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

 From: Massimiliano Maini Subject: Re: [Bug-gnubg] R.Janowski paper "Take-Points in Money Games" Date: Mon, 2 Mar 2009 17:01:10 +0100

Everything in the post on bkgm.com I managed to compute by myself.

Issue is that, even knowing that, I still can't get Janowski eq. 7 (the one for general model, centered cube).
I get a different one 9and hence  different initial double point).

And I used Maxima to do the algebra (much better than me) :)

MaX.

Christian Anthon <address@hidden> wrote on 02/03/2009 16:52:03:

> On Mon, Mar 2, 2009 at 10:02 AM, Massimiliano Maini
>
> I believe you are right, but possibly janowski is as well. Take a look
> a this thread http://www.bkgm.com/rgb/rgb.cgi?view+965, it might make
> you wiser.
>
> Christian.
>
> >
> > 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.
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