Answers to Chow’s Checkerplay Challenge
Scoring: Give yourself 2 points if you chose the top play of
the rollout, and 0 points otherwise, unless indicated explicitly below.
All rollouts were performed with eXtreme Gammon 1.21, Rockwell–Kazaross
MET.
Problem 1: Money play with Jacoby
It is easy, especially over the board, to see only two plays here:
16/10* and 21/16 9/8. However, the blot on the 8pt is not in all
that much danger (there are some rolls where White will decline to
break anchor to hit), and the blot on the 23pt is poorly positioned.
Many players underestimate how weak a blot on the 23pt is when it
is blocked by the opponent’s 8pt.
Shift Black’s blot forward a pip to the 22pt
and the decision is much closer, with 21/16 9/8 apparently best
(see variant below).
Pip counts: White 161, Black 127
Position ID: sHPwBAY2mw4IEg Match ID: cIkUAAAAAAAA
1.  Rollout^{1}  23/22 21/16  eq: +0.289 
 Player: Opponent: 
57.40% (G:14.99% B:0.41%)
42.60% (G:8.44% B:0.34%)  Conf: ± 0.014 (+0.275...+0.303) Duration: 3 hours 49 minutes 

2.  Rollout^{1}  16/10*  eq: +0.196 (0.093) 
 Player: Opponent: 
53.13% (G:20.86% B:0.54%)
46.87% (G:10.00% B:0.49%)  Conf: ± 0.019 (+0.177...+0.215) Duration: 3 hours 56 minutes 

3.  Rollout^{1}  21/16 9/8  eq: +0.191 (0.098) 
 Player: Opponent: 
54.97% (G:14.42% B:0.36%)
45.03% (G:9.33% B:0.40%)  Conf: ± 0.014 (+0.177...+0.205) Duration: 3 hours 27 minutes 

4.  Rollout^{2}  21/16 8/7  eq: +0.169 (0.120) 
 Player: Opponent: 
54.15% (G:14.67% B:0.33%)
45.85% (G:9.23% B:0.37%)  Conf: ± 0.012 (+0.157...+0.181) Duration: 3 hours 42 minutes 


^{1} 2592 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply
^{2} 2592 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Variant:
Pip counts: White 161, Black 126
Position ID: sHPwBAY2mw4ICg Match ID: cIkUAAAAAAAA
1.  Rollout^{1}  21/16 9/8  eq: +0.324 
 Player: Opponent: 
58.79% (G:13.66% B:0.34%)
41.21% (G:7.79% B:0.33%)  Conf: ± 0.011 (+0.313...+0.335) Duration: 5 hours 34 minutes 

2.  Rollout^{1}  16/10*  eq: +0.299 (0.025) 
 Player: Opponent: 
55.71% (G:21.87% B:0.56%)
44.29% (G:9.36% B:0.44%)  Conf: ± 0.012 (+0.287...+0.311) Duration: 5 hours 46 minutes 

3.  Rollout^{1}  22/16  eq: +0.289 (0.035) 
 Player: Opponent: 
56.97% (G:16.67% B:0.44%)
43.03% (G:8.70% B:0.36%)  Conf: ± 0.013 (+0.276...+0.302) Duration: 5 hours 11 minutes 

4.  Rollout^{1}  21/16 8/7  eq: +0.285 (0.039) 
 Player: Opponent: 
57.47% (G:14.23% B:0.33%)
42.53% (G:7.97% B:0.33%)  Conf: ± 0.011 (+0.274...+0.296) Duration: 5 hours 13 minutes 


^{1} 3888 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Problem 2: Money play with Jacoby
The ’tweener play 23/21 9/4 is the top play.
Sometimes in positions like this it is right to hit despite leaving
two homeboard blots, but typically not when the blots are this high
in the board with lower points made.
Similarly, sometimes it is right to cover both blots,
but typically not when there is so little time
to escape the back checkers.
Pip counts: White 124, Black 115
Position ID: zG4LA0C2uhkAGA Match ID: UQkVAAAAAAAA
1.  Rollout^{1}  23/21 9/4  eq: +0.246 
 Player: Opponent: 
47.18% (G:25.56% B:0.75%)
52.82% (G:16.62% B:1.50%)  Conf: ± 0.013 (+0.233...+0.259) Duration: 3 hours 12 minutes 

