Making slow progress on my digest of Axel's experiment
because I want to give a good background on my various
past arguments leading up to it and as it feels tedious, it
is easy for my to get side tracked on some specific topics.
For long years, I thought that mathematicians, gamblers,
bot developers, etc. were making more of backgammon
than what it really is. Today, I started thinking on this again
while doing yard work for several hours and kept wondering
if the complexity of backgammon is exaggerated because
it's harder to create a top level backgammon bot than bots
for chess and other games, simply due to its high branching
factor??
I started searching and reading about the topic... This Wiki
gives a decent overall idea about it and even has a table to
compare the complexity of tens of games.
https://en.wikipedia.org/wiki/Game_complexity
We know that backgammon has a higher average branching
factor (250?) than chess (35?) but chess is considered much
more complex (harder).
While trying to understand and compare the various factors
of complexity of games, I felt like it was as difficult to compare
economic factors of various countries, which can't give a good
picture by themselves or even by a few at a time, but all need
to be considered in retation to one another.
All of a sudden the word "inflation" rang in my head! Can the
high braching factor in backgammon lead to an inflation of
positions and decisions, each with a lower value as a unit
than the less numerous ones in chess (like currency exchange
rates)...??
I hope that my anology works and makes sense to at least
some of you because at this moment I don't know how else
to communicate my thoughts except by analogies. Maybe we
will find a common language later.
Who cares if there are so many more ways to get from Seattle
to New York in backgammon-land than in chess-land..? It just
makes it easier to recover from making the wrong turn in the
backgammon-land.
Who cares if the train ticket in backgammon-land cost much
more than in chess-land..? You are paying with "inflated"
backgammon dollars vs more valuable chess dollars.
Why should it be harder for a human to play backgammon
than chess because it is harder for bots to play backgammon
than chess..!?
Especially when the bots' early game equity esyimates are
totally bogus and worthless for anything. See my last XG
experiment with making the worst move at my first turn:
https://www.montanaonline.net/backgammon/xg.php
Because of the dice and luck, in backgammon no checker
or cube decision is as consequential as in chess or other
similar "skill games". In fact, depending on your opponents
next roll, your huge blunder may end up being a gift from
the sky. This is true only for that game but can be true for
many other similar moves, at a considerable ratio even in
four billion trials...
Frankly, I'm just beyond amazed that more humans can't
beat the bots decisively in meaningfully long sessions. Is
anyone even honestly trying?? (Not trying to play exactly
like bots, with a low PR, of course. You need to try playing
like me..:))
Okay, I think this should be enough to get the discussion
rolling, if any of you find this topic interesting.
MK