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## [Bug-gnubg] R.Janowski paper "Take-Points in Money Games"

 From: Massimiliano Maini Subject: [Bug-gnubg] R.Janowski paper "Take-Points in Money Games" Date: Mon, 2 Mar 2009 10:02:06 +0100

Hi all,

I was reading Rick Janowski's article "Take-Points in Money Games" (you can find it here: http://www.msoworld.com/mindzine/news/classic/bg/cubeformulae.pdf). I didn't dig into the
refined general mode, but in the general model (the one used by gnubg) I get a different
_expression_ for the centered cube equity.

The reasoning in Janowski's paper seems to be (if I got it right):

1) We know the expressions of dead cube equity and dead cube take/cash points.

2) We compute (as shown in Appendix 5, par. 1) the live cube take and cash point.

3) We compute live cube equities expressions:
3.1) Live cube equity owning the cube can be computed as linear interpolation
between the points (p=0%,E=-Cv*L) and (p=TP%,E=-Cv/2)
3.2) Live cube equity with unavailable cube can be computed as linear interpolation
between the points (p=CP%,E=Cv/2) and (p=100%,E=Cv*W)
3.3) Live cube equity with centered cube can be computed as linear interpolation
between the points (p=TP%,E=-Cv) and (p=CP%,E=Cv)
4) At this point we can deduce the live initial double point (No Jacoby), redouble point
and too good point (I don't care yet for beaver/racoon points and initial double point
with Jacoby rule in use).

Up to this point, I get exactly the same results.

5) We compute general cube equities. Here's where it gets fuzzy. I think that general cube
equities are/should be computed by linear interpolation between dead and live equities (that's
even what's written in gnubg manual), with the cube life index x being between 0 and 1:
5.1) Egeneral_own  = Edead*(1-x) + Elive_own*x  : developing this I get the same result
5.2) Egeneral_unav = Edead*(1-x) + Elive_unav*x : developing this I get the same result
5.3) Egeneral_cen  = Edead*(1-x) + Elive_cen*x  : here I get a different result

6) We compute the general TP, IDP, RDP, CP, TGP by definition (i.e. with equations involving
the equities expressions). Of course, with identical own and unav general equities, I get the
same expressions for general TP, RDP, CP and TGP. But with a different _expression_ for the
general centered equity I naturally get a different _expression_ for the IDP (initial double
point, I only checked the No-Jacoby case).

What looks strange to me is that Janowski's _expression_ of the general centered cube equity
is not even linear in x ... Anybody with an idea ?

MaX.