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Othello Quiz 2015, Problem 3 (Variants, etc.)

Posted By: Nack Ballard
Date: Tuesday, 10 November 2015, at 8:11 p.m.

		White is Player 2 score: 0 pip: 80 Unlimited Game Jacoby Beaver pip: 83 score: 0 Blue is Player 1
XGID=-aBBBCC-B---a---A--bbbbbc-:1:-1:1:51:0:0:3:0:10
Original Position

1.	Rollout1	6/1* 2/1	eq: +0.442
	Player: Opponent: 71.60% (G:18.07% B:0.42%) 28.40% (G:9.94% B:0.13%) Conf.: กำ 0.004 (+0.438...+0.446) - [100.0%] Duration: 1 minute 50 seconds
2.	Rollout1	16/11 5/4	eq: +0.374 (-0.068)
	Player: Opponent: 71.77% (G:1.85% B:0.04%) 28.23% (G:1.36% B:0.02%) Conf.: กำ 0.005 (+0.370...+0.379) - [0.0%] Duration: 3 minutes 02 seconds
3.	Rollout1	8/7 6/1*	eq: +0.374 (-0.068)
	Player: Opponent: 72.24% (G:17.23% B:0.41%) 27.76% (G:18.16% B:1.47%) Conf.: กำ 0.006 (+0.369...+0.380) - [0.0%] Duration: 2 minutes 28 seconds
4.	Rollout1	16/15 6/1*	eq: +0.359 (-0.083)
	Player: Opponent: 69.05% (G:16.01% B:0.37%) 30.95% (G:9.93% B:0.14%) Conf.: กำ 0.006 (+0.353...+0.365) - [0.0%] Duration: 2 minutes 47 seconds
5.	Rollout1	6/1* 5/4	eq: +0.355 (-0.087)
	Player: Opponent: 69.00% (G:16.69% B:0.39%) 31.00% (G:10.16% B:0.14%) Conf.: กำ 0.006 (+0.349...+0.361) - [0.0%] Duration: 2 minutes 01 second
6.	Rollout1	16/10	eq: +0.349 (-0.093)
	Player: Opponent: 70.72% (G:1.76% B:0.04%) 29.28% (G:1.12% B:0.02%) Conf.: กำ 0.004 (+0.345...+0.353) - [0.0%] Duration: 2 minutes 18 seconds
7.	Rollout1	16/11 6/5	eq: +0.327 (-0.115)
	Player: Opponent: 69.83% (G:1.63% B:0.03%) 30.17% (G:0.77% B:0.01%) Conf.: กำ 0.004 (+0.323...+0.331) - [0.0%] Duration: 2 minutes 26 seconds
1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller

For reference, here are earlier posts with my Othello variants:

Othello Quiz 2015, Problem 1 Variants
Othello Quiz 2015, Problem 2 Variants

Above is my 1k rollout of Problem 3 (the original position). It is similar to Othello's 1k rollout. (His margins in parallel are .069, .068, .083, .087, .093, .115.) Note that the main hitting alternative of H, i.e., 6/1* and bringing a second builder into range with 8/7, duplicates 4s (13/9 and 5/1). The best play of P (Point, 6/1* 2/1) brings the mountain to Mohammed (by shifting 2/1), while unduplicating 4s.

If we move the 5pt spare to any other available point on the near side (besldes the 2pt, of course), H is best; that is, 8/7 becomes the preferred ace. An example is shown in Variant 1 below.

