I will offer a couple of suggestions
here, while introducing the new concepts of SET's and
MET's, (Set Equity Tables and Match Equity table), for
checker play decisions.
I believe that winning best of three or of five shorter
matches would be harder to win than a single longer
match, but I have no idea by how much, since there
have been no experiments done on the subject.
There is no way to test if winning a single 7-pointer or
even a 9-pointer would be as hard as winning a best of
three 5-pointers using Ex-G or Noo-BG because they do
offer a cubeless variant of gamblegammon but do not
truely implement backgammon, (i.e. allowing doubles
in the opening rolls, without 3-point wins, etc.)
On 2023-02-17, MK <mu...@compuplus.net> wrote:
here, while introducing the new concepts of SET's
and MET's, (Set Equity Tables and Match Equity
table), for checker play decisions.
The "new concept of SET" has been known as
Pascal's triangle for almost 400 years. But its
use is limited to settle unfinished sets (history
reports that Pascal discovered it when working
out this problem for a gambler friend).
As far as play decisions go, this is irrelevant.
Whatever the set score, your goal is to win the
match you are playing.
What make backgammon METs and their influence
on play more complex is that points inside a match
can be won by lots, not only one by one.
I believe that winning best of three or of five shorter
matches would be harder to win than a single longer
match, but I have no idea by how much, since there
have been no experiments done on the subject.
... in GNUbg there are some hints in the unbalanced
jac050 and jac100 METs on how it may work out in
modern backgammon.
There are 3 ways to win a best of three contest: WW,
WLW, LWW. If your winning chance in a single match
is p, that amounts to p*p + p*(1-p)*p + (1-p)*p*p, or
3*p^2-2*p^3.
A quick sanity check confirms that it is 0, 0.5 and 1 if
p is 0, 0.5 and 1.
The math for best of five is similar but a bit more complex.
The jac100 tables suggests that a player 100 Elo stronger
would win a 5 points match 56.1% of them time. For a best
of 3 5-pointers that would imply a 59.1 winning rate.
The same table gives 57.4%, 58.5% and 59.4% for a single
7-, 9- or 11-points match, so best of 3 5-pointers would be
about as selective as a single 11-points match.
The result may be slightly different if the skill difference is
higher or lower or if the jac tables are not that accurate
after all.
Also, as I said before, I have no clear idea at all about
how bots can be made to adjust checker decisions. It
may be done through AI training for match play, which
would require immense amounts of computing power,
of through some magically ingenious system similar
to MET's. I personally don't think it can be done using
"tables" but I use the word to transition from a concept
and terminology that you are all familiar with to a new
concept that I don't know what words to use for. Once
anyone of you understand what I'm trying to explain,
feel free to make suggestions...
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