | 70.81% (G:29.13% B:3.21%)
29.19%
(G:7.24% B:0.18%) | Conf.:
± 0.006 (+0.551...+0.563) - [98.1%]
Duration: 58 minutes 19
seconds |
|
| 2. | Rollout1 | Bar/17*(2) | eq: +0.549 (-0.008) |
| Player:
Opponent: | 71.74% (G:26.47% B:2.33%)
28.26%
(G:6.84% B:0.18%) | Conf.:
± 0.005 (+0.544...+0.554) - [1.9%]
Duration: 54 minutes 48
seconds |
|
| 3. | Rollout1 | Bar/21 Bar/17* 17/13 | eq: +0.481 (-0.076) |
| Player:
Opponent: | 68.81% (G:27.76% B:2.98%)
31.19%
(G:8.12% B:0.19%) | Conf.:
± 0.005 (+0.476...+0.487) - [0.0%]
Duration: 55 minutes 55
seconds |
|
| |
1 5184 Games
rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG
Roller
|
Position 89
XG favors 8/3 7/1, the move that Wiggins suspects “most good players
would choose,” and demotes Jellyfish’s 22/16 8/3 to 6th place.
Note: There are several other uninteresting plays that come out ahead
of 22/16 14/9 but that are not displayed here.
| 1. | Rollout1 | 8/3 7/1 | eq: -0.286 |
| Player:
Opponent: |
32.26% (G:4.40% B:0.11%)
67.74% (G:5.66% B:0.10%) | Conf: ± 0.003 (-0.289...-0.283)
Duration: 18 minutes 00 second |
|
| 2. | Rollout1 | 14/3 | eq: -0.328 (-0.042) |
| Player:
Opponent: |
30.53% (G:2.70% B:0.04%)
69.47% (G:4.04% B:0.07%) | Conf: ± 0.002 (-0.330...-0.326)
Duration: 15 minutes 32 seconds |
|
| 3. | Rollout1 | 14/9 7/1 | eq: -0.346 (-0.060) |
| Player:
Opponent: |
29.86% (G:3.09% B:0.06%)
70.14% (G:4.51% B:0.23%) | Conf: ± 0.002 (-0.348...-0.344)
Duration: 15 minutes 03 seconds |
|
| 4. | Rollout1 | 7/1 6/1 | eq: -0.351 (-0.065) |
| Player:
Opponent: |
30.22% (G:4.41% B:0.11%)
69.78% (G:8.32% B:0.36%) | Conf: ± 0.003 (-0.354...-0.348)
Duration: 16 minutes 59 seconds |
|
| 5. | Rollout1 | 14/9 8/2 | eq: -0.360 (-0.075) |
| Player:
Opponent: |
28.96% (G:2.20% B:0.05%)
71.04% (G:3.96% B:0.09%) | Conf: ± 0.002 (-0.362...-0.358)
Duration: 14 minutes 50 seconds |
|
| 6. | Rollout1 | 22/16 8/3 | eq: -0.364 (-0.078) |
| Player:
Opponent: |
35.55% (G:9.26% B:0.28%)
64.45% (G:22.79% B:0.65%) | Conf: ± 0.003 (-0.367...-0.361)
Duration: 22 minutes 56 seconds |
|
| 7. | Rollout1 | 14/8 7/2 | eq: -0.370 (-0.084) |
| Player:
Opponent: |
28.78% (G:2.51% B:0.06%)
71.22% (G:4.80% B:0.12%) | Conf: ± 0.002 (-0.372...-0.368)
Duration: 13 minutes 26 seconds |
|
| 8. | Rollout1 | 22/16 14/9 | eq: -0.460 (-0.174) |
| Player:
Opponent: |
31.73% (G:7.92% B:0.25%)
68.27% (G:23.47% B:0.73%) | Conf: ± 0.003 (-0.463...-0.457)
Duration: 20 minutes 26 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 92
XG prefers making the 3pt to hitting with 24/18* 13/10.