		White is Player 2 score: 0 pip: 80 Unlimited Game Jacoby Beaver pip: 88 score: 0 Blue is Player 1
XGID=-aBBBBC-B-A-a---A--bbbbbc-:1:-1:1:51:0:0:3:0:10
Variant 1 .....Blue is adjusted 5/10 from the original

1.	Rollout1	8/7 6/1*	eq: +0.403
	Player: Opponent: 73.93% (G:18.43% B:0.45%) 26.07% (G:19.15% B:2.52%) Conf.: กำ 0.005 (+0.398...+0.408) - [100.0%] Duration: 3 minutes 22 seconds
2.	Rollout1	6/1* 2/1	eq: +0.346 (-0.057)
	Player: Opponent: 69.26% (G:18.22% B:0.43%) 30.74% (G:15.01% B:0.44%) Conf.: กำ 0.006 (+0.340...+0.351) - [0.0%] Duration: 3 minutes 00 second
3.	Rollout1	16/10	eq: +0.306 (-0.097)
	Player: Opponent: 69.37% (G:1.97% B:0.04%) 30.63% (G:1.20% B:0.02%) Conf.: กำ 0.004 (+0.302...+0.311) - [0.0%] Duration: 3 minutes 25 seconds
4.	Rollout1	10/9 6/1*	eq: +0.275 (-0.128)
	Player: Opponent: 67.39% (G:16.49% B:0.43%) 32.61% (G:15.24% B:0.38%) Conf.: กำ 0.005 (+0.270...+0.280) - [0.0%] Duration: 2 minutes 50 seconds
5.	Rollout1	16/11 10/9	eq: +0.239 (-0.165)
	Player: Opponent: 66.10% (G:2.30% B:0.04%) 33.90% (G:4.55% B:0.08%) Conf.: กำ 0.005 (+0.234...+0.243) - [0.0%] Duration: 4 minutes 26 seconds
6.	Rollout1	16/11 6/5	eq: +0.224 (-0.179)
	Player: Opponent: 65.22% (G:2.02% B:0.04%) 34.78% (G:3.64% B:0.05%) Conf.: กำ 0.004 (+0.220...+0.228) - [0.0%] Duration: 4 minutes 01 second
7.	Rollout1	16/15 6/1*	eq: +0.216 (-0.187)
	Player: Opponent: 66.02% (G:14.17% B:0.34%) 33.98% (G:15.81% B:0.41%) Conf.: กำ 0.006 (+0.210...+0.222) - [0.0%] Duration: 3 minutes 10 seconds
1 1296 Games rolled with Variance Reduction. Dice Seed: 31027603 Moves: 3-ply, cube decisions: XG Roller

Now let's take a step back. Blue has a nice advantage without hitting. Whether he should risk the hit at all is related to the number of pips White can play before cracking her board in the event that Blue hits and White rolls an ace without a 6 (and it is relevant to the race if Blue doesn't hit).

By putting White's spare on her 1pt, Othello maximizes Blue's incentive to hit -- P beats the best non-hitting play by .068.

Below are two variants (viewable side-by-side if your window is wide enough) that flank the hypothetical cusp. If the 1pt spare is moved to her 4pt (with all else as in the original position), Blue's P play is still in the lead, though by just .011. If White's spare is moved just one more pip, to her 5pt, P falls behind by .012.

		White is Player 2 score: 0 pip: 83 Unlimited Game Jacoby Beaver pip: 83 score: 0 Blue is Player 1
XGID=-aBBBCC-B---a---A--bbcbbb-:1:-1:1:51:0:0:3:0:10
Variant 2 .....White is adjusted 1/4 from the original

