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Othello Quiz 2015, Problem 2 (Variants, etc.)

Posted By: Nack Ballard
Date: Friday, 30 October 2015, at 3:50 p.m.

My variants for the Othello Quiz 2015, Problem 1, can be viewed here.

Near the end of that post, I wrote, "If there is sufficient interest, I'll try to find time to post variants of other Othello-quiz positions." As nobody responded, I was going to stop there. However, as honorable Othello himself has now responded (thank you), I'll work on at least one more problem. Here goes:





White is Player 2

score: 0
pip: 137
5 point match
pip: 76
score: 2

Blue is Player 1
XGID=-BBb-DC-D---b--a-cabb--b--:1:-1:1:31:2:0:0:5:10

Original Position


1.Rollout18/5 2/1eq: +0.419
Player:
Opponent:
73.99% (G:13.95% B:0.39%)
26.01% (G:2.09% B:0.08%)
Conf.: กำ 0.006 (+0.413...+0.425) - [100.0%]
Duration: 13 minutes 52 seconds
2.Rollout18/5 6/5eq: +0.334 (-0.084)
Player:
Opponent:
71.33% (G:14.02% B:0.27%)
28.67% (G:2.79% B:0.13%)
Conf.: กำ 0.006 (+0.328...+0.341) - [0.0%]
Duration: 13 minutes 48 seconds
3.Rollout15/1eq: +0.326 (-0.093)
Player:
Opponent:
71.03% (G:12.37% B:0.23%)
28.97% (G:2.65% B:0.11%)
Conf.: กำ 0.006 (+0.320...+0.332) - [0.0%]
Duration: 11 minutes 26 seconds
4.Rollout18/4eq: +0.323 (-0.095)
Player:
Opponent:
71.19% (G:19.20% B:0.53%)
28.81% (G:3.35% B:0.14%)
Conf.: กำ 0.007 (+0.317...+0.330) - [0.0%]
Duration: 14 minutes 51 seconds
5.Rollout16/2eq: +0.277 (-0.142)
Player:
Opponent:
69.42% (G:12.46% B:0.16%)
30.58% (G:3.10% B:0.12%)
Conf.: กำ 0.007 (+0.271...+0.284) - [0.0%]
Duration: 10 minutes 48 seconds
6.Rollout18/7 8/5eq: +0.233 (-0.185)
Player:
Opponent:
67.78% (G:20.48% B:0.47%)
32.22% (G:3.56% B:0.28%)
Conf.: กำ 0.008 (+0.226...+0.241) - [0.0%]
Duration: 11 minutes 46 seconds
 
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

Above is my rollout of the original position. (The margins in Othello's 1k rollout are similar, though 6/2 is omitted.)

Let's suppose that at some point, White made her 5pt with 31. If we "unmake" half of her 5pt, we get (left-hand) Variant 1 below, which essentially puts 8/4 and 8/5 2/1 into a tie. If we unmake the other half of White's 5pt, we get (right-hand) Variant 2, a clear contrast with the original position.





