About a month ago, Dmitriy Obukhov posted an endgame problem, but to my knowledge did not post a rollout. Below are some rollouts, followed by an attempt to make sense of them.
Dmitriy's original position:
      
 
           
 | | White is Player 2
score: 0
pip: 183 | Money session
Jacoby | pip: 75
score: 0
Blue is Player 1 |
|
| XGID=bBBBcCC-A--Bb-----bbbb----:1:-1:1:61:0:0:1:0:10 |
| Blue to play 61 |
| 1. | Rollout1 | 11/5 8/7 | eq: +1.714 |
| Player:
Opponent: | 92.52% (G:88.17% B:1.92%)
7.48% (G:0.08% B:0.00%) | Conf: ± 0.008 (+1.706...+1.722)
Duration: 1 hour 42 minutes |
|
| 2. | Rollout1 | 8/2 6/5 | eq: +1.694 (-0.020) |
| Player:
Opponent: | 92.01% (G:87.65% B:1.91%)
7.99% (G:0.21% B:0.00%) | Conf: ± 0.008 (+1.686...+1.702)
Duration: 52 minutes 17 seconds |
|
| 3. | Rollout1 | 11/10 8/2 | eq: +1.690 (-0.024) |
| Player:
Opponent: | 91.87% (G:87.63% B:1.94%)
8.13% (G:0.17% B:0.00%) | Conf: ± 0.008 (+1.682...+1.698)
Duration: 28 minutes 44 seconds |
|
| 4. | Rollout1 | 11/5 6/5 | eq: +1.673 (-0.041) |
| Player:
Opponent: | 91.45% (G:87.25% B:1.80%)
8.55% (G:0.42% B:0.00%) | Conf: ± 0.008 (+1.665...+1.681)
Duration: 30 minutes 34 seconds |
|
| 5. | Rollout1 | 11/10 11/5 | eq: +1.653 (-0.061) |
| Player:
Opponent: | 90.87% (G:86.62% B:1.99%)
9.13% (G:0.41% B:0.01%) | Conf: ± 0.009 (+1.644...+1.662)
Duration: 1 hour 39 minutes |
|
| 6. | Rollout1 | 8/1 | eq: +1.652 (-0.062) |
| Player:
Opponent: | 90.89% (G:86.27% B:1.88%)
9.11% (G:0.23% B:0.01%) | Conf: ± 0.008 (+1.644...+1.660)
Duration: 1 hour 13 minutes |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21
Daniel Murphy's suggested variant, with only one on the bar:
| | White is Player 2
score: 0
pip: 166 | Money session
Jacoby | pip: 75
score: 0
Blue is Player 1 |
|
| XGID=aBBBcCC-A--Bb----abbbb----:1:-1:1:61:0:0:1:0:10 |
| Blue to play 61 |
| 1. | Rollout1 | 11/5 6/5 | eq: +1.462 |
| Player:
Opponent: | 89.60% (G:72.32% B:0.33%)
10.40% (G:0.62% B:0.02%) | Conf: ± 0.009 (+1.453...+1.471)
Duration: 2 hours 28 minutes |
|
| 2. | Rollout1 | 11/5 8/7 | eq: +1.432 (-0.030) |
| Player:
Opponent: | 88.69% (G:71.93% B:0.31%)
11.31% (G:0.78% B:0.02%) | Conf: ± 0.009 (+1.423...+1.441)
Duration: 1 hour 20 minutes |
|
| 3. | Rollout1 | 8/2 6/5 | eq: +1.430 (-0.031) |
| Player:
Opponent: | 88.39% (G:72.03% B:0.30%)
11.61% (G:0.74% B:0.02%) | Conf: ± 0.008 (+1.422...+1.438)
Duration: 1 hour 05 minutes |
|
| 4. | Rollout1 | 8/1 | eq: +1.383 (-0.078) |
| Player:
Opponent: | 87.44% (G:69.72% B:0.27%)
12.56% (G:0.75% B:0.02%) | Conf: ± 0.009 (+1.374...+1.392)
Duration: 2 hours 05 minutes |
|
| 5. | XG Roller+ | 11/10 11/5 | eq: +1.400 (-0.062) |
| Player:
Opponent: | 86.75% (G:72.24% B:0.67%)
13.25% (G:1.15% B:0.03%) | |
|
| 6. | XG Roller+ | 11/10 8/2 | eq: +1.398 (-0.064) |
| Player:
Opponent: | 86.81% (G:71.78% B:0.66%)
13.19% (G:1.01% B:0.02%) | |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21
Two more variants of my own, basically the same as the two above but where White has a stronger board:
| | White is Player 2
score: 0
pip: 153 | Money session
Jacoby | pip: 75
score: 0
Blue is Player 1 |
|
| XGID=bBBBcCC-A--B-------bbbbb--:1:-1:1:61:0:0:1:0:10 |
| Blue to play 61 |
| 1. | Rollout1 | 11/5 8/7 | eq: +1.614 |
| Player:
Opponent: | 91.72% (G:79.54% B:2.27%)
8.28% (G:0.06% B:0.00%) | Conf: ± 0.008 (+1.606...+1.622)
Duration: 53 minutes 55 seconds |
|
| 2. | Rollout1 | 8/2 6/5 | eq: +1.601 (-0.012) |
| Player:
Opponent: | 91.33% (G:79.40% B:2.07%)
8.67% (G:0.16% B:0.00%) | Conf: ± 0.008 (+1.593...+1.609)
Duration: 28 minutes 07 seconds |
|
| 3. | Rollout1 | 11/10 8/2 | eq: +1.601 (-0.013) |
| Player:
Opponent: | 91.27% (G:79.31% B:2.15%)
8.73% (G:0.12% B:0.00%) | Conf: ± 0.008 (+1.593...+1.609)
Duration: 12 minutes 55 seconds |
|
| 4. | Rollout1 | 11/5 6/5 | eq: +1.568 (-0.046) |
| Player:
Opponent: | 90.39% (G:78.62% B:2.09%)
9.61% (G:0.57% B:0.02%) | Conf: ± 0.009 (+1.559...+1.577)
Duration: 16 minutes 06 seconds |
|
| 5. | Rollout1 | 11/10 11/5 | eq: +1.566 (-0.047) |
| Player:
Opponent: | 90.09% (G:78.69% B:2.31%)
9.91% (G:0.56% B:0.02%) | Conf: ± 0.008 (+1.558...+1.574)
Duration: 7 minutes 35 seconds |
|
| 6. | Rollout1 | 8/1 | eq: +1.563 (-0.050) |
| Player:
Opponent: | 90.28% (G:78.36% B:2.03%)
9.72% (G:0.16% B:0.00%) | Conf: ± 0.008 (+1.555...+1.571)