| 1. | Rollout1 | 9/3 6/3 | eq: +0.459 |
| Player:
Opponent: |
60.89% (G:20.15% B:1.47%)
39.11% (G:19.13% B:2.94%) | Conf: ± 0.008 (+0.451...+0.467)
Duration: 50 minutes 13 seconds |
|
| 2. | Rollout1 | 24/18* 13/10 | eq: +0.420 (-0.039) |
| Player:
Opponent: |
58.97% (G:21.28% B:1.68%)
41.03% (G:21.76% B:2.25%) | Conf: ± 0.009 (+0.411...+0.429)
Duration: 58 minutes 29 seconds |
|
| 3. | Rollout2 | 24/18* 10/7 | eq: +0.384 (-0.075) |
| Player:
Opponent: |
57.92% (G:20.25% B:1.54%)
42.08% (G:21.16% B:1.54%) | Conf: ± 0.015 (+0.369...+0.399)
Duration: 15 minutes 05 seconds |
|
| 4. | Rollout2 | 24/18* 18/15 | eq: +0.366 (-0.093) |
| Player:
Opponent: |
57.53% (G:20.96% B:1.69%)
42.47% (G:23.54% B:2.39%) | Conf: ± 0.017 (+0.349...+0.383)
Duration: 14 minutes 40 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
2 1296 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 93 (subsequent cube action)
Wiggins says that anchoring will provoke a double from White
whereas the hit will not.
The XG rollouts indicate that both doubling decisions are close,
but that if anything, it is the other way around.
If the XG rollouts are correct,
then we have here an example of a cube provocation play,
where the play that provokes a cube is to be preferred over
the play that does not provoke the cube.
White’s cube decision after Black hits on the 18pt:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 61.47% (G: 24.69% B: 0.89%) |
| Opponent Winning Chances: | 38.53% (G: 8.85% B: 0.54%) |
| Double/Take |
| Player Winning Chances: | 61.40% (G: 26.60% B: 0.94%) |
| Opponent Winning Chances: | 38.60% (G: 9.40% B: 0.60%) |
| |
| Cubeless Equities |
| No Double: | +0.229 |
| Double: | +0.807 |
| |
| Cubeful Equities |
| No Double: | +0.509 (-0.004) |
| Double/Take: | +0.513 |
| Double/Drop: | +1.000 (+0.487) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.007 (+0.503...+0.516) |
| Confidence Double: | ± 0.010 (+0.504...+0.523) |
| |
| Double Decision confidence: | 75.7% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 25 minutes |
White’s cube decision after Black anchors:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 70.02% (G: 11.52% B: 0.27%) |
| Opponent Winning Chances: | 29.98% (G: 3.98% B: 0.15%) |
| Double/Take |
| Player Winning Chances: | 70.06% (G: 11.55% B: 0.28%) |
| Opponent Winning Chances: | 29.94% (G: 4.07% B: 0.16%) |
| |
| Cubeless Equities |
| No Double: | +0.400 |
| Double: | +0.954 |
| |
| Cubeful Equities |
| No Double: | +0.766 |
| Double/Take: | +0.753 (-0.013) |
| Double/Drop: | +1.000 (+0.234) |
| |
| Best Cube action: No Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.007 (+0.759...+0.773) |
| Confidence Double: | ± 0.007 (+0.745...+0.760) |
| |
| Double Decision confidence: | 99.6% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 34 minutes |
Position 94 (subsequent cube action)
Wiggins implies that after Black’s play,
if White enters a checker,
then White will be able to take Black’s double.
However, here is the XG rollout of Black’s cube decision
after White enters one checker on Black’s 4pt:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 65.28% (G: 48.46% B: 0.44%) |
| Opponent Winning Chances: | 34.72% (G: 7.71% B: 0.43%) |
| Double/Take |
| Player Winning Chances: | 66.63% (G: 50.77% B: 0.40%) |
| Opponent Winning Chances: | 33.37% (G: 8.35% B: 0.58%) |
| |
| Cubeless Equities |
| No Double: | +0.306 |
| Double: | +1.510 |
| |
| Cubeful Equities |
| No Double: | +0.712 (-0.288) |
| Double/Take: | +1.234 (+0.234) |
| Double/Drop: | +1.000 |
| |
| Best Cube action: Double / Drop |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.006 (+0.706...+0.718) |
| Confidence Double: | ± 0.010 (+1.224...+1.245) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 47 minutes 07 seconds |
Position 100
XG favors hitting with 8/7* over 6/5.