White is Player 2

score: 0
pip: 140
5 point match
pip: 76
score: 2

Blue is Player 1
XGID=-BBb-DC-D---b--a-daba--b--:1:-1:1:31:2:0:0:5:10

Variant 1


1.Rollout18/4eq: +0.448
Player:
Opponent:
74.68% (G:20.45% B:0.73%)
25.32% (G:2.54% B:0.16%)
Conf.: กำ 0.003 (+0.445...+0.451) - [99.5%]
Duration: 2 hours 08 minutes
2.Rollout18/5 2/1eq: +0.442 (-0.006)
Player:
Opponent:
74.61% (G:16.47% B:0.34%)
25.39% (G:2.01% B:0.06%)
Conf.: กำ 0.003 (+0.439...+0.445) - [0.5%]
Duration: 2 hours 00 minute
3.Rollout28/7 8/5eq: +0.397 (-0.051)
Player:
Opponent:
72.77% (G:21.65% B:0.42%)
27.23% (G:2.36% B:0.16%)
Conf.: กำ 0.007 (+0.390...+0.403) - [0.0%]
Duration: 44 minutes 28 seconds
4.Rollout28/5 6/5eq: +0.363 (-0.085)
Player:
Opponent:
72.35% (G:16.66% B:0.39%)
27.65% (G:2.64% B:0.08%)
Conf.: กำ 0.007 (+0.356...+0.369) - [0.0%]
Duration: 45 minutes 24 seconds
5.Rollout25/1eq: +0.357 (-0.091)
Player:
Opponent:
71.87% (G:15.00% B:0.35%)
28.13% (G:2.57% B:0.10%)
Conf.: กำ 0.007 (+0.351...+0.364) - [0.0%]
Duration: 44 minutes 27 seconds
6.Rollout38/7 5/2eq: +0.323 (-0.125)
Player:
Opponent:
70.48% (G:21.09% B:0.72%)
29.52% (G:2.81% B:0.12%)
Conf.: กำ 0.015 (+0.308...+0.339) - [0.0%]
Duration: 7 minutes 21 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

3 252 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller




White is Player 2

score: 0
pip: 141
5 point match
pip: 76
score: 2

Blue is Player 1
XGID=-BBb-DC-D---b--a-dac---b--:1:-1:1:31:2:0:0:5:10

Variant 2


1.Rollout18/4eq: +0.529
Player:
Opponent:
77.40% (G:19.77% B:0.56%)
22.60% (G:1.91% B:0.08%)
Conf.: กำ 0.006 (+0.523...+0.535) - [100.0%]
Duration: 38 minutes 25 seconds
2.Rollout18/5 2/1eq: +0.473 (-0.056)
Player:
Opponent:
75.48% (G:17.61% B:0.58%)
24.52% (G:1.82% B:0.11%)
Conf.: กำ 0.006 (+0.467...+0.480) - [0.0%]
Duration: 36 minutes 18 seconds
3.Rollout18/7 8/5eq: +0.470 (-0.058)
Player:
Opponent:
74.74% (G:23.49% B:0.63%)
25.26% (G:2.06% B:0.12%)
Conf.: กำ 0.007 (+0.464...+0.477) - [0.0%]
Duration: 42 minutes 38 seconds
4.Rollout18/5 6/5eq: +0.404 (-0.125)
Player:
Opponent:
73.52% (G:18.15% B:0.61%)
26.48% (G:2.25% B:0.08%)
Conf.: กำ 0.007 (+0.397...+0.410) - [0.0%]
Duration: 37 minutes 34 seconds
5.Rollout18/7 5/2eq: +0.390 (-0.138)
Player:
Opponent:
72.85% (G:17.75% B:0.30%)
27.15% (G:2.13% B:0.09%)
Conf.: กำ 0.006 (+0.384...+0.397) - [0.0%]
Duration: 33 minutes 26 seconds
6.Rollout15/1eq: +0.378 (-0.151)
Player:
Opponent:
72.57% (G:16.23% B:0.44%)
27.43% (G:2.49% B:0.12%)
Conf.: กำ 0.006 (+0.371...+0.384) - [0.0%]
Duration: 27 minutes 17 seconds
 
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
 

If we remake White's 5pt (returning to the original position) and instead move White's blot from 7pt to 1pt, we get Variant 3 below, which is a cusp. Any White board weaker than that will make Blue's 8/4 a clear winner. [For example, see Tim's variant (second diagram of that post).]





