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"Too good" Mystery -- SOLUTION

Posted By: Nack Ballard
Date: Thursday, 2 May 2019, at 6:04 a.m.

In Response To: "Too good" Mystery (Nack Ballard)





White is Player 2

score: 1
pip: 167
7 point match
pip: 167
score: 1

Blue is Player 1
XGID=-b----E-C---eE---c-e----B-:0:0:1:00:1:1:0:7:10
One checker play on each side, too good to redouble
(Score: –6–6)

At a score of 1–1 in a 7-point match (as shown above), Blue wins the (non-doublet) opening roll and makes a play. White (foolishly) doubles, rolls and hits a blot. Blue, back on roll, is too good to redouble, according to XGR++ evaluation.

What is Blue's play, and what is White's play?

SOLUTION

Congratulations to Bob Koca, Joe Russell and Brian Lonergan, for solving the "Too good" mystery! Honorable mention goes to Casper (as will be presently explained).

The diagram below encapsulates the solution:





White is Player 2

score: 1
pip: 147
7 point match
pip: 165
score: 1

Blue is Player 1
XGID=-b---AD-C---eE---c-a--A-dA:1:1:1:00:1:1:0:7:10

21W-C-55I-R


Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 74.37% (G:26.94% B:1.16%) 75.05% (G:26.90% B:1.15%)
Opponent Winning Chances: 25.63% (G:5.33% B:0.10%) 24.95% (G:5.10% B:0.10%)
Cubeless Equities +0.739 +1.356
Cubeful Equities
No redouble:+1.001
Redouble/Take:+1.201 (+0.200)
Redouble/Pass:+1.000 (-0.001)
Best Cube action: Too good to redouble / Pass
Percentage of wrong take needed to make the double decision right: 0.7%

Blue opens with 21W (Wild, 24/22 6/5), White doubles and Blue takes.
White then rolls 55 and plays I (Inside, 6/1*(4)), leading to the above diagram.

Blue is now (barely) TOO GOOD to redouble, according to the official arbiter, XGR++ evaluation.

Casper submitted the same except with Blue's play as 31W (Wild 24/21 6/5, Blue blot on 21pt instead of 22pt) without consulting XG. I informed him that his solution didn't quite work (.994), but he didn't get around to looking further.

Bob Koca (with 21W-C-55I as his official submission) pointed out that 31W-C-55I diversifies Blue's 2s on the next roll (actually, the relevant difference is only 52 vs 22), and wondered why it doesn't evaluate quite as well.

Out of curiosity, I rolled out both 21W-C-55I and 31W-C-55I. After 10k trials, the comparison is TCTC, but both roll out as easily too good to redouble (1.036 and 1.037).

To be clear, though: with XGR++ evaluation as arbiter, the solution of the diagrammed position is unique.

Nack

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