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 <[EMAIL PROTECTED]> 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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