White is Player 2

score: 0
pip: 131
5 point match
pip: 76
score: 2

Blue is Player 1
XGID=-BBb-DC-D---b--a-c-bb--ba-:1:-1:1:31:2:0:0:5:10

Variant 3


1.Rollout18/4eq: +0.469
Player:
Opponent:
75.54% (G:20.25% B:0.75%)
24.46% (G:2.55% B:0.12%)
Conf.: กำ 0.003 (+0.466...+0.473) - [92.3%]
Duration: 1 hour 38 minutes
2.Rollout18/5 2/1eq: +0.466 (-0.003)
Player:
Opponent:
76.62% (G:11.98% B:0.34%)
23.38% (G:1.63% B:0.07%)
Conf.: กำ 0.003 (+0.463...+0.469) - [7.7%]
Duration: 1 hour 21 minutes
3.Rollout28/7 8/5eq: +0.410 (-0.059)
Player:
Opponent:
73.27% (G:22.31% B:0.95%)
26.73% (G:2.62% B:0.21%)
Conf.: กำ 0.007 (+0.403...+0.417) - [0.0%]
Duration: 21 minutes 12 seconds
4.Rollout28/5 6/5eq: +0.395 (-0.074)
Player:
Opponent:
74.37% (G:12.79% B:0.32%)
25.63% (G:2.10% B:0.11%)
Conf.: กำ 0.006 (+0.389...+0.402) - [0.0%]
Duration: 16 minutes 50 seconds
5.Rollout25/1eq: +0.383 (-0.087)
Player:
Opponent:
73.69% (G:11.05% B:0.30%)
26.31% (G:2.00% B:0.06%)
Conf.: กำ 0.006 (+0.376...+0.389) - [0.0%]
Duration: 13 minutes 37 seconds
6.Rollout38/7 5/2eq: +0.337 (-0.132)
Player:
Opponent:
71.50% (G:18.82% B:0.76%)
28.50% (G:2.81% B:0.10%)
Conf.: กำ 0.021 (+0.316...+0.358) - [0.0%]
Duration: 1 minute 44 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

3 132 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller


Finally, the original board position is restored but the match score reversed, as shown in Variant 4 below.





White is Player 2

score: 2
pip: 137
5 point match
pip: 76
score: 0

Blue is Player 1
XGID=-BBb-DC-D---b--a-cabb--b--:1:-1:1:31:0:2:0:5:10

Variant 4


1.Rollout18/4eq: +0.595
Player:
Opponent:
71.49% (G:17.01% B:0.38%)
28.51% (G:2.88% B:0.14%)
Conf.: กำ 0.003 (+0.593...+0.598) - [100.0%]
Duration: 1 hour 38 minutes
2.Rollout18/5 2/1eq: +0.582 (-0.013)
Player:
Opponent:
74.46% (G:11.35% B:0.12%)
25.54% (G:2.00% B:0.09%)
Conf.: กำ 0.002 (+0.580...+0.585) - [0.0%]
Duration: 1 hour 38 minutes
3.Rollout28/7 8/5eq: +0.531 (-0.064)
Player:
Opponent:
69.17% (G:16.64% B:0.24%)
30.83% (G:2.78% B:0.22%)
Conf.: กำ 0.006 (+0.525...+0.538) - [0.0%]
Duration: 28 minutes 38 seconds
4.Rollout28/5 6/5eq: +0.516 (-0.080)
Player:
Opponent:
72.07% (G:10.74% B:0.12%)
27.93% (G:2.41% B:0.10%)
Conf.: กำ 0.005 (+0.511...+0.520) - [0.0%]
Duration: 26 minutes 32 seconds
5.Rollout25/1eq: +0.501 (-0.095)
Player:
Opponent:
71.54% (G:10.03% B:0.06%)
28.46% (G:2.46% B:0.09%)
Conf.: กำ 0.005 (+0.496...+0.505) - [0.0%]
Duration: 27 minutes 40 seconds
6.Rollout36/2eq: +0.463 (-0.133)
Player:
Opponent:
69.96% (G:10.02% B:0.18%)
30.04% (G:2.80% B:0.17%)
Conf.: กำ 0.014 (+0.449...+0.477) - [0.0%]
Duration: 3 minutes 23 seconds
7.Rollout38/7 5/2eq: +0.458 (-0.138)
Player:
Opponent:
66.75% (G:15.59% B:0.10%)
33.25% (G:2.78% B:0.12%)
Conf.: กำ 0.016 (+0.442...+0.473) - [0.0%]
Duration: 3 minutes 48 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

3 134 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller


[If the match score is bumped from 0 to 2, up to 1 to 3 (to 5 points), the situation escalates to gammon go, and 8/4 rolls out as best by .034, not shown.]

Nack

 

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