| 1. | Rollout1 | Bar/21 8/7* | eq: -0.629 |
| Player:
Opponent: |
38.77% (G:8.88% B:0.46%)
61.23% (G:29.74% B:4.41%) | Conf: ± 0.012 (-0.641...-0.617)
Duration: 1 hour 05 minutes |
|
| 2. | Rollout1 | Bar/21 6/5 | eq: -0.675 (-0.046) |
| Player:
Opponent: |
35.42% (G:7.92% B:0.35%)
64.58% (G:24.64% B:2.32%) | Conf: ± 0.010 (-0.685...-0.665)
Duration: 58 minutes 07 seconds |
|
| 3. | Rollout1 | Bar/21 24/23 | eq: -0.789 (-0.160) |
| Player:
Opponent: |
34.68% (G:7.95% B:0.35%)
65.32% (G:29.18% B:1.67%) | Conf: ± 0.010 (-0.799...-0.779)
Duration: 52 minutes 18 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Wiggins says that 6/5
“staves off White’s double”
but the XG rollout says that it may be a marginal double:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 64.60% (G: 24.44% B: 2.19%) |
| Opponent Winning Chances: | 35.40% (G: 7.85% B: 0.34%) |
| Double/Take |
| Player Winning Chances: | 64.67% (G: 24.60% B: 2.31%) |
| Opponent Winning Chances: | 35.33% (G: 7.96% B: 0.36%) |
| |
| Cubeless Equities |
| No Double: | +0.292 |
| Double: | +0.959 |
| |
| Cubeful Equities |
| No Double: | +0.667 (-0.007) |
| Double/Take: | +0.674 |
| Double/Drop: | +1.000 (+0.326) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.008 (+0.659...+0.674) |
| Confidence Double: | ± 0.010 (+0.663...+0.684) |
| |
| Double Decision confidence: | 85.7% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 43 minutes |
For comparison, here is the rollout for White’s cube action after 8/7*:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 61.40% (G: 29.44% B: 3.95%) |
| Opponent Winning Chances: | 38.60% (G: 8.85% B: 0.41%) |
| Double/Take |
| Player Winning Chances: | 61.36% (G: 29.69% B: 4.29%) |
| Opponent Winning Chances: | 38.64% (G: 8.91% B: 0.45%) |
| |
| Cubeless Equities |
| No Double: | +0.228 |
| Double: | +0.947 |
| |
| Cubeful Equities |
| No Double: | +0.598 (-0.026) |
| Double/Take: | +0.624 |
| Double/Drop: | +1.000 (+0.376) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.009 (+0.589...+0.606) |
| Confidence Double: | ± 0.012 (+0.611...+0.636) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 58 minutes |
Position 102
Wiggins accepts Jellyfish’s verdict that 18/9 and 13/4 are tied,
but XG clearly favors 18/9, and it even ranks 18/15 13/7 (which Wiggins
does not mention as a candidate) ahead of 13/4.
| 1. | Rollout1 | 18/9 | eq: +0.368 |
| Player:
Opponent: |
67.26% (G:20.12% B:0.84%)
32.74% (G:6.00% B:0.21%) | Conf: ± 0.010 (+0.358...+0.378)
Duration: 13 minutes 28 seconds |
|
| 2. | Rollout1 | 18/15 13/7 | eq: +0.339 (-0.029) |
| Player:
Opponent: |
66.45% (G:19.98% B:0.79%)
33.55% (G:6.54% B:0.24%) | Conf: ± 0.010 (+0.329...+0.349)
Duration: 12 minutes 55 seconds |
|
| 3. | Rollout1 | 13/4 | eq: +0.324 (-0.044) |
| Player:
Opponent: |
66.21% (G:19.60% B:0.58%)
33.79% (G:6.17% B:0.24%) | Conf: ± 0.010 (+0.314...+0.334)
Duration: 12 minutes 43 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 105
There is only a small discrepancy here, but
XG thinks that the break-even point occurs when White’s outfield
blot is shifted forwards two pips, to White’s 8pt.
Rollout of original position:
| 1. | Rollout1 | 6/4 6/3 | eq: +0.914 |
| Player:
Opponent: |
92.00% (G:9.36% B:0.23%)
8.00% (G:0.00% B:0.00%) | Conf: ± 0.001 (+0.913...+0.915)
Duration: 4 minutes 18 seconds |
|
| 2. | Rollout1 | 3/0ff 2/0ff | eq: +0.900 (-0.014) |
| Player:
Opponent: |
88.93% (G:15.14% B:0.49%)
11.07% (G:0.00% B:0.00%) | Conf: ± 0.001 (+0.899...+0.901)
Duration: 4 minutes 47 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Rollout of variant in which White’s 10pt checker is moved to her 8pt:
| 1. | Rollout1 | 6/4 6/3 | eq: +0.920 |
| Player:
Opponent: |
92.84% (G:8.10% B:0.17%)
7.16% (G:0.00% B:0.00%) | Conf: ± 0.001 (+0.919...+0.921)
Duration: 4 minutes 09 seconds |
|
| 2. | Rollout1 | 3/0ff 2/0ff | eq: +0.919 (-0.001) |
| Player:
Opponent: |
89.95% (G:14.74% B:0.45%)
10.05% (G:0.00% B:0.00%) | Conf: ± 0.002 (+0.917...+0.921)
Duration: 4 minutes 26 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 109
Wiggins does not mention 13/7 8/4*, which the XG rollout
thinks is a contender for first place.
