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Blue's 22 play before the ho-hum 61

Posted By: Nack Ballard
Date: Sunday, 22 June 2014, at 5:12 p.m.

In Response To: Ho-Hum 61 (Nack Ballard)

		White is Player 2 score: 0 pip: 88 Unlimited Game Jacoby Beaver pip: 127 score: 0 Blue is Player 1
XGID=---BBBC---A-dC----Babbbbb-:1:-1:1:22:0:0:3:0:10
43S-44P-21@-55J-55C-52I-62P-33P-31P-11E-C-21D-55R-22

1.	Rollout1	13/11 6/2 4/2	eq: -0.5309
	Player: Opponent: 33.26% (G:2.88% B:0.07%) 66.74% (G:3.07% B:0.12%) Conf.: ±0.0010 (-0.5319...-0.5298) - [99.9%] Duration: 5 hours 02 minutes
2.	Rollout1	13/11 10/8 6/2	eq: -0.5331 (-0.0023)
	Player: Opponent: 32.96% (G:2.78% B:0.07%) 67.04% (G:2.34% B:0.04%) Conf.: ±0.0010 (-0.5341...-0.5321) - [0.1%] Duration: 4 hours 21 minutes
3.	Rollout2	10/2	eq: -0.5344 (-0.0035)
	Player: Opponent: 32.89% (G:2.80% B:0.07%) 67.11% (G:2.38% B:0.03%) Conf.: ±0.0012 (-0.5356...-0.5332) - [0.0%] Duration: 2 hours 32 minutes
4.	Rollout2	13/7 4/2	eq: -0.5349 (-0.0040)
	Player: Opponent: 33.42% (G:3.15% B:0.08%) 66.58% (G:4.64% B:0.27%) Conf.: ±0.0012 (-0.5361...-0.5336) - [0.0%] Duration: 2 hours 41 minutes
5.	Rollout3	6/2(2)	eq: -0.5352 (-0.0043)
	Player: Opponent: 33.10% (G:2.81% B:0.07%) 66.90% (G:3.27% B:0.11%) Conf.: ±0.0015 (-0.5366...-0.5337) - [0.0%] Duration: 1 hour 35 minutes
6.	Rollout3	13/7 10/8	eq: -0.5363 (-0.0055)
	Player: Opponent: 32.64% (G:2.79% B:0.08%) 67.36% (G:1.99% B:0.02%) Conf.: ±0.0015 (-0.5378...-0.5349) - [0.0%] Duration: 1 hour 09 minutes
7.	Rollout3	13/9 6/2	eq: -0.5370 (-0.0062)
	Player: Opponent: 33.22% (G:2.91% B:0.07%) 66.78% (G:3.92% B:0.13%) Conf.: ±0.0015 (-0.5385...-0.5356) - [0.0%] Duration: 1 hour 13 minutes
8.	Rollout4	10/8 6/2 4/2	eq: -0.5385 (-0.0076)
	Player: Opponent: 32.82% (G:2.77% B:0.07%) 67.18% (G:3.14% B:0.07%) Conf.: ±0.0031 (-0.5416...-0.5354) - [0.0%] Duration: 41 minutes 39 seconds
9.	Rollout3	13/9 10/8 4/2	eq: -0.5396 (-0.0088)
	Player: Opponent: 33.13% (G:2.98% B:0.07%) 66.87% (G:4.38% B:0.21%) Conf.: ±0.0015 (-0.5411...-0.5381) - [0.0%] Duration: 1 hour 16 minutes
10.	Rollout3	13/9 4/2(2)	eq: -0.5410 (-0.0102)
	Player: Opponent: 32.60% (G:2.81% B:0.07%) 67.40% (G:2.67% B:0.05%) Conf.: ±0.0015 (-0.5425...-0.5395) - [0.0%] Duration: 1 hour 42 minutes
11.	Rollout5	13/7 6/4	eq: -0.5452 (-0.0143)
	Player: Opponent: 32.25% (G:2.71% B:0.07%) 67.75% (G:2.08% B:0.03%) Conf.: ±0.0021 (-0.5472...-0.5431) - [0.0%] Duration: 1 hour 19 minutes
12.	Rollout4	13/9 10/8 6/4	eq: -0.5493 (-0.0185)
	Player: Opponent: 32.17% (G:2.71% B:0.07%) 67.83% (G:2.19% B:0.03%) Conf.: ±0.0029 (-0.5522...-0.5464) - [0.0%] Duration: 18 minutes 35 seconds
13.	Rollout4	13/5	eq: -0.5499 (-0.0191)
	Player: Opponent: 32.19% (G:2.76% B:0.07%) 67.81% (G:2.21% B:0.03%) Conf.: ±0.0028 (-0.5527...-0.5471) - [0.0%] Duration: 33 minutes 01 second
14.	Rollout4	13/11 10/4	eq: -0.5500 (-0.0192)
	Player: Opponent: 32.14% (G:2.76% B:0.07%) 67.86% (G:2.26% B:0.03%) Conf.: ±0.0028 (-0.5529...-0.5472) - [0.0%] Duration: 23 minutes 24 seconds
15.	Rollout4	13/9 10/6	eq: -0.5515 (-0.0206)
	Player: Opponent: 32.03% (G:2.74% B:0.07%) 67.97% (G:2.21% B:0.03%) Conf.: ±0.0030 (-0.5545...-0.5485) - [0.0%] Duration: 21 minutes 55 seconds
1 41472 Games rolled with Variance Reduction. Dice Seed: 1019915 Moves: 3-ply, cube decisions: XG Roller 2 31104 Games rolled with Variance Reduction. Dice Seed: 1019915 Moves: 3-ply, cube decisions: XG Roller 3 20736 Games rolled with Variance Reduction. Dice Seed: 1019915 Moves: 3-ply, cube decisions: XG Roller 4 5184 Games rolled with Variance Reduction. Dice Seed: 1019915 Moves: 3-ply, cube decisions: XG Roller 5 10368 Games rolled with Variance Reduction. Dice Seed: 1019915 Moves: 3-ply, cube decisions: XG Roller

