First of all, many thanks for the help in figuring it out. The request for
its inclusion in GNU stands of course, since this would obviously affect
GNU's analysis of checker play and cubes, and consequently our understanding
of the correct move/approach in a position.
Thanks again for the explanation though. :-)
Albert
> -----Original Message-----
> From: Christian Anthon [mailto:address@hidden
> Sent: Saturday, July 29, 2006 12:16 PM
> To: Albert Silver
> Cc: address@hidden
> Subject: Re: [Bug-gnubg] Analyzing with table stakes
>
> Constructing the MET is the simplest thing since you don't have to
> consider the implications of the match not being over as you do in
> normal matchplay.
>
> In the example of 5/20$ you may think of it like both of you
> contributing 4 points to a pot of a total of 8 points. Depending on
> the result you get to pull a certain amount of the pot. Say if you win
> 3 points you get to pull 7 points from the pot and you corresponding
> match equity is 7/8 or 87.5% and the match equity of your opponent
> would be 12.5%. The full match equity table would be:
>
> win 4 100%
> win 3 87.5%
> win 2 75%
> win 1 62.5%
> win 0 50%
> lose 1 37.5%
> lose 2 25%
> lose 3 12.5%
> lose 4 0%
>
> All other scores in this 4 point match is off course unreachable.
>
> In a bit more complicated example of a 4$ game with a 10$ limit the
> match length would be 3 and the MET would be:
>
> 0/-3 win 3 5/5 = 100%
> -1/-3 win 2 4.5/5 = 90%
> -2/-3 win 1 3.5/5 = 70%
> -3/-3 win 0 2.5/5 = 50%
> -3/-2 lose 1 1.5/5 = 30%
> -3/-2 lose 2 0.5/5 = 10%
> -3/-2 lose 3 0/5 = 0%
>
> since if you for example win 2 points you get to pull 2.5+2 = 4.5
> points from the pot.
>
> I'll leave it to you to construct the general formula needed.
>
> Christian.
>
> On 7/29/06, Albert Silver <address@hidden> wrote:
> > At both TMG and PartyGammon (don't know about others) one can set
> various
> > table stakes limits for money games. For example, I could be playing at
> $5 a
> > point with a limit of $20 per game. Naturally this means that not only
> are
> > backgammons useless, but recubes take on a very different nature as
> well. If
> > I set the limit to $25 or $30, it becomes more subtle yet. All this will
> > also severely affect the respective checker play too.
> >
> > I was asking myself how one might analyze this, and realized that in a
> sense
> > it is a bit like match play with the Jacoby rule tossed in, and no
> Crawfords
> > to consider.
> >
> > I'm not a mathematician, so forgive me if I don't realize what I'm
> > requesting, but would it be possible to add this support? It would be
> nice
> > to have this be a manual setting so that one could train against GNU,
> > testing the conditions and learning about the effects it has on the
> > decisions.
> >
> > Albert
> >
> >
> >
> >
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> >