| 1. | Rollout1 | 15/9 8/4* | eq: -0.474 |
| Player:
Opponent: |
37.90% (G:11.54% B:0.22%)
62.10% (G:17.32% B:1.10%) | Conf: ± 0.007 (-0.481...-0.467)
Duration: 1 hour 03 minutes |
|
| 2. | Rollout1 | 13/7 8/4* | eq: -0.474 |
| Player:
Opponent: |
38.20% (G:12.04% B:0.27%)
61.80% (G:19.61% B:1.52%) | Conf: ± 0.008 (-0.482...-0.466)
Duration: 1 hour 04 minutes |
|
| 3. | Rollout1 | 15/9 13/9 | eq: -0.578 (-0.103) |
| Player:
Opponent: |
34.57% (G:8.84% B:0.19%)
65.43% (G:14.45% B:0.75%) | Conf: ± 0.007 (-0.585...-0.571)
Duration: 1 hour 02 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 110
No disagreement here about the top play,
but XG thinks the second-best play is bar/22 8/7,
which Wiggins does not mention as a candidate play at all.
| 1. | Rollout1 | Bar/22 24/23 | eq: -0.445 |
| Player:
Opponent: | 39.29% (G:10.08% B:0.43%)
60.71%
(G:17.06% B:0.97%) | Conf.:
± 0.009 (-0.454...-0.436) - [100.0%]
Duration: 7 hours 06
minutes |
|
| 2. | Rollout1 | Bar/22 8/7 | eq: -0.497 (-0.052) |
| Player:
Opponent: | 37.94% (G:10.04% B:0.45%)
62.06%
(G:18.07% B:1.23%) | Conf.:
± 0.008 (-0.505...-0.489) - [0.0%]
Duration: 6 hours 53
minutes |
|
| 3. | Rollout1 | Bar/21 | eq: -0.512 (-0.067) |
| Player:
Opponent: | 37.80% (G:9.66% B:0.40%)
62.20%
(G:18.60% B:1.36%) | Conf.:
± 0.008 (-0.520...-0.504) - [0.0%]
Duration: 6 hours 48
minutes |
|
| 4. | Rollout1 | Bar/22 6/5 | eq: -0.541 (-0.096) |
| Player:
Opponent: | 38.48% (G:9.70% B:0.47%)
61.52%
(G:21.67% B:1.91%) | Conf.:
± 0.009 (-0.550...-0.531) - [0.0%]
Duration: 7 hours 06
minutes |
|
| |
1 5184 Games
rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG
Roller
|
Position 114 (variant)
Wiggins says that after 6/4*(2) 3/1*(2),
“White won’t be able to take the cube that is coming next turn
unless he enters with 5-5, 3-3, or 2-2.”
However, here for example is an XG rollout of Black’s cube decision
if White rolls 3-2 and enters with bar/23 bar/22:
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 60.78% (G: 30.68% B: 1.82%) |
| Opponent Winning Chances: | 39.22% (G: 10.09% B: 0.54%) |
| Double/Take |
| Player Winning Chances: | 61.09% (G: 31.63% B: 2.30%) |
| Opponent Winning Chances: | 38.91% (G: 10.28% B: 0.54%) |
| |
| Cubeless Equities |
| No Double: | +0.216 |
| Double: | +0.906 |
| |
| Cubeful Equities |
| No Double: | +0.520 (-0.073) |
| Double/Take: | +0.593 |
| Double/Drop: | +1.000 (+0.407) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.008 (+0.512...+0.527) |
| Confidence Double: | ± 0.011 (+0.582...+0.604) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 45 minutes |
Position 115 (cube decision before roll)
The XG rollout below is of Black’s cube decision before
the roll that Wiggins discusses. According to XG,
Black should have doubled before rolling.