2.  Rollout^{1}  23/16*  eq: +0.151 (0.095) 
 Player: Opponent: 
47.39% (G:25.66% B:0.73%)
52.61% (G:21.09% B:2.20%)  Conf: ± 0.010 (+0.141...+0.161) Duration: 3 hours 08 minutes 

3.  Rollout^{1}  9/4 7/5  eq: +0.084 (0.162) 
 Player: Opponent: 
42.45% (G:22.66% B:0.48%)
57.55% (G:11.91% B:0.52%)  Conf: ± 0.009 (+0.075...+0.093) Duration: 2 hours 33 minutes 


^{1} 3888 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Problem 3: 1 point match
As a general rule, one should try to “fight prime with prime,”
especially at DMP (double match point).
This position is no exception; aggressively slotting the back of the prime
will lose more gammons than the obvious safe play 15/8,
but gammon losses are irrelevant at DMP.
Pointing on White’s blot might be right
if Black’s fiveprime were shifted forwards a pip
(and the roll changed to 54),
but here 8/4* 7/4 sacrifices too much structure.
Pip counts: gnubg 114, tchow 159
Position ID: ZruBAwSwbcMEMA Match ID: cIkxAAAAAAAA
1.  Rollout^{1}  15/11 13/10  eq: 0.171 
 Player: Opponent: 
41.47% (G:7.18% B:0.49%)
58.53% (G:35.23% B:16.26%)  Conf: ± 0.008 (0.179...0.163) Duration: 5 hours 34 minutes 

2.  Rollout^{1}  8/4* 7/4  eq: 0.216 (0.046) 
 Player: Opponent: 
39.19% (G:7.49% B:0.73%)
60.81% (G:36.35% B:17.16%)  Conf: ± 0.007 (0.223...0.209) Duration: 5 hours 22 minutes 

3.  Rollout^{1}  13/10 13/9  eq: 0.218 (0.047) 
 Player: Opponent: 
39.12% (G:5.78% B:0.41%)
60.88% (G:38.17% B:17.93%)  Conf: ± 0.007 (0.225...0.211) Duration: 4 hours 55 minutes 

4.  Rollout^{1}  15/11 7/4*  eq: 0.220 (0.050) 
 Player: Opponent: 
38.98% (G:5.89% B:0.49%)
61.02% (G:39.45% B:17.61%)  Conf: ± 0.007 (0.227...0.213) Duration: 5 hours 50 minutes 

5.  Rollout^{1}  15/8  eq: 0.238 (0.067) 
 Player: Opponent: 
38.11% (G:6.11% B:0.47%)
61.89% (G:28.86% B:9.18%)  Conf: ± 0.006 (0.244...0.232) Duration: 4 hours 38 minutes 

6.  Rollout^{2}  13/10 8/4*  eq: 0.300 (0.129) 
 Player: Opponent: 
35.02% (G:4.95% B:0.33%)
64.98% (G:47.07% B:30.43%)  Conf: ± 0.012 (0.312...0.288) Duration: 3 hours 44 minutes 

7.  Rollout^{2}  13/9 7/4*  eq: 0.302 (0.131) 
 Player: Opponent: 
34.92% (G:4.58% B:0.42%)
65.08% (G:45.10% B:27.61%)  Conf: ± 0.012 (0.314...0.290) Duration: 3 hours 49 minutes 

8.  Rollout^{2}  13/6  eq: 0.302 (0.131) 
 Player: Opponent: 
34.92% (G:4.61% B:0.31%)
65.08% (G:39.09% B:18.07%)  Conf: ± 0.009 (0.311...0.293) Duration: 2 hours 25 minutes 


