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Summation

Posted By: Daniel Murphy
Date: Monday, 17 March 2008, at 6:21 a.m.

In Response To: Summation (Stick)

The Gnubg rollouts were 1296 trials except one, and the Snowie cubeless rollout's win percentages and cubeless equities ought to be comparable to to the Gnubg cubeful rollouts' cubeless win percentages and the cubeless equities.

Repost from http://www.gammonu.com/members/board/config.cgi?read=158986 :

Updated, extended, corrected.

Positions: Money game. Player on roll holds 2-cube, has a prime and 3 spares as indicated in the table. Opponent has 4 checkers off, 10 on his 1 point, and 1 at the edge of the prime (but on the bar against a closed board).

Rollout parameters: GNUBG 2-ply (narrow)/2-ply cubeful, 1296 full trials (except prime 12-17, 432 trials). Win and gammon loss percentages are the D/T (cubeless) percentages.

Position Evaluation Rollout
Prime + spares Action WinLose G D/T EquityAction WinLose GRollout D/T CubelessD/T Cubeful
1-6 + 4 5 6 Pass 83.4% 0.0% 1.223 Pass 85.6% 0.0% 1.422 1.345
1-6 + 19 22 23 Pass 83.4% 1.0% 1.205 Pass 84.2% 0.0% 1.366 1.280
2-7 + 19 22 23 Pass 84.7% 0.9% 1.265 Pass 83.5% 0.0% 1.341 1.250
3-8 + 19 22 23 Pass 84.8% 1.4% 1.261 Pass 82.6% 0.2% 1.301 1.208
4-9 + 19 22 23 Pass 83.6% 2.6% 1.181 Pass 82.1% 0.3% 1.277 1.175
5-10 + 19 22 23 Pass 81.2% 5.0% 1.015 Pass 81.3% 0.5% 1.244 1.144
6-11 + 19 22 23 ND/Take 75.9% 13.1% 0.600 Pass 80.8% 0.8% 1.215 1.109
7-12 + 19 22 23 ND/Take 75.0% 14.3% 0.530 Pass 80.1% 1.5% 1.174 1.067
8-13 + 19 22 23 ND/Take 74.5% 14.8% 0.494 ND/Take78.7% 2.8% 1.093 0.985
9-14 + 19 22 23 ND/Take 70.6% 18.8% 0.225 ND/Take75.6% 2.4% 0.899 0.791
10-15 + 19 22 23 Beaver 67.3% 22.8% -0.009 ND/Take72.7% 10.2% 0.705 0.607
11-16 + 19 22 23Beaver 62.9% 27.1% -0.301 ND/Take71.5% 11.5% 0.628 0.523
12-17 + 19,22,23Beaver 61.2% 27.2% -0.388 ND/Take67.3% 15.8% 0.373 0.262

Commments:

1. 2-ply eval begins to fail badly when the prime is on the 6 to 11 points.

2. I've no reason to think Gnubg plays less than world class for primes 1-6, 2-7, 3-8 and, but not perfectly, 4-9.

3. I think Gnubg it gives away something on primes 5-10 and 6-11, noticeably more on primes 7-12, 8-13 and 9-14, (note the gammon losses, as well as the drop-off in wins), and blunders on primes 9-14 and higher.

4. Gnubg loses too many gammons for primes 6-11 and higher. In 100+ manual rollouts, I've never lost a gammon.

5. I think they're all passes, even with my less-than-world class play. Since Gnubg rolls out prime 8-13 to a take, I analyzed a few games played from that position. As it turns out, it's very easy to collect obvious examples of serious misplays by Gnubg. I think a take on prime 8-13 is a blunder.

Move number 11: Blue to play 15

White28


aX1O1O ' ' ' ' ' ' ' '2O

' ' ' ' ' '1X2O2O2O2O3O

Blue183

Position ID: /wMACADYthtAAQ Match ID: QokUAAAAAAAA

• Blue moves 22/21 12/7*

Alert: bad move ( -0.070)

Alert: very unlucky roll! ( -0.001)

# Ply Move Equity
1 2 23/18 22/21 +0.331
0.756 0.000 0.000 - 0.244 0.096 0.001
2 2 23/17 +0.320 ( -0.011)
0.752 0.000 0.000 - 0.248 0.099 0.001
• 6 2 22/21 12/7* +0.262 ( -0.070)
0.729 0.000 0.000 - 0.271 0.103 0.001

There's no reason not to attack immediately with 12/7*.

Move number 13: Blue to play 33

White28


aX '1O ' ' '1O ' ' ' '2O

' ' ' ' ' '1X2O2O2O3O2O

Blue177

Position ID: /wMACADYdhuEAA Match ID: QokNAAAAAAAA

• Blue moves 13/7*(2)

Alert: doubtful move ( -0.027)

# Ply Move Equity
1 2 22/16 18/12 +0.379
0.765 0.000 0.000 - 0.235 0.071 0.000
2 2 22/10 +0.356 ( -0.023)
0.756 0.000 0.000 - 0.244 0.074 0.000
• 4 2 13/7*(2) +0.352 ( -0.027)
0.757 0.000 0.000 - 0.243 0.079 0.001

Advancing the prime with 13/7*(2) is obviously best.

