On July 23, 2023 at 10:56:53 AM UTC-6, Axel Reichert wrote:
Timothy Chow <tchow...@yahoo.com> writes:
On 7/22/2023 5:37 AM, MK wrote:
On July 19, 2023 at 9:51:40 AM UTC-6, Axel Reichert wrote:
20 matches each is certainly to few, which
possibly explains the non-monotoneous growth.
What the heck "non-monotoneous" means? Can't
you bring yourself to say say non-linear? ;)
Let me start by being nice to say that I appreciate
your below work and I did my contributing part by
copy-pasting it into spreadsheets and generating
pretty looking charts to help you folks see things
more clearly. As opposed to Axel's misinterpreting
his own findings, once again, they indeed bolster
my arguments more clearly, decisively. Let's begin.
I think he meant "non-monotonic".
https://en.wikipedia.org/wiki/Monotonic_function
Yes, indeed. And of course, but at least you know
this, there is a difference between non-monotonic
and non-linear,
If you are alluding to my comments, I had sait that
"non-monotonic" necessarily meant "non-linear",
which doesn't mean that there is no difference
between them but that once you say something is
"non-monotonic", you can no longer use the word
"linear"! But of course you will keep arguing that it
is "non-monotonic" and "linear" at the same time.
which is why I tried to use the former on purpose.
Ha ha! :) Bullshit! Tim licked the shit off of your ass.
Just be thankful to him and leave it well alone. You
don't need to be pathetic trying to return the favor by
wiping it off of his lips... :(
I have automated things with GNU Backgammon
(IMHO /the/ killer feature compared to XG)
I totally agree with this. They just added the ability
to specify a session length to run. I was going to
suggest that they also add the ability to specify the
number of matches to run, i.e. a "session of matches"
like a "session of (money) games", but I decided to
not waste my time with them weird bunch. I'm sure
they will implement it if someone other than Murat
suggests it... Then, others won't need to "automate
things" as you have done with Noo-BG.
and run 100 matches for all match lengths from 1
to 64 (the maximum allowed in GNU Backgammon).
I suppose you will only share some results but not
your data as for you previous experiments??
Here are the results (a plot shows games and
moves to fit very nicely to straight lines),
They are not lines. They are "non-monotonic curves".
which do not bear out the hypothesis that there
might be a different relation between the match
length and the number of games played than O(n):
I can't believe how stubbornly stupid you guys are.
O(n) was spiteful Walt's lack of understanding what
Paul was talking about, i.e. the relation between the
match length and the total number of plays, which
is non-monotonic decreasing but perhaps not by
not enough to warrant different clock rules. See:
https://montanaonline.net/backgammon/mlg.pdf
Paul was clearly talking about clock time which is
depleated per move/play not per game. One must
be a moron to miss that. Interestingly Paul would
have a very strong case in backgammon even if
not in gamblegammon.
In backgammon, number of plays per game is also
non-monotonic but increasing! and significatly. See:
https://montanaonline.net/backgammon/mlb.pdf
I also generated a chat for only 25 gamblegammon
matches for easier visual comparing. See:
https://montanaonline.net/backgammon/mlg25.pdf
For one thing, you are calculating your "moves per
game" column wrongly using the effective match
lengths. One must be twice a moron to miss that,
in his original post, Paul wrote "... give each player
2 * n minutes for the match". So, I added a column
showing plays per stated match length for which
the curves look similar im gamblegammon but not
in backgammon.
So the number of games is pretty constant at
about 2/3 of the match length.
It is not constant!. It is not a line! It is not linear!