^{1} 2592 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
^{2} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Problem 4: Money play with Jacoby
Did you consider hitting loose?
If not, then you should learn to put such “banana split” plays
on your radar screen, especially when you have a much stronger board
than your opponent does.
However, here the banana split does not gain quite enough
(though see the variant position below).
But even if you reject (or fail to consider!) the banana split,
there are still several ways to go wrong.
The right plan is to maximize your chances
of hitting next turn;
if you realize this, then you should find bar/24 7/4.
Anchoring might look plausible, but with such a powerful board,
you should be attacking, not defending.
Pip counts: White 136, Black 112
Position ID: mOeGAxCz7QIBSA Match ID: QYkFAAAAAAAA
1.  Rollout^{1}  Bar/24 7/4  eq: 0.089 
 Player: Opponent: 
49.31% (G:23.54% B:0.20%)
50.69% (G:9.71% B:0.58%)  Conf: ± 0.009 (0.098...0.080) Duration: 2 hours 01 minute 

2.  Rollout^{1}  Bar/24 5/2*  eq: 0.153 (0.064) 
 Player: Opponent: 
47.66% (G:27.26% B:0.16%)
52.34% (G:17.87% B:2.09%)  Conf: ± 0.010 (0.163...0.143) Duration: 2 hours 11 minutes 

3.  Rollout^{1}  Bar/24 13/10  eq: 0.155 (0.067) 
 Player: Opponent: 
47.00% (G:23.58% B:0.21%)
53.00% (G:11.11% B:0.71%)  Conf: ± 0.009 (0.164...0.146) Duration: 1 hour 54 minutes 

4.  Rollout^{1}  Bar/22 3/2*  eq: 0.162 (0.074) 
 Player: Opponent: 
47.69% (G:27.05% B:0.18%)
52.31% (G:17.66% B:2.00%)  Conf: ± 0.010 (0.172...0.152) Duration: 2 hours 07 minutes 

5.  Rollout^{2}  Bar/22 7/6  eq: 0.213 (0.125) 
 Player: Opponent: 
45.87% (G:20.03% B:0.28%)
54.13% (G:11.05% B:0.65%)  Conf: ± 0.013 (0.226...0.200) Duration: 1 hour 01 minute 

6.  Rollout^{2}  Bar/24 23/20  eq: 0.235 (0.147) 
 Player: Opponent: 
45.28% (G:21.72% B:0.25%)
54.72% (G:14.31% B:1.18%)  Conf: ± 0.012 (0.247...0.223) Duration: 58 minutes 08 seconds 

7.  Rollout^{2}  Bar/22 23/22  eq: 0.330 (0.241) 
 Player: Opponent: 
42.73% (G:17.50% B:0.14%)
57.27% (G:9.99% B:0.39%)  Conf: ± 0.013 (0.343...0.317) Duration: 54 minutes 30 seconds 


^{1} 2592 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
^{2} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Variant:
Pip counts: White 135, Black 112
Position ID: mNeGAxCz7QIBSA Match ID: QYkMAAAAAAAA
1.  XG Roller+  Bar/24 5/2*  eq: +0.016 
 Player: Opponent: 
50.85% (G:35.36% B:0.46%)
49.15% (G:19.63% B:2.75%)  

2.  XG Roller+  Bar/22 3/2*  eq: 0.052 (0.068) 
 Player: Opponent: 
49.20% (G:33.20% B:0.53%)
50.80% (G:19.34% B:2.50%)  

3.  XG Roller+  Bar/24 7/4  eq: 0.085 (0.101) 
 Player: Opponent: 
48.55% (G:24.97% B:0.41%)
51.45% (G:11.35% B:0.65%)  

Problem 5: 1 point match
It might look suicidal to hit loose, but attacking
White’s two blots is the best chance
to win from this inferior position.
18/11* sends the more advanced blot back,
but sacrifices too much structure in comparison with 6/5*.
Scoring: Give yourself 1 point if you chose 13/7 6/5*.
Pip counts: White 135, Black 177
Position ID: bBvwBQLgc3AwMA Match ID: cAknAAAAAAAA
1.  Rollout^{1}  24/18 6/5*  eq: 0.272 
 Player: Opponent: 
36.40% (G:6.98% B:0.59%)
63.60% (G:35.55% B:6.33%)  Conf: ± 0.005 (0.277...0.267) Duration: 15 hours 15 minutes 

