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Cubeful equities: how to derive from cubeless?

Posted By: Matt Ryder
Date: Wednesday, 6 January 2010, at 6:37 a.m.

I'm still figuring out how to calculate 'cubeful' equity from 'cubeless' equity using the Janowski technique. The GNU manual provides some insight, but it lacks clear examples so (as a non-mathematician), I'm struggling with some of the concepts.

I'd be most grateful if somebody with a mathematical background (Tim Chow maybe?) could provide an example (showing workings!) illustrating step by step how a cubeless equity is translated into a cubeful one using Janowski's basic formula.

I'm battling at the point where the GNU manual suggests:

"The live cube equity is now based on piecewise linear interpolation between the points (0%,-L), (TP,-1), (CP,+1), and (100%,+W): if my winning chance is 0 I lose L points, at my take point I lose 1 point, at my cash point I cash 1 point, and when I have a certain win I win W points."

It seems that TP, L and W are described by Janowski's generalisation:

TP = (L-0.5)/(W+L+0.5)

where W is the average cubeless value of games ultimately won, and L is the average cubeless value of games ultimately lost.

But I'm not sure if the CP (cash point) is simply the inverse of the TP (take point)? Or is it separately derived?

I've looked up 'piecewise linear interpolation' and it seems clear the points (0%,-L), (TP,-1), (CP,+1), and (100%,+W) represent the 'known' X/Y pairs. But what is the 'new' X value to be interpolated here? Is it the cubeless win probability?

Any assistance negotiating these turbid waters would be greatly appreciated!

Messages In This Thread

• Cubeful equities: how to derive from cubeless?
  Matt Ryder -- Wednesday, 6 January 2010, at 6:37 a.m.
  • Cubeful equities: how to derive from cubeless?
    Michael Depreli -- Wednesday, 6 January 2010, at 8:55 a.m.
    • Cubeful equities: how to derive from cubeless?
      Matt Ryder -- Wednesday, 6 January 2010, at 8:39 p.m.
      • Cubeful equities: how to derive from cubeless?
        Timothy Chow -- Thursday, 7 January 2010, at 2:33 a.m.
        • Cubeful equities: how to derive from cubeless?
          NJ -- Thursday, 7 January 2010, at 8:27 a.m.
          • Cubeful equities: how to derive from cubeless?
            Matt Ryder -- Friday, 8 January 2010, at 5:58 a.m.
            • Cubeful equities: how to derive from cubeless?
              NJ -- Friday, 8 January 2010, at 4:24 p.m.
              • Cubeful equities: how to derive from cubeless?
                Matt Ryder -- Saturday, 9 January 2010, at 6:16 a.m.
                • Cubeful equities: how to derive from cubeless?
                  NJ -- Saturday, 9 January 2010, at 11:28 a.m.
          • Cubeful equities: how to derive from cubeless?
            Philippe Michel -- Saturday, 9 January 2010, at 8:10 p.m.
            • Cubeful equities: how to derive from cubeless?
              Tom Keith -- Sunday, 10 January 2010, at 7:15 p.m.
  • Cubeful equities: how to derive from cubeless?
    NJ -- Thursday, 7 January 2010, at 6:59 a.m.
    • Cubeful equities: how to derive from cubeless?
      Bob Koca -- Thursday, 7 January 2010, at 7:31 a.m.
      • Cubeful equities: how to derive from cubeless?
        NJ -- Thursday, 7 January 2010, at 9:04 a.m.
    • Cubeful equities: how to derive from cubeless?
      Matt Ryder -- Friday, 8 January 2010, at 5:07 a.m.
      • Cubeful equities: how to derive from cubeless?
        NJ -- Friday, 8 January 2010, at 4:09 p.m.
        • Cubeful equities: how to derive from cubeless?
          Matt Ryder -- Saturday, 9 January 2010, at 6:30 a.m.
          • Cubeful equities: how to derive from cubeless?
            NJ -- Saturday, 9 January 2010, at 11:21 a.m.