1.	Rollout1	6/1* 2/1	eq: +0.394
	Player: Opponent: 70.00% (G:17.76% B:0.41%) 30.00% (G:11.29% B:0.17%) Conf.: กำ 0.002 (+0.392...+0.396) - [100.0%] Duration: 7 minutes 10 seconds
2.	Rollout1	16/11 5/4	eq: +0.383 (-0.011)
	Player: Opponent: 72.23% (G:1.62% B:0.03%) 27.77% (G:0.95% B:0.01%) Conf.: กำ 0.002 (+0.381...+0.385) - [0.0%] Duration: 9 minutes 41 seconds
3.	Rollout1	16/10	eq: +0.359 (-0.035)
	Player: Opponent: 71.40% (G:1.48% B:0.03%) 28.60% (G:0.80% B:0.01%) Conf.: กำ 0.002 (+0.357...+0.361) - [0.0%] Duration: 8 minutes 24 seconds
4.	Rollout2	16/11 6/5	eq: +0.343 (-0.051)
	Player: Opponent: 70.56% (G:1.46% B:0.02%) 29.44% (G:0.85% B:0.01%) Conf.: กำ 0.004 (+0.339...+0.347) - [0.0%] Duration: 2 minutes 59 seconds
5.	Rollout2	8/7 6/1*	eq: +0.337 (-0.058)
	Player: Opponent: 71.14% (G:16.79% B:0.39%) 28.86% (G:19.43% B:1.81%) Conf.: กำ 0.004 (+0.332...+0.341) - [0.0%] Duration: 3 minutes 05 seconds
6.	Rollout2	6/1* 5/4	eq: +0.310 (-0.084)
	Player: Opponent: 67.34% (G:16.38% B:0.38%) 32.66% (G:11.47% B:0.16%) Conf.: กำ 0.003 (+0.307...+0.314) - [0.0%] Duration: 2 minutes 24 seconds
7.	Rollout2	16/15 6/1*	eq: +0.303 (-0.091)
	Player: Opponent: 67.51% (G:15.63% B:0.37%) 32.49% (G:11.14% B:0.15%) Conf.: กำ 0.004 (+0.300...+0.307) - [0.0%] Duration: 2 minutes 56 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

		White is Player 2 score: 0 pip: 84 Unlimited Game Jacoby Beaver pip: 83 score: 0 Blue is Player 1
XGID=-aBBBCC-B---a---A--bcbbbb-:1:-1:1:51:0:0:3:0:10
Variant 3 .....White is adjusted 1/5 from the original

1.	Rollout1	16/11 5/4	eq: +0.396
	Player: Opponent: 72.87% (G:1.55% B:0.03%) 27.13% (G:0.92% B:0.01%) Conf.: กำ 0.002 (+0.394...+0.399) - [100.0%] Duration: 11 minutes 34 seconds
2.	Rollout1	6/1* 2/1	eq: +0.385 (-0.012)
	Player: Opponent: 69.55% (G:17.46% B:0.40%) 30.45% (G:11.75% B:0.19%) Conf.: กำ 0.002 (+0.383...+0.387) - [0.0%] Duration: 9 minutes 28 seconds
3.	Rollout1	16/10	eq: +0.376 (-0.021)
	Player: Opponent: 72.06% (G:1.46% B:0.03%) 27.94% (G:0.82% B:0.01%) Conf.: กำ 0.002 (+0.373...+0.378) - [0.0%] Duration: 10 minutes 12 seconds
4.	Rollout2	16/11 6/5	eq: +0.359 (-0.038)
	Player: Opponent: 71.20% (G:1.40% B:0.03%) 28.80% (G:0.72% B:0.01%) Conf.: กำ 0.003 (+0.356...+0.362) - [0.0%] Duration: 5 minutes 41 seconds
5.	Rollout3	8/7 6/1*	eq: +0.326 (-0.070)
	Player: Opponent: 70.89% (G:16.60% B:0.38%) 29.11% (G:19.87% B:1.79%) Conf.: กำ 0.005 (+0.321...+0.330) - [0.0%] Duration: 3 minutes 13 seconds
6.	Rollout3	6/1* 5/4	eq: +0.302 (-0.095)
	Player: Opponent: 66.93% (G:16.15% B:0.38%) 33.07% (G:11.75% B:0.17%) Conf.: กำ 0.003 (+0.298...+0.305) - [0.0%] Duration: 2 minutes 28 seconds
7.	Rollout3	16/15 6/1*	eq: +0.292 (-0.105)
	Player: Opponent: 66.95% (G:15.78% B:0.36%) 33.05% (G:12.13% B:0.19%) Conf.: กำ 0.003 (+0.288...+0.295) - [0.0%] Duration: 2 minutes 29 seconds
1 5184 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller 2 2592 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller 3 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller

 

Completing the slide: if the White spare is moved back to her 8pt, P drops to fourth best (behind all three safe plays), an error of .051. (Rollout not shown.)

Nack