2.  Rollout^{1}  13/7 6/5*  eq: 0.292 (0.020) 
 Player: Opponent: 
35.39% (G:6.14% B:0.51%)
64.61% (G:35.23% B:11.81%)  Conf: ± 0.005 (0.297...0.287) Duration: 14 hours 12 minutes 

3.  Rollout^{2}  13/7 8/7  eq: 0.325 (0.053) 
 Player: Opponent: 
33.75% (G:6.74% B:0.41%)
66.25% (G:29.32% B:5.40%)  Conf: ± 0.008 (0.333...0.317) Duration: 3 hours 22 minutes 

4.  Rollout^{2}  24/23 24/18  eq: 0.344 (0.072) 
 Player: Opponent: 
32.80% (G:5.77% B:0.48%)
67.20% (G:31.84% B:3.34%)  Conf: ± 0.008 (0.352...0.336) Duration: 3 hours 22 minutes 

5.  Rollout^{2}  24/18 8/7  eq: 0.358 (0.086) 
 Player: Opponent: 
32.11% (G:5.70% B:0.24%)
67.89% (G:35.98% B:5.17%)  Conf: ± 0.008 (0.366...0.350) Duration: 3 hours 06 minutes 

6.  XG Roller+  8/2 6/5*  eq: 0.364 (0.092) 
 Player: Opponent: 
31.81% (G:5.11% B:0.18%)
68.19% (G:33.39% B:3.93%)  

7.  XG Roller+  24/23 13/7  eq: 0.381 (0.109) 
 Player: Opponent: 
30.93% (G:5.53% B:0.19%)
69.07% (G:32.60% B:2.38%)  

8.  XG Roller+  24/17  eq: 0.405 (0.133) 
 Player: Opponent: 
29.73% (G:4.89% B:0.18%)
70.27% (G:36.64% B:2.03%)  

9.  XG Roller+  18/11*  eq: 0.421 (0.149) 
 Player: Opponent: 
28.97% (G:4.93% B:0.19%)
71.03% (G:32.75% B:3.89%)  


^{1} 5184 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
^{2} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Problem 6: Money play with Jacoby
Playing 8/2 here is a gargantuan blunder,
turning a position in which you have a significant advantage
into a position in which your opponent has a significant advantage.
But even if you realize that 23/17 is mandatory,
the choice between 17/14 and 8/5 is a difficult technical decision.
It might seem natural to minimize shots with 17/14, duplicating
White’s threes to hit.
However, 8/5 cleans up a blot and somewhat duplicates White’s sixes
to hit and escape.
The balance is a delicate one and seemingly small changes
can tip things the other way; see the variants below, for example.
Pip counts: White 141, Black 105
Position ID: bLcBATi23QkAGA Match ID: cAkPAAAAAAAA
1.  Rollout^{1}  23/17 8/5  eq: +0.486 
 Player: Opponent: 
58.02% (G:25.04% B:3.37%)
41.98% (G:8.42% B:0.29%)  Conf: ± 0.009 (+0.477...+0.495) Duration: 3 hours 43 minutes 

2.  Rollout^{1}  23/14  eq: +0.386 (0.101) 
 Player: Opponent: 
56.93% (G:23.54% B:2.77%)
43.07% (G:11.06% B:0.54%)  Conf: ± 0.007 (+0.379...+0.393) Duration: 2 hours 43 minutes 

3.  Rollout^{2}  23/17 6/3  eq: +0.322 (0.164) 
 Player: Opponent: 
55.31% (G:24.20% B:3.24%)
44.69% (G:12.85% B:0.69%)  Conf: ± 0.027 (+0.295...+0.349) Duration: 33 minutes 00 second 

4.  Rollout^{2}  23/17 5/2  eq: +0.299 (0.188) 
 Player: Opponent: 
54.41% (G:24.49% B:3.47%)
45.59% (G:12.76% B:0.62%)  Conf: ± 0.028 (+0.271...+0.327) Duration: 26 minutes 14 seconds 

5.  Rollout^{2}  8/2 6/3  eq: 0.355 (0.841) 
 Player: Opponent: 
40.47% (G:13.89% B:1.26%)
59.53% (G:15.16% B:0.58%)  Conf: ± 0.019 (0.374...0.336) Duration: 30 minutes 35 seconds 

