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Fewest-rolls Puzzle -- SOLUTION

Posted By: Nack Ballard
Date: Monday, 2 November 2015, at 1:55 a.m.

In Response To: Fewest-rolls Puzzle (Taper_Mike)

 White is Player 2 score: 0 pip: 160 Unlimited GameJacoby Beaver pip: 156 score: 0 Blue is Player 1
XGID=-b---BD-C---cDa--d-e--A-A-:0:0:1:00:0:0:3:0:10

Fewest-rolls Puzzle

Congratulations, Mike (for 21\$-62S-22G-51Z). You nailed it!

Stick is correct that either player can be on roll. I felt that was implied, but in the future I'll state it explicitly.

The reason 52S-52D-31 is not a solution, even though it is perfectly played according to rollouts, is that XGR++ doesn't evaluate 52D as best! That is why I imposed the condition copied below. I even added the words "strictly" and "current" (which I don't normally do).

According strictly to current XGR++ evaluation...

 White is Player 2 score: 0 pip: 167 Unlimited GameJacoby Beaver pip: 160 score: 0 Blue is Player 1
XGID=-b----E-D---eD---c-e--A-A-:0:0:-1:52:0:0:3:0:10

White to play 52 .. (XGR++ evaluation)

1.XG Roller++24/22 13/8eq: -0.138
 Player:Opponent: 46.69% (G:11.02% B:0.36%)53.31% (G:13.89% B:0.48%)
2.XG Roller++13/11 13/8eq: -0.142 (-0.005)
 Player:Opponent: 46.65% (G:12.08% B:0.41%)53.35% (G:14.91% B:0.77%)

Deciding best plays with rollouts rather than evaluations can burden the solver with a prohibitive amount of CPU time. Even if all solvers know their first- and second-roll plays cold, they won't have thoroughly memorized past that. That is why, for puzzles, I use XGR++ evaluation as arbiter.

If the XGR++ evaluation did not get 52S-52 wrong (sharing that tidbit was part of my point in presenting it, the other part was to play a little prank on the opening mavens like Stick), I would have instead phrased the problem thusly:

From the opening position, how can the above position be reached in exactly four perfectly-played moves (two by each player)? The arbiter of "perfect" is XGR++ evaluation.

Either color may move first, and either color may move last. Please include your sequence of rolls.

Indeed, when a future version of XG evaluates 52S-52D correctly, it will be necessary to change to the four-move condition.

I'll recap the correct solution for anyone who missed it:

Blue opens with 21\$, and White replies with 62S, reaching this position:

 White is Player 2 score: 0 pip: 159 Unlimited GameJacoby Beaver pip: 164 score: 0 Blue is Player 1

Blue to play 22 .. (XGR++ evaluation)

1.XG Roller++24/22 11/7* 7/5eq: +0.489
 Player:Opponent: 60.63% (G:20.03% B:0.99%)39.37% (G:8.68% B:0.34%)
2.XG Roller++13/7* 7/5eq: +0.475 (-0.013)
 Player:Opponent: 60.10% (G:20.84% B:1.10%)39.90% (G:9.60% B:0.45%)

Blue now rolls 22, with which he hits, makes the 5pt, and splits the fourth deuce. Finally, White enters with 51, making the obvious move and reaching the puzzle position (the initial diagram of this post).

Nack

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