Duration: 21 minutes 43 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21
| | White is Player 2
score: 0
pip: 134 | Money session
Jacoby | pip: 75
score: 0
Blue is Player 1 |
|
| XGID=aBBBcCC-A--B-------cbbbb--:1:-1:1:61:0:0:1:0:10 |
| Blue to play 61 |
| 1. | Rollout1 | 11/5 6/5 | eq: +1.160 |
| Player:
Opponent: | 88.55% (G:43.92% B:0.33%)
11.45% (G:0.73% B:0.02%) | Conf: ± 0.007 (+1.153...+1.167)
Duration: 57 minutes 49 seconds |
|
| 2. | Rollout1 | 8/2 6/5 | eq: +1.145 (-0.014) |
| Player:
Opponent: | 87.52% (G:44.94% B:0.31%)
12.48% (G:0.47% B:0.01%) | Conf: ± 0.007 (+1.138...+1.152)
Duration: 31 minutes 50 seconds |
|
| 3. | Rollout1 | 8/1 | eq: +1.113 (-0.047) |
| Player:
Opponent: | 86.66% (G:43.89% B:0.28%)
13.34% (G:0.48% B:0.01%) | Conf: ± 0.007 (+1.106...+1.120)
Duration: 49 minutes 21 seconds |
|
| 4. | Rollout1 | 11/5 8/7 | eq: +1.112 (-0.047) |
| Player:
Opponent: | 86.85% (G:43.62% B:0.36%)
13.15% (G:1.16% B:0.03%) | Conf: ± 0.007 (+1.105...+1.119)
Duration: 26 minutes 42 seconds |
|
| 5. | XG Roller+ | 11/10 8/2 | eq: +1.073 (-0.086) |
| Player:
Opponent: | 84.96% (G:43.21% B:0.53%)
15.04% (G:1.38% B:0.04%) | |
|
| 6. | XG Roller+ | 11/10 11/5 | eq: +1.058 (-0.101) |
| Player:
Opponent: | 84.36% (G:43.32% B:0.55%)
15.64% (G:1.94% B:0.06%) | |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21
My choice in both of the original positions was 8/2 6/5, which is not a huge blunder but which is also not the top play. 8/2 6/5 fares slightly better in my variants.
Obviously, Blue's game plan is to get home safely. There are both tactical and strategical considerations here. Tactically, we want to minimize immediate shots, all other things being equal. Strategically, we want to put our checkers on certain points and not others, for longer-term safety and flexibility.
As I mentioned before, strategically, the best points to occupy are the inner-board points in front of the anchor. Desirability falls off as you move in either direction (until you get to the point 7 away from the anchor; I'll come back to this in a moment). Checkers on deep inner-board points waste pips for the gammon race, are not very flexible, and represent pips that you might have more fruitfully used to bring your outside checkers home. Checkers within direct-shot range of the anchor represent liabilities because you need to clear them urgently as soon as the opponent is no longer on the bar. The further from home they are, the harder they are to safety.
The point 7 away from the anchor is actually pretty good because it's not in direct-shot range of the anchor. It's noticeably preferable to the 6-away point for this reason. As you move further away, of course, the points get less desirable because they're further from home.
Let's now analyze the positions above in light of these theories. The latter two positions are IMO easier to understand because the tactical effect of getting hit is sharpened, due to White's powerful board. An immediate hit is fatal. When White has two on the bar, we see that the plays that leave 1 shot out of 36 (with double 4's from the bar) are out of contention. Bringing a checker in efficiently with 11/5 seems to be the top choice (though note the residual statistical variance), but there are two other reasonable plays that leave no shots. When White has one on the bar, then the top two plays leave 1 and 0 shots respectively. I'm slightly surprised that 8/2 6/5 leaving no immediate shots isn't on top (though again, note the residual variance); however, since White has only one on the bar and is thus more likely to enter quickly, there is more urgency to scoot the back checkers home while it's still relatively safe to leave 1 shot out of 36.
Returning now to Dmitriy's original position, the relative ranking of the top plays is the same as in my variant. There are some quantitative differences but I'm not sure they're statistically significant. In Daniel Murphy's position, 8/2 6/5 drops to third place; I would attribute this to White's weaker front position. The downside of leaving an immediate shot, while serious, is not as severe as in my variant, and trying to get a distant checker home efficiently while White is still on the bar increases in relative importance.