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arguing against the definition

Posted By: rambiz
Date: Tuesday, 21 June 2011, at 8:58 a.m.

In Response To: What I did over the board (Timothy Chow)

Granted! "Arguing against the definition" would have surely been the more appropriate expression. EPC is the definition for the length of the race, whereas Thorp's count, Keith's count etc are definitely no definitions. I assume you don't want me to define the term "definition", but I am going to elaborate on my understanding of it....(feedbacks highly appreciated)

OK! If we want to handle the race, the first thing we want to know for sure is the "length" of it or a "measure" for its length. EPC devided by 8.167 gives the average number of rolls to bear off all checkers. This is the "definition" of EPC! So what is actually going on here, is that we assume we knew the average number of rolls and then we go on and calculate EPC. Now, if we are smart enough, we can get out, what we have already put in.

The apparent shortcoming of EPC to fully qualify for the prestigious title "Holy Grail" is that it doesn't tell us the exact distribution (that is percentages of successful bear offs in 1-roll, 2-rolls,3-rolls, etc) . It is only a measure for the average. However, I think, EPC has a tighter grip on races than any other effort to linearize a highly non-linear function. That function being the percentage of wins as a function of the distribution of checkers.

Messages In This Thread

• bear off cube
  rambiz -- Sunday, 19 June 2011, at 12:17 p.m.
  • bear off cube
    Udo Moerschbach -- Sunday, 19 June 2011, at 3:33 p.m.
    • bear off cube
      rambiz -- Sunday, 19 June 2011, at 4:16 p.m.
      • bear off cube
        Udo Moerschbach -- Sunday, 19 June 2011, at 6:23 p.m.
        • bear off cube
          Udo Moerschbach -- Sunday, 19 June 2011, at 6:26 p.m.
        • bear off cube
          rambiz -- Sunday, 19 June 2011, at 7:45 p.m.
          • bear off cube
            Udo Moerschbach -- Sunday, 19 June 2011, at 8:43 p.m.
            • bear off cube
              Turz -- Monday, 20 June 2011, at 10:05 a.m.
            • Udo's Count
              rambiz -- Monday, 20 June 2011, at 12:03 p.m.
              • Udo's Count
                Udo Moerschbach -- Monday, 20 June 2011, at 2:42 p.m.
              • another example
                Udo Moerschbach -- Wednesday, 22 June 2011, at 9:43 a.m.
                • another example
                  Bob Koca -- Wednesday, 22 June 2011, at 6:32 p.m.
    • bear off cube
      Bob Koca -- Sunday, 19 June 2011, at 9:19 p.m.
  • bear off cube
    Timothy Chow -- Sunday, 19 June 2011, at 5:41 p.m.
    • bear off cube
      rambiz -- Sunday, 19 June 2011, at 7:42 p.m.
      • bear off cube
        Timothy Chow -- Sunday, 19 June 2011, at 8:47 p.m.
  • bear off cube....etc etc etc
    neilkaz -- Monday, 20 June 2011, at 4:09 a.m.
    • What I did over the board
      rambiz -- Monday, 20 June 2011, at 12:39 p.m.
      • What I did over the board
        Timothy Chow -- Monday, 20 June 2011, at 3:45 p.m.
        • arguing against the definition
          rambiz -- Tuesday, 21 June 2011, at 8:58 a.m.