6.  Rollout^{2}  8/2 5/2  eq: 0.380 (0.866) 
 Player: Opponent: 
39.41% (G:13.53% B:1.11%)
60.59% (G:15.94% B:0.64%)  Conf: ± 0.019 (0.399...0.361) Duration: 17 minutes 59 seconds 


^{1} 10368 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
^{2} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Variant 1: Note that the decision below can be made noticeably closer
by shifting Black’s 4pt spare to the 5pt.
Pip counts: White 141, Black 104
Position ID: bLuBADi22wkAGA Match ID: cAkaAAAAAAAA
1.  Rollout^{1}  23/13  eq: +0.343 
 Player: Opponent: 
55.64% (G:23.08% B:2.66%)
44.36% (G:10.66% B:0.51%)  Conf: ± 0.010 (+0.333...+0.353) Duration: 3 hours 39 minutes 

2.  Rollout^{1}  23/17 8/4  eq: +0.290 (0.052) 
 Player: Opponent: 
53.93% (G:23.23% B:2.77%)
46.07% (G:9.35% B:0.35%)  Conf: ± 0.010 (+0.280...+0.300) Duration: 3 hours 04 minutes 

3.  Rollout^{2}  23/17 6/2  eq: +0.110 (0.233) 
 Player: Opponent: 
50.58% (G:21.97% B:2.64%)
49.42% (G:13.41% B:0.66%)  Conf: ± 0.021 (+0.089...+0.131) Duration: 27 minutes 17 seconds 

4.  Rollout^{2}  8/2 6/2  eq: 0.505 (0.848) 
 Player: Opponent: 
36.81% (G:11.87% B:1.03%)
63.19% (G:16.43% B:0.67%)  Conf: ± 0.017 (0.522...0.488) Duration: 27 minutes 46 seconds 


^{1} 7776 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
^{2} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Variant 2:
Pip counts: gnubg 141, tchow 105
Position ID: bLuBADi23QkAGA Match ID: cAkPAAAAAAAA
1.  XG Roller+  23/17 8/5  eq: +0.410 
 Player: Opponent: 
56.15% (G:23.94% B:3.08%)
43.85% (G:8.16% B:0.31%)  

2.  XG Roller+  23/14  eq: +0.319 (0.092) 
 Player: Opponent: 
55.07% (G:23.40% B:3.10%)
44.93% (G:11.28% B:0.61%)  

3.  XG Roller+  23/17 6/3  eq: +0.252 (0.158) 
 Player: Opponent: 
53.29% (G:22.66% B:2.90%)
46.71% (G:11.98% B:0.64%)  

Problem 7: Gammon go (2 point match, Black 0, White 1, Crawford)
At gammon go, gammon wins are worth twice as much as they usually are
and gammon losses do not matter.
Therefore one should usually play aggressively at this score,
hitting and making homeboard points.
The obvious aggressive play here is 9/3* 8/3.
However, even at gammon go, there are limits
to how aggressively one should play.
White’s board is simply too strong to be ignored here,
and anything other than the seemingly craven 23/18 8/2 is a big mistake.
Pip counts: White 148, Black 152
Position ID: zM7gASTgc8NBEA Match ID: 8AlXABAAAAAA
1.  Rollout^{1}  23/18 8/2  eq: +0.166 
 Player: Opponent: 
47.71% (G:10.60% B:0.68%)
52.29% (G:17.22% B:1.95%)  Conf: ± 0.010 (+0.156...+0.176) Duration: 2 hours 56 minutes 

2.  Rollout^{1}  9/3* 8/3  eq: +0.102 (0.064) 
 Player: Opponent: 
42.29% (G:12.81% B:1.91%)
57.71% (G:25.18% B:4.01%)  Conf: ± 0.011 (+0.091...+0.113) Duration: 2 hours 43 minutes 

3.  Rollout^{1}  23/18 13/7  eq: +0.091 (0.075) 
 Player: Opponent: 
44.72% (G:9.83% B:0.77%)
55.28% (G:20.52% B:2.46%)  Conf: ± 0.011 (+0.080...+0.102) Duration: 3 hours 09 minutes 

