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5's are wild.

Posted By: Chuck Bower
Date: Saturday, 23 June 2007, at 10:49 p.m.

In Response To: Jumping a 5-prime (Daniel Murphy)

This should be an easy thing to remember.

Assuming the five prime isn't broken in the meantime (not the case in your illustration), trapped checker is a favorite to jump in the first five rolls, but not before. In fact, a 55% favorite to jump in the first 5 rolls! The mean number of rolls to jump isn't far off -- very close to 6 rolls. (I need to look up sums of infinite series. At worst I'll post to GammonU and let the professors there tell us how to do it.) But if anyone here wants to give it a try, the infinite sum is:

Sum (i=1 --> infinity) of [ i*A0*r^(i-1) + i*(i-1)*A1*r^(i-2) ]

Looks suspiciously integrable....

A0 = 1/18, A1 = 99/1296, r = 25/36 for our situation.

Messages In This Thread

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  Ian Dunstan -- Saturday, 23 June 2007, at 2:55 a.m.
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    Peter G. -- Saturday, 23 June 2007, at 8:53 a.m.
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    Daniel Murphy -- Saturday, 23 June 2007, at 1:05 p.m.
    • Crawford backgame - part 4
      Ian Dunstan -- Sunday, 24 June 2007, at 11:20 a.m.
  • Crawford backgame - part 4
    neilkaz -- Saturday, 23 June 2007, at 1:33 p.m.
  • Jumping a 5-prime
    Daniel Murphy -- Saturday, 23 June 2007, at 3:40 p.m.
    • 5's are wild.
      Chuck Bower -- Saturday, 23 June 2007, at 10:49 p.m.
      • 5's are wild.
        Bryce -- Monday, 25 June 2007, at 12:13 a.m.
    • Jumping a 5-prime
      Ian Dunstan -- Sunday, 24 June 2007, at 11:42 a.m.
      • Jumping a 5-prime
        Daniel Murphy -- Sunday, 24 June 2007, at 4:22 p.m.
        • Jumping a 5-prime
          Chuck Bower -- Sunday, 24 June 2007, at 11:04 p.m.
  • Crawford backgame - part 4
    Stick -- Saturday, 23 June 2007, at 5:11 p.m.
  • Rollout 2-ply
    Ian Dunstan -- Sunday, 24 June 2007, at 11:13 a.m.