Move number 13: Blue to play 62

White28


aX1O ' ' ' ' ' ' ' '1O3O

' ' ' ' ' '1X2O2O2O2O2O

Blue176

Position ID: /wMACADYtl0AAQ Match ID: QgkLAAAAAAAA

• Blue moves 14/12 13/7*

Alert: doubtful move ( -0.013)

# Ply Move Equity
1 2 23/17 13/11 +0.354
0.759 0.000 0.000 - 0.241 0.082 0.001
• 2 2 14/12 13/7* +0.340 ( -0.013)
0.754 0.000 0.000 - 0.246 0.084 0.001

13/7* is obvious, 14/12 puts a spare in a good place.

Move number 15: Blue to play 16

White31


aX1O ' ' ' ' ' ' ' ' '2O

' ' '1X ' '1O2O2O2O2O3O

Blue168

Position ID: /wMAQAC0bTcAAQ Match ID: QokYAAAAAAAA

• Blue moves 13/7 12/11

Alert: bad move ( -0.073)

# Ply Move Equity
1 2 23/16 +0.415
0.780 0.000 0.000 - 0.220 0.068 0.000
2 2 13/12 13/7 +0.408 ( -0.008)
0.771 0.000 0.000 - 0.229 0.055 0.000
• 9 2 13/7 12/11 +0.342 ( -0.073)
0.746 0.000 0.000 - 0.254 0.063 0.001

13/7 is clear and 12/11 good, for the same reason as before.

Move number 19: Blue to play 52

White30


aX1O ' ' ' ' ' ' ' ' '1O

' ' ' '1X2O2O2O2O2O2O1O

Blue150

Position ID: /wMAIAC2bSsAAQ Match ID: QokKAAAAAAAA

• Blue moves 12/5*

Alert: doubtful move ( -0.010)

# Ply Move Equity
1 2 13/8 12/10 +0.479
0.795 0.000 0.000 - 0.205 0.041 0.000
2 2 23/21 13/8 +0.473 ( -0.005)
0.796 0.000 0.000 - 0.204 0.049 0.000
• 3 2 12/5* +0.468 ( -0.010)
0.791 0.000 0.000 - 0.209 0.043 0.000

12/5* has to be right; the game plan is to advance the prime.

Move number 11: Blue to play 44

White28


aX1O1O ' ' ' ' ' '1O '2O

' ' ' ' ' '1X2O2O2O2O2O

Blue186

Position ID: /wMACADYtk1AAQ Match ID: QgkSAAAAAAAA

• Blue moves 22/14 15/7*

Alert: doubtful move ( -0.031)

# Ply Move Equity
1 2 23/11 22/18 +0.339
0.755 0.000 0.000 - 0.245 0.087 0.001
2 2 23/19 22/10 +0.335 ( -0.004)
0.752 0.000 0.000 - 0.248 0.085 0.001
• 7 2 22/14 15/7* +0.308 ( -0.031)
0.741 0.000 0.000 - 0.259 0.084 0.001

Again, hitting on the 7* point follows the game plan.

Move number 17: Blue to play 66

White28


aX '2O ' ' ' ' ' ' ' '2O

' ' ' ' ' '1X2O2O2O2O2O

Blue195

Position ID: /wMACADYtg1gBA Match ID: QgkbAAAAAAAA

• Blue moves bar/19 22/16 13/7*(2)

Alert: bad move ( -0.051)

# Ply Move Equity
1 2 bar/19 22/10 22/16 +0.330
0.750 0.000 0.000 - 0.250 0.083 0.001
2 2 bar/7* 22/16 +0.311 ( -0.019)
0.745 0.000 0.000 - 0.255 0.092 0.001
• 5 2 bar/19 22/16 13/7*(2) +0.279 ( -0.051)
0.739 0.000 0.000 - 0.261 0.108 0.001

And once again ...

And finally, there were many other positions where Gnubg and I did not agree and the difference in equity may be small but cumulatively large. Gnubg likes to put a spare three away from the next point in the prime much more often than I do, and likes to put a spare 5 away, 6 away and 7 away much less often than I do. Here's example illustrating both types:

Move number 27: Blue to play 61

White31


aX ' ' ' ' ' ' ' ' ' '1O

' ' '1X '1O2O2O2O3O2O2O

Blue143

Position ID: /wMAQADadlsAAA Match ID: QgkHAAAAAAAA

• Blue moves 12/11 12/6

Alert: doubtful move ( +0.000)

# Ply Move Equity
• 1 R 12/11 12/6 +0.552
0.8070.0000.000-0.1930.0110.000 +0.603 +0.552
0.0030.0000.000-0.0030.0030.000 0.008 0.009
Full cubeful rollout with var.redn.
124 games, Mersenne Twister dice gen. with seed 1049627572 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
2 R 12/6 10/9 +0.534 ( -0.018)
0.8030.0000.000-0.1970.0140.000 +0.592 +0.534
0.0030.0000.000-0.0030.0020.000 0.007 0.009
Full cubeful rollout with var.redn.
124 games, Mersenne Twister dice gen. with seed 1049627572 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

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