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 61.22% (G: 34.54% B: 1.78%) |
| Opponent Winning Chances: | 38.78% (G: 9.63% B: 0.59%) |
| Double/Take |
| Player Winning Chances: | 61.58% (G: 36.80% B: 1.72%) |
| Opponent Winning Chances: | 38.42% (G: 10.16% B: 0.64%) |
| |
| Cubeless Equities |
| No Double: | +0.224 |
| Double: | +1.017 |
| |
| Cubeful Equities |
| No Double: | +0.605 (-0.103) |
| Double/Take: | +0.708 |
| Double/Drop: | +1.000 (+0.292) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller |
| |
| Confidence No Double: | ± 0.010 (+0.594...+0.615) |
| Confidence Double: | ± 0.017 (+0.691...+0.725) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 16 minutes 10 seconds |
Position 118
XG prefers 6/2* to 23/22 8/5, and also thinks that 8/5 6/5
is a serious candidate. Wiggins does not mention 8/5 6/5.
| 1. | Rollout1 | 6/2* | eq: -0.251 |
| Player:
Opponent: |
35.61% (G:12.54% B:1.02%)
64.39% (G:22.03% B:1.35%) | Conf: ± 0.006 (-0.257...-0.245)
Duration: 55 minutes 16 seconds |
|
| 2. | Rollout1 | 8/5 6/5 | eq: -0.255 (-0.005) |
| Player:
Opponent: |
34.44% (G:12.35% B:0.71%)
65.56% (G:19.21% B:1.03%) | Conf: ± 0.006 (-0.261...-0.249)
Duration: 47 minutes 06 seconds |
|
| 3. | Rollout1 | 23/22 8/5 | eq: -0.272 (-0.021) |
| Player:
Opponent: |
36.59% (G:13.67% B:1.16%)
63.41% (G:27.71% B:1.21%) | Conf: ± 0.006 (-0.278...-0.266)
Duration: 44 minutes 37 seconds |
|
| 4. | Rollout1 | 13/10 6/5 | eq: -0.290 (-0.039) |
| Player:
Opponent: |
33.56% (G:11.39% B:0.68%)
66.44% (G:19.75% B:1.13%) | Conf: ± 0.006 (-0.296...-0.284)
Duration: 46 minutes 46 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 121
Not much disagreement here between the bots, except that XG
puts 24/20 10/5 (a candidate that is not mentioned by Wiggins)
in second place, ahead of 10/1 and 10/6 7/2.
| 1. | Rollout1 | 24/15 | eq: -0.802 |
| Player:
Opponent: |
12.56% (G:0.01% B:0.00%)
87.44% (G:8.95% B:0.05%) | Conf: ± 0.001 (-0.803...-0.801)
Duration: 8 minutes 07 seconds |
|
| 2. | Rollout1 | 24/20 10/5 | eq: -0.824 (-0.021) |
| Player:
Opponent: |
12.41% (G:0.00% B:0.00%)
87.59% (G:11.19% B:0.12%) | Conf: ± 0.001 (-0.825...-0.823)
Duration: 6 minutes 11 seconds |
|
| 3. | Rollout1 | 10/1 | eq: -0.862 (-0.060) |
| Player:
Opponent: |
10.75% (G:0.00% B:0.00%)
89.25% (G:10.73% B:0.26%) | Conf: ± 0.001 (-0.863...-0.861)
Duration: 5 minutes 58 seconds |
|
| 4. | Rollout1 | 10/6 7/2 | eq: -0.870 (-0.068) |
| Player:
Opponent: |
10.09% (G:0.00% B:0.00%)
89.91% (G:10.39% B:0.25%) | Conf: ± 0.001 (-0.871...-0.869)
Duration: 5 minutes 14 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
Position 128
Again, not much to note here other than that Wiggins fails to
mention 24/20 13/7 as a candidate.
| 1. | Rollout1 | 24/14 | eq: -0.026 |
| Player:
Opponent: |
50.11% (G:12.26% B:0.61%)
49.89% (G:15.49% B:0.49%) | Conf: ± 0.007 (-0.033...-0.019)
Duration: 1 hour 17 minutes |
|
| 2. | Rollout1 | 24/20 13/7 | eq: -0.066 (-0.040) |
| Player:
Opponent: |
48.74% (G:13.92% B:0.75%)
51.26% (G:16.36% B:0.62%) | Conf: ± 0.008 (-0.074...-0.058)
Duration: 1 hour 14 minutes |
|
| 3. | Rollout1 | 8/2* 6/2 | eq: -0.071 (-0.045) |
| Player:
Opponent: |
47.38% (G:16.29% B:0.73%)
52.62% (G:14.86% B:0.79%) | Conf: ± 0.008 (-0.079...-0.063)
Duration: 1 hour 07 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3 ply, cube decisions: XG Roller
|
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