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

[Massimiliano Maini]

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.