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Postscript

Posted By: Nack Ballard
Date: Tuesday, 9 February 2010, at 7:24 a.m.

In Response To: Postscript (Steve Mellen)

However, I did reclaim a smidgen of glory in that after a roll of 43 in the 5543 position, there are 6 ways to get off on the next shake rather than 4 because 65 also works.

Well done. I'm glad you found something :)

I agree with 350, 326 and 506.

I promised a brief resummary, so...

With 6/5, Yellow bears off an extra 1/36 in one roll, parlayed with the 506/1296 Brown bears off in two minus the 1/36 he bears off in one, for a gain of (36*506 - 36) / 1296^2, which is 18180 / 1296^2.

In exchange, Yellow gives up (350 - 326) / 1296 in two rolls, parlayed with the 790/1296 Brown can't bear off in two, for a loss of 24*790 / 1296^2, which is 18960 / 1296^2.

The two paragraphs net 780 / 1296^2, which is a bit under 0.05% in favor of 3/2. I won't bother enumerating the third roll scenarios as before, but clearly those would only serve to boost 3/2's edge.

As Bob says, it is less difficult to solve this OTB if one deals in differences rather than totals. A slight misstep could still cause one to make the wrong play, but it won't lead to a serious error here as the decision is so close.

In case Don Thompson is reading this, I'd be interested to see how his breakdown of the problem looks using senary numbers.

Nack

Messages In This Thread

• Do I set up 55? What could be more simple?
  neilkaz -- Friday, 5 February 2010, at 8:31 p.m.
  • Do I set up 55? What could be more simple?
    Stick -- Friday, 5 February 2010, at 8:37 p.m.
    • Do I set up 55? What could be more simple?
      Matt Cohn-Geier -- Friday, 5 February 2010, at 10:14 p.m.
  • Do I set up 55? What could be more simple?
    Bob Koca -- Friday, 5 February 2010, at 9:33 p.m.
    • Do I set up 55? What could be more simple?
      Steve Mellen -- Friday, 5 February 2010, at 11:00 p.m.
  • Do I set up 55? What could be more simple?
    Timothy Chow -- Friday, 5 February 2010, at 10:03 p.m.
  • Do I set up 55? What could be more simple?
    Steve Mellen -- Friday, 5 February 2010, at 10:49 p.m.
    • Do I set up 55? What could be more simple?
      Nack Ballard -- Saturday, 6 February 2010, at 4:02 a.m.
      • Do I set up 55? What could be more simple?
        Steve Mellen -- Saturday, 6 February 2010, at 5:28 a.m.
        • Do I set up 55? What could be more simple?
          Nack Ballard -- Saturday, 6 February 2010, at 5:39 a.m.
          • Postscript
            Steve Mellen -- Monday, 8 February 2010, at 6:20 p.m.
            • Postscript
              Bob Koca -- Monday, 8 February 2010, at 8:49 p.m.
            • Postscript
              Nack Ballard -- Tuesday, 9 February 2010, at 7:24 a.m.
      • Do I set up 55? What could be more simple?
        Matt Cohn-Geier -- Saturday, 6 February 2010, at 9:36 a.m.
  • OTB etc
    neilkaz -- Monday, 8 February 2010, at 8:56 p.m.