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Opening moves at DMP -- Puzzle

Posted By: Nack Ballard
Date: Friday, 9 July 2010, at 1:56 a.m.

In Response To: Opening move at DMP -- Puzzle (Nack Ballard)

Here's the puzzle again, for reference:

At DMP, player "X" is given the following handicap:

(a) He chooses his opening roll (a non-doublet) and play, but he is not permitted to make a point.
(b) He chooses the opponent's reply roll and play.
(c) His next roll is random and play proceeds normally.

What rolls and plays should X select for (a) and (b)?

The clearest aspect of the puzzle, which all respondents (David, Bob, Jake and Stick) grasped, is that the opponent should be made to bury four checkers, leaving a blot on her 6pt. That is more devastating than any multiple blot-leaving move (e.g., with double 3s or double 4s). In short, Opp's roll will be 44 played 6/2(4) or 55 played 6/1(4). [If I were to nactate these plays, I'd use "2" and "1" respectively, but henceforth I'll assume you know what I mean when I list just the rolls of 44 and 55.]

As I see it, answers break down into three types:

(1) Two checkers played on the near side. ($ = Slot, & = double slot, N = Near, O = Outer)
(2) One near-side checker, one back checker. (S = Split, Z = reverse split, W = Wild, C = Cross, E = Each)
(3) Two back checkers. (U = Up, V = Variant-Up)

The advantage of (1) is that it gives "X" (the player going first and choosing the rolls and plays) the best potential for building one or more points of a prime on the following roll.

The advantage of (2) is that it vacates Opp's ace point so that her roll can be worsened from 44 to 55, while still getting some of the (1) benefit.

The advantage of (3) is that it gains the first part of (2) without being on the roof (which means part of the next roll has to be used to enter, and 11 fans). However it gives up all of the (1) advantage.

I mentally eliminated (3) in direct comparison to (2). Having an offensive key point already slotted means X is much more likely to make a point, even with part of his roll committed to entering. (Otherwise, a natural point-making number is required to break even offensively.) Admittedly, if X doesn't cover it, he will regret having slotted, but not by much (given the horrid condition of Opp's board). In other words, there's little to lose, a lot to gain. Note, too, that hitting with a direct 6 from the roof will be as good as hitting with a 5 would be from the 24pt.

[Of the (3) plays, I don't know which two-up play is optimal, but it makes sense to me to include a 4 so that aces (the number that will stay off after Opp butchers her 55) can hit on the 19pt. But remember, I declined (3) in favor of (1) or (2).]

I found it difficult to choose between (1) and (2). However, I was able to decide what I like most within each type.

For type (1), I chose 61N-44 (also Jake's choice). This offers a great diversity of 6s, 5s, 3s, 2s and 1s to hit and/or cover a key point, and it brings an eighth checker into the zone. As runner-ups, I considered 41$-44, Stick's 21$-44 suggestion, and Bob's 21&-44 (double-slot of the 5pt and 4pt).

For type (2), I chose 31W-55, with my second choice being Stick's other suggestion 41W-55. The former gives our player X a use for his deuces (21/19*), though the interplay of duplication and diversification is not always clear.

In short, my two equally regarded top picks, before punching up evals, were 61N-44 and 31W-55. In consulting Snowie evals, 61N-44 is the early favorite (kudos, Jake), as shown below. Perhaps these eval winning percentages will help Stick decide which candidate positions to roll out. The "Others" footnotes list sequences that are under 70% (plus I stuck 63O-44 and 64O-44 there as inferior distribution versions of 61N-44 and 62N-44).

Type (1)
61N-44 72.7
41$-44 72.3
62N-44 71.9
31$-44 71.8
21$-44 71.5
21&-44 71.0
64D-44 70.8
51$-44 70.3
32&-44 70.2
62D-44 70.0
-------------
Others: 63O-44 70.5, 64O-44 70.1, 63D-44 69.6, 43D-44 69.5, 42D-44 69.4, 65D-44 69.3, 62$-44 69.0, 54D-44 68.9, 32D-44 68.9, 53D-44 68.4, 52D-44 67.9, 63N-44 69.6, 31&-44 68.8

Type (2)
41W-55 71.4
31W-55 71.3
43S-55 70.6
42W-55 70.5
21W-55 70.5
54S-55 70.4
43Z-55 70.4
42Z-55 70.4
42S-55 70.2
-------------
Others: 43W-55 69.9, 64Z-55 69.7, 32S-55 69.7, 32Z-55 69.7, 53S-55 69.7, 63Z-55 69.7, 52S-55 69.7, 41S-55 69.7, 62Z-55 69.5, 32W-55 69.3, 31S-55 69.2, 43E-55 69.1, 32c-55 69.1, 21S-55 69.1, 51S-55 69.1, 61Z-55 68.9, 21w-55 68.8

Type (3)
43U-55 70.0
---------------
Others: 42V-55 69.7, 41U-55 69.4, 32U-55 69.7, 31V-55 69.6, 21V-55 69.2

Nack

Messages In This Thread

• Opening move at DMP -- Puzzle
  Nack Ballard -- Wednesday, 7 July 2010, at 11:31 p.m.
  • Opening move at DMP -- Puzzle
    David Rockwell -- Thursday, 8 July 2010, at 12:52 a.m.
    • Opening move at DMP -- Puzzle
      Jake Jacobs -- Thursday, 8 July 2010, at 1:10 a.m.
    • Opening move at DMP -- Puzzle
      Stick -- Thursday, 8 July 2010, at 8:29 a.m.
      • Opening move at DMP -- Puzzle
        David Rockwell -- Thursday, 8 July 2010, at 12:17 p.m.
  • Opening move at DMP -- Puzzle
    Bob Koca -- Thursday, 8 July 2010, at 12:53 a.m.
    • Opening move at DMP -- Puzzle
      Stick -- Thursday, 8 July 2010, at 8:24 a.m.
  • Opening moves at DMP -- Puzzle
    Nack Ballard -- Friday, 9 July 2010, at 1:56 a.m.