4.  Rollout^{1}  23/18 9/3*  eq: +0.082 (0.084) 
 Player: Opponent: 
43.24% (G:10.85% B:0.85%)
56.76% (G:25.04% B:3.07%)  Conf: ± 0.011 (+0.071...+0.093) Duration: 3 hours 20 minutes 

5.  XG Roller+  18/13 8/2  eq: 0.052 (0.218) 
 Player: Opponent: 
39.39% (G:8.03% B:0.32%)
60.61% (G:23.22% B:0.90%)  

6.  XG Roller+  18/7  eq: 0.062 (0.228) 
 Player: Opponent: 
38.84% (G:8.06% B:0.30%)
61.16% (G:21.77% B:0.95%)  

7.  XG Roller+  18/13 9/3*  eq: 0.085 (0.252) 
 Player: Opponent: 
37.08% (G:8.65% B:0.36%)
62.92% (G:24.90% B:1.56%)  

8.  XG Roller+  9/3* 6/1*  eq: 0.104 (0.270) 
 Player: Opponent: 
35.95% (G:8.86% B:0.28%)
64.05% (G:29.17% B:3.18%)  


^{1} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Problem 8: Money play with Jacoby
The obvious play here is 13/5, but then most sixes on the next roll
will force us to leave a double shot. 6/1 5/2 is safe but ugly.
White’s weak board allows us to make the bold, flexible
play of 13/8 5/2, duplicating White’s ones.
Strengthen White’s board (see Variant 1 below)
and we have to play 6/1 5/2.
Note that 13/5 may not be correct even if we still have
four checkers on the midpoint; see Variant 2 below.
Pip counts: White 127, Black 91
Position ID: TJ+DwQC8vQEHAA Match ID: QYkOAAAAAAAA
1.  Rollout^{1}  13/8 5/2  eq: +0.339 
 Player: Opponent: 
70.19% (G:6.97% B:0.21%)
29.81% (G:2.34% B:0.11%)  Conf: ± 0.007 (+0.332...+0.346) Duration: 1 hour 47 minutes 

2.  Rollout^{1}  6/1 5/2  eq: +0.278 (0.061) 
 Player: Opponent: 
68.03% (G:4.68% B:0.10%)
31.97% (G:2.64% B:0.12%)  Conf: ± 0.005 (+0.273...+0.283) Duration: 1 hour 38 minutes 

3.  Rollout^{1}  13/5  eq: +0.276 (0.063) 
 Player: Opponent: 
67.90% (G:6.35% B:0.20%)
32.10% (G:2.09% B:0.06%)  Conf: ± 0.006 (+0.270...+0.282) Duration: 1 hour 20 minutes 


^{1} 2592 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Variant 1:
Pip counts: White 121, Black 91
Position ID: bD2DwQC8vQEHAA Match ID: QYkOAAAAAAAA
1.  Rollout^{1}  6/1 5/2  eq: +0.242 
 Player: Opponent: 
65.99% (G:3.33% B:0.04%)
34.01% (G:2.74% B:0.10%)  Conf: ± 0.007 (+0.235...+0.249) Duration: 52 minutes 58 seconds 

2.  Rollout^{1}  6/1 4/1  eq: +0.202 (0.039) 
 Player: Opponent: 
64.58% (G:3.17% B:0.03%)
35.42% (G:3.31% B:0.13%)  Conf: ± 0.007 (+0.195...+0.209) Duration: 47 minutes 18 seconds 

3.  Rollout^{1}  13/8 5/2  eq: +0.167 (0.075) 
 Player: Opponent: 
62.33% (G:9.78% B:0.23%)
37.67% (G:4.33% B:0.24%)  Conf: ± 0.008 (+0.159...+0.175) Duration: 58 minutes 52 seconds 

4.  Rollout^{1}  13/5  eq: +0.144 (0.097) 
 Player: Opponent: 
62.76% (G:3.91% B:0.11%)
37.24% (G:2.27% B:0.07%)  Conf: ± 0.007 (+0.137...+0.151) Duration: 50 minutes 11 seconds 