With double 2s in the position above, it never occurred to me that n.(near, 13/11 6/2 4/2) might be the best play. I merely used it as a way of reaching the position diagrammed in the Ho-Hum 61 post in 14 rolls (without it and the 51 play that followed it, I needed 15 rolls), while making sure that all moves are "well played" (within .02 of best).

OTB, I would have played the natural-looking n (near, 13/11 10/8 6/2). Okay, that apparent error is a mere .002+ in equity, but my concern is that XG's rollout projects that breaking the 4pt to cover the 2pt is better—with 99.9% confidence—and I don't understand why.

Below is additional support for NOT shifting with 4/2. It is a rollout of the 51 play made immediately following it (just prior to the Ho-Hum 61 position), and a second rollout of the 51 choice that White would have been faced with if Blue had played his 22 more naturally (with 10/8).

		White is Player 2 score: 0 pip: 88 Unlimited Game Jacoby Beaver pip: 119 score: 0 Blue is Player 1
XGID=--BBABB---AAdB----Babbbbb-:1:-1:-1:51:0:0:3:0:10
43S-44P-21@-55J-55C-52I-62P- -33P-31P-11E-C-21D-55R-22n.-51

1.	Rollout1	13/8 6/5	eq: +0.384
	Player: Opponent: 59.33% (G:7.67% B:0.50%) 40.67% (G:5.06% B:0.10%) Conf.: ± 0.002 (+0.382...+0.387) - [100.0%] Duration: 1 hour 15 minutes
2.	Rollout1	6/1 5/4	eq: +0.370 (-0.015)
	Player: Opponent: 60.55% (G:2.55% B:0.03%) 39.45% (G:6.00% B:0.16%) Conf.: ± 0.002 (+0.368...+0.372) - [0.0%] Duration: 1 hour 21 minutes
1 10368 Games rolled with Variance Reduction. Dice Seed: 44860624 Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 0 pip: 88 Unlimited Game Jacoby Beaver pip: 119 score: 0 Blue is Player 1
XGID=--ABBBB-A--AdB----Babbbbb-:0:0:-1:51:0:0:3:0:10
43S-44P-21@-55J-55C-52I-62P- -33P-31P-11E-C-21D-55R-22n-51

1.	Rollout1	6/1 5/4	eq: +0.284
	Player: Opponent: 60.26% (G:3.23% B:0.04%) 39.74% (G:6.29% B:0.17%) Conf.: ± 0.005 (+0.278...+0.289) - [100.0%] Duration: 25 minutes 44 seconds
2.	Rollout1	13/8 6/5	eq: +0.243 (-0.041)
	Player: Opponent: 58.34% (G:9.38% B:0.34%) 41.66% (G:5.48% B:0.11%) Conf.: ± 0.006 (+0.237...+0.249) - [0.0%] Duration: 22 minutes 40 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 44860624 Moves: 3-ply, cube decisions: XG Roller

In the first (left-hand) position, White is emboldened to start the 8pt, mainly so that her future rolls rate to play more safely. For example, she might cover the 8pt and subsequently clear the midpoint with 54 53 52 while leaving a single shot, or avoid a later double-blot disaster (e.g., with 51, 42 or 41), or just having a checker or two advanced to the 8pt will help her manage some of her rolls (such as the next 51 or two consecutive small 4s, etc.) She also keeps her 5pt.

