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A Somehow Satisfactory Solution

Posted By: rambiz
Date: Sunday, 18 March 2012, at 1:50 p.m.

In Response To: Do you remember this position? (Daniel Murphy)

Almost all problems are easy when solved. :)
The gammon value for playing on, is normally the ratio of reward in case you win an extra point, to the loss in case you lose 1 point instead of winning 1 point.
In the case at hand -if you don't cash now- you may lose (or win) 2 points (I neglect the possibility of losing 4 points, due to low probability), which complicates the issue to some extent.
Here is my approach to sort the things out:
Your loss consists of (approximately) %50 single losses plus %50 2-point losses. So all in all you lose: 0.5*(difference between MWCs at 4*-0 and 3-1~%84-%67=%17)+ 0.5*(difference between MWCs at 4*-0 and 3-2~%84-%60=%24)=%8.5+%12=%20.5 .
Your reward for playing on is ~%16, whether you win a gammon on a centered cube or win a single game with the cube at 2.
Therefore the adjusted Gammon Value is: 16/20.5~ 0.78 which is not too bad compared with the 0.9 "original" gammon value. The good news is that you can add the games you win with the cube at 2 to your gammons! The bad news, we still don't know how to estimate the gammons won.
Example:
Suppose Blue thinks he loses %10 of the games, if he plays on. He also estimates, that half of the time, he loses 1 point and half of the time he loses 2 points. This would mean an adjusted gammon value of 0.78 as calculated above. In how many games shall he win 2 points to justify a play on?
The answer simply is: He needs to win %10/0.78~%10/0.8=%100/8=%12.5 games on 2, either by winning a gammon or winning a 2-point game after getting hit.

Messages In This Thread

• Do you remember this position?
  rambiz -- Friday, 16 March 2012, at 9:47 p.m.
  • Do you remember this position?
    Casper van der Tak -- Friday, 16 March 2012, at 10:01 p.m.
    • Do you remember this position?
      rambiz -- Saturday, 17 March 2012, at 7:29 p.m.
      • Do you remember this position?
        Daniel Murphy -- Saturday, 17 March 2012, at 10:11 p.m.
        • Do you remember this position?
          rambiz -- Sunday, 18 March 2012, at 1:40 a.m.
          • Do you remember this position?
            Daniel Murphy -- Sunday, 18 March 2012, at 1:50 a.m.
            • A Somehow Satisfactory Solution
              rambiz -- Sunday, 18 March 2012, at 1:50 p.m.
  • Do you remember this position?
    lenny -- Saturday, 17 March 2012, at 3:21 a.m.
    • Do you remember this position?
      rambiz -- Saturday, 17 March 2012, at 10:21 a.m.