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Level 1: 4 puzzles

Posted By: AP
Date: Sunday, 3 February 2013, at 7:23 p.m.

In Response To: Level 1: 4 puzzles (Mr Majestyk)

I think I finally understood Zare's article on Gammons after Closeouts this morning. To anyone else attempting to understand this article, consider this advice:

-Read only the summary

-Understand what he is talking about when he refers to 'extra crossovers': it seems that you take the number of outside pips, and determine the minimum number of crossovers that would be required to get them in. Then calculate: Extra crossovers=Actual crossovers-Minimum crossovers.

-One important point from body of article: Other factors that influence gammon rates (besides pip count and crossovers) include distribution of spares on Blue's home board, and distribution of Whites home board. These residual factors should swing the gammon rate no more than 10%.

So applying this new understanding to the posted positions, heres what I get:

i) Outside pips is 14. whites chance to save the gammon are ~ equal to his chance to win a straight race of 44 to 50 pips. If white had 54 pips on roll it would be a coin flip, and he is 10 pips better than that. Assume 2.5% GWC/pip, and whites chance to save gammon equals 50+10*2.5=75%. So at this point gammons are at 25%. Now for crossover adjustment: 14 outside pips could bear in in 3 crossovers, but here there are 5 crossovers, so we have 2 extra crossovers which hurts us by ~1 pip each which is worth ~ 2*2.5%=5%. So final estimate: gammon rate=25+5=30%.

ii) I know adjustment from #1 should be <10%. Playing around with it before I found that moving a spare down 2 points in the home board hurt about 2%. Here that happens three times...total reduction in gammons by 6%. So gammon estimate is 30-6-24%.

I didn't yet investigate the sensitivity to the distribution after checkers are already borne off, like in problems 3 and 4. On the one hand, taking checkers off should improve gammon chances. But on the other hand, having one lone spare on 6-point may leave more blotting numbers...not really sure what to do here...maybe you can share your thoughts.

Messages In This Thread

• Gammons After Closeout
  AP -- Saturday, 2 February 2013, at 12:44 a.m.
  • Gammons After Closeout
    neilkaz -- Saturday, 2 February 2013, at 4:30 a.m.
  • Gammons After Closeout
    Bill Calton -- Saturday, 2 February 2013, at 4:15 p.m.
  • Gammons After Closeout
    Casper van der Tak -- Saturday, 2 February 2013, at 4:52 p.m.
  • Gammons After Closeout
    David Rockwell -- Saturday, 2 February 2013, at 10:59 p.m.
  • ** Bot content ** Gammons After Closeout
    Chase -- Sunday, 3 February 2013, at 1:34 p.m.
    • Level 1: 4 puzzles
      Mr Majestyk -- Sunday, 3 February 2013, at 4:19 p.m.
      • Level 1: 4 puzzles
        AP -- Sunday, 3 February 2013, at 7:23 p.m.