White's ace-shot is worth the risk only if Blue has downgraded her board as in the left-hand position. White's gain in equity is .015, and thus .015/18 = .0008 has to be charged to Blue's 4/2 play (because 51 is rolled 1/18 of the time). In other words, the 4/2 play is .0023 ahead of the 10/8 play in spite of the .0008 penalty it incurs from White's correctly bold response of 51. This means that we are actually looking for .0023 + .0008 = .0031 of equity to explain.

An upside to 4/2 (versus 10/8) is in the greater likelihood of making the fifth point in the board a roll sooner, due to the ability to cover with 6s, 52 43 (and sometimes 54) instead of just 6s and 54. Let's call the difference 3 numbers, which occur 1/12 of the time. However, the only two-roll combinations I see with which White will leave a shot are 51+65 and 51+11, and these have already been accounted for by (the difference in) the 51 rollouts. [Even if not, the effect would only be (6/1296*25/36)/12 = .0003, and for that only the subset of games swung by not having covered the 2pt!]

We are still left with .0031 of equity to explain. Anyone have an idea?

Finally, consider the fourth-ranked play of 13/7 4/2, which leaves both the 4pt and 2pt slotted. In this case, White gains .068 in equity by leaving a shot with 51 (according to the XGR++ evaluation below). Hmm... so, despite sacrificing .068 / 18 = .0038 in the immediate 51 (plus whatever it might cost to have 11 fewer numbers that make a five-point board on the following roll), Blue's 13/7 6/4 play is only .0017 worse than the solid 13/11 10/8 6/2? This means that the double-blotting move gains .0021 in other variations... somehow.

Is it possible that bots have a built-in bias towards slightly unsound shifts and multiple slots (that modern players try to mimic) in preparation for a shot that somehow don't correspond to real equity? (For example, it might sometimes make less bold plays than it should for the opponent that don't take full advantage of the player's temporarily compromised board.)

Food for thought.

Nack

		White is Player 2 score: 0 pip: 88 Unlimited Game Jacoby Beaver pip: 119 score: 0 Blue is Player 1
XGID=--ABABCA--A-dB----Babbbbb-:1:-1:-1:51:0:0:3:0:10
White's bold 51 gains substantial equity

1.	XG Roller++	13/8 6/5	eq: +0.462
	Player: Opponent: 62.47% (G:7.57% B:0.36%) 37.53% (G:4.44% B:0.07%)
2.	XG Roller++	6/1 5/4	eq: +0.395 (-0.068)
	Player: Opponent: 61.38% (G:2.56% B:0.02%) 38.62% (G:5.42% B:0.09%)

eXtreme Gammon Version: 2.10

Messages In This Thread

• Ho-Hum 61
  Nack Ballard -- Friday, 20 June 2014, at 5:41 a.m.
  • Ho-Hum 61
    David Rennie -- Friday, 20 June 2014, at 5:47 a.m.
    • Ho-Hum 61
      Taper_Mike -- Friday, 20 June 2014, at 6:02 a.m.
      • Ho-Hum 61
        Havard Raddum -- Friday, 20 June 2014, at 7:10 a.m.
  • Ho-Hum 61
    Timothy Chow -- Friday, 20 June 2014, at 2:42 p.m.
    • Ho-Hum 61
      Timothy Chow -- Friday, 20 June 2014, at 2:44 p.m.
  • Ho-Hum 61
    Robert Chow -- Friday, 20 June 2014, at 5:04 p.m.
  • Ho-Hum 61, Rollout and analysis
    Nack Ballard -- Sunday, 22 June 2014, at 4:57 a.m.
  • Blue's 22 play before the ho-hum 61
    Nack Ballard -- Sunday, 22 June 2014, at 5:12 p.m.
    • Blue's 22 play before the ho-hum 61
      Timothy Chow -- Sunday, 22 June 2014, at 6:53 p.m.
    • Blue's 22 play before the ho-hum 61
      Taper_Mike -- Monday, 23 June 2014, at 12:13 a.m.
    • Blue's 22 play before the ho-hum 61
      Robert Chow -- Monday, 23 June 2014, at 3:03 a.m.
      • Blue's 22 play before the ho-hum 61
        Timothy Chow -- Monday, 23 June 2014, at 5:58 p.m.
        • Blue's 22 play before the ho-hum 61
          Robert Chow -- Tuesday, 24 June 2014, at 3:11 a.m.
          • Blue's 22 play before the ho-hum 61
            Nack Ballard -- Monday, 30 June 2014, at 6:48 a.m.
  • White rolls the bad 61... Cube Action Problems
    Nack Ballard -- Monday, 23 June 2014, at 6:54 p.m.
    • White rolls the bad 61... Cube Action Problems
      Timothy Chow -- Tuesday, 24 June 2014, at 2:08 a.m.
      • White rolls the bad 61... Cube Action Problems
        Nack Ballard -- Tuesday, 24 June 2014, at 3:50 p.m.
        • P.S.
          Nack Ballard -- Tuesday, 24 June 2014, at 11:58 p.m.