^{1} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Variant 2:
Pip counts: White 121, Black 101
Position ID: tpyRwQDc3oAHAA Match ID: QYkOAAAAAAAA
1.  Rollout^{1}  6/1 5/2  eq: +0.277 
 Player: Opponent: 
67.87% (G:2.03% B:0.03%)
32.13% (G:1.84% B:0.04%)  Conf: ± 0.005 (+0.272...+0.282) Duration: 1 hour 58 minutes 

2.  Rollout^{1}  13/5  eq: +0.257 (0.020) 
 Player: Opponent: 
66.88% (G:2.03% B:0.06%)
33.12% (G:1.44% B:0.04%)  Conf: ± 0.004 (+0.253...+0.261) Duration: 1 hour 37 minutes 

3.  Rollout^{1}  13/8 5/2  eq: +0.211 (0.066) 
 Player: Opponent: 
64.37% (G:7.05% B:0.22%)
35.63% (G:3.50% B:0.10%)  Conf: ± 0.006 (+0.205...+0.217) Duration: 1 hour 33 minutes 


^{1} 2592 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Problem 9: Gammon save (2 point match, Black 1, White 0, Crawford)
These final two problems are variants of positions from
Mary Hickey and Marty Storer’s upcoming book,
which they let me have a sneak peek at.
At gammon save, losing a gammon is twice as costly as usual,
and gammon wins have no extra value.
Safe play is usually indicated.
Here, it may seem automatic to safety the outfield blot with 14/13
and then play either 5/3 or 3/1.
The trouble is that we still have that 22pt blot to worry about.
White will gladly hit loose and initiate a blothitting contest,
when our weak home board will become a serious liability.
Priority number one is to strengthen our board with 3/2,
and then 14/12 falls out as the rest of the play.
Note that if it were DMP then 13/10* would probably be best,
but it loses too many gammons at this score.
Pip counts: White 116, Black 116
Position ID: ZncDBAY6N4MFCA Match ID: 8AlFAAAACAAA
1.  Rollout^{1}  14/12 3/2  eq: 0.988 
 Player: Opponent: 
34.59% (G:10.73% B:0.79%)
65.41% (G:33.97% B:2.76%)  Conf: ± 0.008 (0.996...0.980) Duration: 1 hour 42 minutes 

2.  Rollout^{1}  3/1 2/1  eq: 1.068 (0.081) 
 Player: Opponent: 
32.08% (G:9.80% B:0.40%)
67.92% (G:35.50% B:2.64%)  Conf: ± 0.008 (1.076...1.060) Duration: 1 hour 39 minutes 

3.  Rollout^{1}  13/10*  eq: 1.077 (0.089) 
 Player: Opponent: 
36.63% (G:11.59% B:1.18%)
63.37% (G:40.46% B:9.25%)  Conf: ± 0.009 (1.086...1.068) Duration: 2 hours 09 minutes 

4.  Rollout^{1}  5/2  eq: 1.109 (0.122) 
 Player: Opponent: 
30.79% (G:8.34% B:0.60%)
69.21% (G:36.26% B:2.72%)  Conf: ± 0.009 (1.118...1.100) Duration: 1 hour 38 minutes 

5.  Rollout^{1}  14/13 3/1  eq: 1.121 (0.133) 
 Player: Opponent: 
29.03% (G:10.77% B:0.52%)
70.97% (G:35.09% B:1.83%)  Conf: ± 0.009 (1.130...1.112) Duration: 1 hour 51 minutes 

6.  Rollout^{1}  14/13 5/3  eq: 1.123 (0.135) 
 Player: Opponent: 
28.98% (G:9.53% B:0.74%)
71.02% (G:35.12% B:2.03%)  Conf: ± 0.008 (1.131...1.115) Duration: 1 hour 46 minutes 


