On June 8, 2023 at 7:02:32 AM UTC-6, Timothy Chow wrote:
> On 6/7/2023 2:14 PM, MK wrote:
>> ..... Since my first days on FIBS in 1997, I
>> always objected to it and called it a horse-fart
> > based on arbitrary constant. I'm glad to see it
> > being questioned so many years later.
Small but important correction: I meant to type
"constants" in plural, as there more than one in
the formula and that I objected to them all!
Your saying "I have also had my doubts about the
way match length enters that formula" is a much
"timid" (pun intended ;) expression of a doubt but
I'll say fair enough.
However, I don't understand what you are trying to
get at when you ask Maik: "Are you saying that the
dependence on match length in that formula is
surprisingly simple?" and add: "I have *also* had..."
indicating that you *also* think it's "...surprisingly
simple"; and then asking him another question: "Or
are you saying that the concept of "backgammon
skill" is too complex a concept to be captured by a
I really couln't understand his response to you and
you haven't said anything more to clearly indicate
your stance. Would you mind explaining now?
To expand on what I said in a previous response to
you in this thread: A single number may work well
enough for backgammon but not gamblegammon.
A 5-point backgammon match can't last less than
3 games, (i.e. 2 gammons + 1 single win vs. 0), or
more than 9 games, (i.e. 5 single wins vs. 4 single
wins). The numbers for a 7-point match are 4 and
In contrast, a 15-point gamblegammon match can
be over in 1 game, (i.e. 1 single win with 16 cube or
1 gammon or backgammon win with 8 cube vs. 0),
or last 29 games, (i.e. 15 single wins vs. 14 single
wins). The numbers for a 25-point match are again
1 and 49 respectively.
In backgammon, the minimum number of games
in matches do "necessarily" increase as the match
lengths increase but not in gamblegammon where
a match of any length can be over in one game.
In backgammon, different formulas for different
match lengths can also work and perhaps better.
I'm glad I'm not a mentally ill gambler mathematician
facing the task of concocting different formulas for
different match lengths or to come with other ways
of solving the problem...
BTW: I found some really good, long threads on the
issue from 1998, that I had initiated and attracted
lengthy articles from many RGB heavy-weights of
that era when ideas hadn't petrified, people weren't
indogtrained yet. I printed them into PDF's and may
share them with comments if/when I find the time.
Just to give you a taste, here are two litle snippets.
Among my suggestions was different rating formulas
for "lackgammon" (the name I coined for 1-pointers
without gammon wins), backgammon (the real thing)
and "jackgammon" (the name I coined for cubeful play).
I was sooo ahead of my time... :)
And below is a long quote that Tim may really like, (the
last sentence of which was "music to Murat's ears"... :)
Posted by Jim Williams on Oct 21, 1998.
This touches on a question I have been evaluating. I am suspicious of
the fibs rating forumla in the way it accounts for match length. I have
collected a lot of match results and checked empirically whether the
winning probability as predicted by the FIBS rating formula actually
matches the observed winning probability for a given match between
of known ratings. I sampled the players ratings before recording any
matches so that the random errors in the ratings would be uncorrelated
with with the outcome of the observed games. Only matches where both
players had at least 1000 experience points were included. Currently
the number of recorded results is as follows:
1 point matches 19926
3 point matches 12036
5 point matches 8621
1, 3, and 5 account for 90% of all matches.
I then took the fibs ratings formula for win probability:
P = 1/(1 + 10^(D*sqrt(N)/2000))
Rather than using the match length for N, I used an effective
match length where the effective match length was chosen so
that the formula gave the best fit with the observed data.
The results were what I expected only more extreme. The effective
match lengths which gave the best fit were as follows:
match length effective match length
Due to the limited number of matches recorded, the standard error
on these effective match lengths is about 0.25 . If anyone notices
zbest lurking on fibs, he is collecting more data to try to get
a more accurate fix on these numbers.
These numbers suggest that a 3 point match has exactly the same
skill component as a 1 point match, and a 5 point match only
I am at a loss to explain these numbers, but the implication is
that if you want to increase you rating, play 1 point matches
agains the weakest opponents you can find, and play long matches
against the strongest opponents you can find. It also suggests
that if we want to make backgammon more a game of skill and less
a game of luck, we should eliminate the doubling cube.