BGonline.org Forums

41S-54 at four scores

Posted By: Nack Ballard
Date: Thursday, 27 May 2010, at 5:32 p.m.

In Response To: 41S-54 at four scores (David Rockwell)

Technical Four-score Position?
41S-54

This position is of great interest to me.

In 2003 (or so), I noticed that 41S-54 produced different best plays at each of the four scores in a Snowie rollout (done by Paul Weaver). In 2006, I extended the Snowie rollout to 31k (thanks to Dennis Nilsson and Garry MacDonald) and obtained these results (money, dmp, save, go):

Snowie
m[S X4 R9 D20]
d[R S3 X5 D20]
s[X S4 R9 D26]
g[D X12 S13 R32]

However, Snowie does not play the checkers according to score. So, on 6/16/09, I e-mailed Stick to see what rollouts he had AtS. Adding his dmp, gammon save and gammon go results to the one I had for money gave me:

GnuBG
m[X S6.3 R9 D18] 46k 15kD
d[R S1.2 X3] 10k
s[X S4.2 R17] 15k
g[X D5.2 S9] 5k

From these results, we concluded that 41S-54 is probably not a four-score position. However, in the course of seeing Snowie and XG results for early game positions, I have observed that GnuBG has a clear bias towards X (hit-and-split) when hitting on the ace point. I generally assume that some of a bot's bias carries over to other scores, which suggests that not only Gnu's money but also its gammon save and/or gammon go X-winner results could be overturned by a bot with no X bias.

Now, thanks to David, we have XG results, and to a significant 31k (i.e., 31000+ trials):

XG 3-ply
m[S X1 R10]
d[R S1 X5]
s[X S9 R24]
g[D X5 S12]

From these results, it appears that 41S-54 could be what I call a "technical four-score position" after all. (A "model four-score position," which is exceedingly rare and difficult to construct, is one in which none of the plays are "tied" according to the Ballard/Weaver error scale -- i.e., not within .01 for money, nor .007 at GS or GG, nor .0045 at DMP.)

Key: S = Split (24/20 13/8), R = Run (24/15), X = hit-and-split (24/20 13/1*), D = Down (13/9 13/8). Error sizes are in thousandths. A letter before the brackets denotes score (m = money, d = dmp, s = gammon save, g = gammon go). For example, "g[D X5 S12]" means that at gammon go, D is best, X is -.005, and S is -.012.

It would be interesting to see if 41S-54 holds up as a technical four-score position with XG 4-ply rollouts.

Nack

Technical Four-score Position?
41S-54

Messages In This Thread

• 41S-54 at four scores
  David Rockwell -- Thursday, 27 May 2010, at 12:36 p.m.
  • Attn Xavier
    Chase -- Thursday, 27 May 2010, at 3:36 p.m.
    • Attn Xavier
      Nack Ballard -- Thursday, 27 May 2010, at 4:33 p.m.
      • Rollout Seed part deux
        eXtreme Gammon -- Thursday, 27 May 2010, at 6:12 p.m.
        • Rollout Seed part deux
          Nack Ballard -- Thursday, 27 May 2010, at 6:30 p.m.
          • Rollout Seed part deux
            David Rockwell -- Thursday, 27 May 2010, at 6:53 p.m.
        • Rollout Seed part deux
          Chase -- Thursday, 27 May 2010, at 7:19 p.m.
          • Rollout Seed part deux
            Stick -- Thursday, 27 May 2010, at 7:24 p.m.
            • Rollout Seed part deux
              Chase -- Thursday, 27 May 2010, at 9:03 p.m.
          • Rollout Seed part deux
            eXtreme Gammon -- Friday, 28 May 2010, at 1:03 a.m.
  • 41S-54 at four scores
    Nack Ballard -- Thursday, 27 May 2010, at 5:32 p.m.
  • 41S-54 at dmp
    Stick -- Thursday, 27 May 2010, at 8:40 p.m.
    • 41S-54 at dmp
      Daniel Murphy -- Thursday, 27 May 2010, at 9:53 p.m.
    • 41S-54 at dmp
      Nack Ballard -- Friday, 28 May 2010, at 12:28 a.m.