A common bearoff dilemma

[Timothy Chow]

XGID=aCCBBB-------a----adcbba--:1:-1:1:43:0:0:0:0:10

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-+
| O O | | O O O O O | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X |
| | | X X X X X |
| | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 33 O: 99 X-O: 0-0
Cube: 2, O own cube
X to play 43

---
Tim Chow

[peps...@gmail.com]

At the risk of being anti-QF, I'd really rather not remove any checkers right now, thanks.
The alternative play might bear off very slightly faster but it blots to 61/51/41 which seems not worth it.

My play is uniquely defined as the only play that doesn't blot and that doesn't remove any checkers.

Paul

[peps...@gmail.com]

Not changing my play by any means (although I'm less than 90% confident in it).
But I do have further comments.
Parity arguments are very important in these postions where we want a speedy bearoff (for the gammon, in this case.)
I believe that, although the greedy play blots too often in my judgement, the parity (whether we have an even number
or odd number of checkers when it matters) actually points in favour of the greedy play.
I'll explain why. We are big underdogs for the gammon and will need the opponent to dance on our four point board.
After that dance, we can expect to remove exactly one checker -- half of the roll is used for safety.
We will then have 11 checkers left in my variation, but 10 in the greedy variation so the greedy play is considerably faster.
Note however that, in the greedy variation, it's not only an immediate 61/51/41 that blots. Other aces subject us to a risk
of 61/51/41 afterwards.

Still playing safe rather than greedy though -- I'm playing the DMP way.

Paul

[badgolferman]

Two points are acceptable to me. The chance of getting four points
isn't worth the risk of leaving a blot on the next turn, especially
since O's home board is strong.

5/1, 5/2

[J R]

If it's common (and esp. if it's during the bearoff) it should be nowhere near a dilemma.

Stick

[Timothy Chow]

There's a tradeoff between wins and gammons here, but according to XG
it's about a 1:1 tradeoff rather than the 1:2 tradeoff that we are
looking for in a money game.

1. Rollout¹ 5/2 5/1 eq:+1.117
Player: 99.79% (G:12.18% B:0.03%)
Opponent: 0.21% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.116..+1.118) - [100.0%]

2. Rollout¹ 4/1 4/Off eq:+1.069 (-0.048)
Player: 96.58% (G:15.27% B:0.06%)
Opponent: 3.42% (G:0.00% B:0.00%)
Confidence: ±0.002 (+1.067..+1.071) - [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

---------
Gammon go
---------

XGID=aCCBBB-------a----adcbba--:0:0:1:43:0:1:1:2:10

X:Player 1 O:Player 2

Score is X:0 O:1 2 pt.(s) match.

+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O | | O O O O O |
| | | O O O O |
| | | O O |
| | | O |
| | | |

| |BAR| |
| | O | |
| | | |
| | | X X |
| | | X X X X X |
| | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pip count X: 33 O: 99 X-O: 0-1/2 Crawford
Cube: 1
X to play 43

1. Rollout¹ 5/2 5/1 eq:+1.240
Player: 99.80% (G:12.18% B:0.09%)
Opponent: 0.20% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.238..+1.241) - [99.9%]

2. Rollout¹ 4/1 4/Off eq:+1.236 (-0.003)
Player: 96.65% (G:15.17% B:0.17%)
Opponent: 3.35% (G:0.00% B:0.00%)
Confidence: ±0.002 (+1.235..+1.238) - [0.1%]

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, MET: Kazaross XG2

---
Tim Chow

[peps...@gmail.com]

And, of course, as Stick says, the fact that it's only a 1-1 tradeoff
and not worth the greedy play is trivially obvious.
Not a dilemma at all.
Easiest bg quiz since bacon was invented.

Paul

[J R]

That's not even the ballpark of what I said. (iks)

Stick

[peps...@gmail.com]

What does iks mean?

Paul

[peps...@gmail.com]

It depends on how you interpret "if it's common".
If you mean "I agree that it's common" and therefore it's not a dilemma,
you are kind of saying the problem is trivially easy.

But you might mean "I don't think it's common, actually. Because if it was common, it wouldn't be a dilemma (which it is)."
Under this interpretation, yes, I was wrong about what you said.

What did you mean?

Did I miss some other interpretation?

Paul

[Timothy Chow]

It's an acronym for the International Kolping Society.

---
Tim Chow