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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.	Rollout1	8/5 2/1	eq: +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.	Rollout1	8/5 6/5	eq: +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.	Rollout1	5/1	eq: +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.	Rollout1	8/4	eq: +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.	Rollout1	6/2	eq: +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.	Rollout1	8/7 8/5	eq: +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.	Rollout1	8/4	eq: +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.	Rollout1	8/5 2/1	eq: +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.	Rollout2	8/7 8/5	eq: +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.	Rollout2	8/5 6/5	eq: +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.	Rollout2	5/1	eq: +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.	Rollout3	8/7 5/2	eq: +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.	Rollout1	8/4	eq: +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.	Rollout1	8/5 2/1	eq: +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.	Rollout1	8/7 8/5	eq: +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.	Rollout1	8/5 6/5	eq: +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.	Rollout1	8/7 5/2	eq: +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.	Rollout1	5/1	eq: +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.	Rollout1	8/4	eq: +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.	Rollout1	8/5 2/1	eq: +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.	Rollout2	8/7 8/5	eq: +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.	Rollout2	8/5 6/5	eq: +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.	Rollout2	5/1	eq: +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.	Rollout3	8/7 5/2	eq: +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.	Rollout1	8/4	eq: +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.	Rollout1	8/5 2/1	eq: +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.	Rollout2	8/7 8/5	eq: +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.	Rollout2	8/5 6/5	eq: +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.	Rollout2	5/1	eq: +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.	Rollout3	6/2	eq: +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.	Rollout3	8/7 5/2	eq: +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