^{1} 2592 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Problem 10: Money play with Jacoby
This problem may stump even very strong players,
who will see that Black’s strategic goal is
to escape that back checker and avoid getting any other
checkers sent back.
Even at the cost of a triple shot, 23/18 should present itself
as a tempting candidate. (See for example the variant position
below where 23/18 8/7 is the top play.)
However, certain peculiar features of this particular position
collude to make 23/22 8/3* the top play by a surprisingly large margin.
Shift White’s outfield blot forwards a pip or two,
or give White cube ownership,
or move one of the spares from Black’s 8pt to his 7pt,
and hitting becomes much less attractive.
Pip counts: White 160, Black 126
Position ID: 2M7QADKwu8cAEA Match ID: cIkGAAAAAAAA
1.  Rollout^{1}  23/22 8/3*  eq: +0.398 
 Player: Opponent: 
57.85% (G:22.47% B:2.60%)
42.15% (G:11.83% B:0.52%)  Conf: ± 0.020 (+0.378...+0.418) Duration: 3 hours 23 minutes 

2.  Rollout^{1}  23/18 8/7  eq: +0.274 (0.124) 
 Player: Opponent: 
56.22% (G:18.76% B:1.54%)
43.78% (G:11.01% B:0.42%)  Conf: ± 0.016 (+0.258...+0.290) Duration: 3 hours 01 minute 

3.  Rollout^{1}  23/22 11/6  eq: +0.269 (0.129) 
 Player: Opponent: 
55.38% (G:20.74% B:1.91%)
44.62% (G:10.39% B:0.36%)  Conf: ± 0.017 (+0.252...+0.286) Duration: 3 hours 24 minutes 

4.  Rollout^{2}  23/18 6/5  eq: +0.240 (0.158) 
 Player: Opponent: 
55.40% (G:18.43% B:1.55%)
44.60% (G:11.05% B:0.40%)  Conf: ± 0.023 (+0.217...+0.263) Duration: 1 hour 44 minutes 

5.  Rollout^{2}  23/18 7/6  eq: +0.240 (0.158) 
 Player: Opponent: 
55.04% (G:18.48% B:1.55%)
44.96% (G:10.83% B:0.42%)  Conf: ± 0.023 (+0.217...+0.263) Duration: 1 hour 30 minutes 

6.  Rollout^{2}  11/5  eq: +0.233 (0.165) 
 Player: Opponent: 
54.79% (G:20.50% B:1.64%)
45.21% (G:10.67% B:0.33%)  Conf: ± 0.024 (+0.209...+0.257) Duration: 1 hour 48 minutes 

7.  Rollout^{2}  8/3* 7/6  eq: +0.230 (0.168) 
 Player: Opponent: 
54.22% (G:21.49% B:2.12%)
45.78% (G:12.89% B:0.52%)  Conf: ± 0.025 (+0.205...+0.255) Duration: 1 hour 49 minutes 

8.  Rollout^{2}  8/3* 6/5  eq: +0.219 (0.179) 
 Player: Opponent: 
54.55% (G:21.00% B:2.17%)
45.45% (G:13.30% B:0.63%)  Conf: ± 0.027 (+0.192...+0.246) Duration: 1 hour 57 minutes 

9.  Rollout^{2}  8/7 8/3*  eq: +0.218 (0.180) 
 Player: Opponent: 
54.05% (G:21.63% B:2.28%)
45.95% (G:13.25% B:0.58%)  Conf: ± 0.028 (+0.190...+0.246) Duration: 1 hour 42 minutes 


^{1} 2592 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
^{2} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply

Variant:
Pip counts: White 157, Black 126
Position ID: 2M7CADKwu8cAEA Match ID: cIkGAAAAAAAA
1.  Rollout^{1}  23/18 8/7  eq: +0.424 
 Player: Opponent: 
60.21% (G:19.50% B:1.65%)
39.79% (G:10.05% B:0.34%)  Conf: ± 0.018 (+0.406...+0.442) Duration: 1 hour 20 minutes 

2.  Rollout^{1}  23/22 8/3*  eq: +0.343 (0.081) 
 Player: Opponent: 
57.61% (G:21.83% B:2.35%)
42.39% (G:13.22% B:0.54%)  Conf: ± 0.026 (+0.317...+0.369) Duration: 1 hour 31 minutes 

3.  Rollout^{1}  11/5  eq: +0.327 (0.097) 
 Player: Opponent: 
56.93% (G:20.75% B:1.82%)
43.07% (G:10.26% B:0.37%)  Conf: ± 0.022 (+0.305...+0.349) Duration: 1 hour 42 minutes 


^{1} 1296 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
