On Tuesday, December 21, 2021 at 4:46:39 AM UTC, Tim Chow wrote:
XGID=a-BbBCCbB---AB---bbbb-b---:1:-1:1:63:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O O | +---+
| X O O | | O O O | | 2 |
| | | | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X |
| X O | | X X X O X |
| X X O | | X X X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 99 O: 163 X-O: 0-0
Cube: 2, O own cube
X to play 63
I sometimes see players playing safe in this sort of position. I
think their reasoning is that they have the game in the bag so long
as they don't get hit, so the main thing is to avoid giving the
opponent a joker hitting roll from the bar. But in fact, if you
still have checkers in the outfield, then there's probably a good
chance that you're going to have to leave blots at some point as
you bear in. Would you rather leave a blot when your opponent is
on the bar, or when your opponent has come in? Clearly if you have
to leave a blot, you'd rather do it when your opponent is on the bar.
So usually the strategy should be to take some minor risks to clear difficult points and bear in as quickly as possible.
In this position, though, that principle alone may not lead you to
find the best play. Should X bear in two checkers or just one? Is
the 8pt hardest to clear because both 1's and 5's are blocked, or is
the midpoint the hardest to clear because there are very few rolls
that clear it safely?
The answer is that it's the midpoint that is hardest to clear. So
start by playing 13/10, and then 12/6 bears in the harder checker
to bear in, as well as duplicating O's 3's to enter and to hit.
1. Rollout¹ 13/10 12/6 eq:+0.551
Player: 69.46% (G:32.76% B:0.74%)
Opponent: 30.54% (G:3.96% B:0.15%)
Confidence: ±0.008 (+0.543..+0.560) - [100.0%]
2. Rollout¹ 13/4 eq:+0.454 (-0.098)
Player: 66.41% (G:31.86% B:0.77%)
Opponent: 33.59% (G:4.81% B:0.18%)
Confidence: ±0.009 (+0.445..+0.462) - [0.0%]
3. Rollout¹ 12/6 5/2 eq:+0.450 (-0.101)
Player: 66.16% (G:30.69% B:0.52%)
Opponent: 33.84% (G:4.11% B:0.14%)
Confidence: ±0.008 (+0.442..+0.458) - [0.0%]
4. Rollout¹ 12/6 8/5 eq:+0.376 (-0.176)
Player: 63.20% (G:31.32% B:0.72%)
Opponent: 36.80% (G:4.82% B:0.17%)
Confidence: ±0.009 (+0.367..+0.385) - [0.0%]
5. Rollout¹ 8/5 8/2 eq:+0.353 (-0.199)
Player: 62.40% (G:31.43% B:0.69%)
Opponent: 37.60% (G:5.15% B:0.20%)
Confidence: ±0.009 (+0.344..+0.362) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.207.pre-release
Good problem and analysis. I'm familiar with this sort
of position, and I think I would have got this right.
But I'm too indisciplined for Walting so it's hard to be sure.
I would like to add: The ultra-safe approach often works well if you
have a 5 point board rather than a 4 point board. Volunteering indirects
isn't particularly common in that scenario, and where it is correct, the margin is usually smaill.
I see duplication as being absolutely key here in explaining why the top play is better than 13/4. I wouldn't present the analysis as saying that the 12 point
is harder to clear than the midpoint, while relegating the duplication to an "as well".
Paul
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