Even though longer matches would offer the the
opportunity for higher cubes, thus drastically
reducing the number of games played,
I dont remember if/what I had said on this but I'm
a little disappointed that the curve doesn't bend as
I had envisioned. Maybe because of that there are
increasingly more matches of different lengths
between cube value increments, i.e. between 4 and
8 cube there are 4, 5, 6, 7-points; between 8 and 16
cube there are 8, 9, 10, 11, 12, 13, 14, 15-points,
and the matches of lengths closer after the cube
value will be effected worse, i.e shortened by more
games. Those are the zigzags, non-monotonic drops
along the curve of effective match lengths.
seems that the likelyhood of higher cubes (with
proper cube skill) diminishes faster than the match
length increases. See
This is wishful bullshit.
https://www.bkgm.com/rgb/rgb.cgi?view+662
for how rare already a cube of 8 is.
How rare in matches of what lengths? Nubers there
seems for money games. Meaningless for matches.
I have done a similar thing for cubeless backgammon
(but only for matches up to 25 point),
There is no such thing as "cubeless backgammon"!
What you are referring to is a "cubeless variant of
gamblegammon". None of the past or current bots
offer "backgammon", i.e. without 3-point wins, etc.
The number of moves per game is again about 54,
no surprise here.
I don't know what that "no surprise" is supposed to
mean but you are wrongly dividing the total number
of moves/plays by the effective match length, not by
the stated match length. When you do it right, it's a
range from 53.75 to 73.76 moves/plays per game.
On a side note, I used the magic 54 in a mutant cube
experiment draft that I never got around to posting.
There are some stats out there which point at about
that average but it's not always clear whether they're
based on match games and/or money games. See:
https://zooescape.com/backgammon-stats.pl
The number of games per match is pretty constant
again, this time at about 4/3 of the match length.
It is not constant again! It is not a line again! It is not
linear again! It is a *monotonic* increasing curve!
If we put this together we end up with
54 * 4/3 * m = 72 * m
42 * 2/3 * m = 28 * m
False! You are presenting your fantasies as facts.
This of course does not amount to cubeless
backgammon being the more skillful game:
Of course it does. When referred to it correctly, even
"cubeless gamblegammon" is a more skillful game,
as your own experiment has demonstrated, because
without the cube luck isn't magnified.
Your experiment is between equally checker skilled
players. Thus skill is already level and only luck can
fluctuate.
Look at the charts carefully.
In "cubeless gamblegammon" luck fluctuates but
never enough to overtake checker skill. That's why
the effective match length is a *monotonic* curve.
In "cubeful gamblegammon" luck fluctuations are
magnified by the cube and overtake checker skill,
(and cube skill for that matter), causing the dips
in the non-monotic curve.
With 4 cube, a 4-point match is more likely to end in
a single game than a 5-point match. A 6-point match
is less likely and a 7-point point match is even lesser
like yet. The curve will dip again at 8-point match and
again at 16-point match and again at 32-point match.
If you don't believe me, try to believe yourself. What
more proof do you want that cube add more luck to
gamblegammon than it adds skill.
And look at how smooth the effective match length,
or number of games in a match as you say, curve is
for "cubeless gamblegammon" compared to the one
for "cubeful gamblegammon". You guys need to read
what I had written in the thread "Circular Circus". See:
https://groups.google.com/g/rec.games.backgammon/c/CiG54VoJvq8
Here are a couple of snippets:
"... real question is how quickly the match-winning
"chances increase with match length". I couldn't
"guess how quicky but in my opinion it will increase
"more smoothly and steadily in backgammon, more
"erratically in gamblegammon ...
"As I had pointed out many times in the past,
"doubling cube shortens matches. A 13 or a 17
"point gamblegammon match may be equivalent
"of a 5 point backgammon match, similarly a 19
"or 25 point gamblegammon match may be
"equivalent of a 7 point backgammon match.
Lo and behold! Your total moves for a 5-point cubeless
gamblegammon match is 324, for a 13-point cubeful
gamblegammon match is 351. Similarly, for a 7-point
cubeless gamblegammon match is 465, for a 19-point
gamblegammon match is 530. Backgammon numbers
would be higher as matches would last longer without
3-point wins and thus would prove my guestimates to
be pretty darn accurate, if not almost exact.
1. Cashing a boring (in the sense of low equity
difference between candidate plays) race or other
low-skill games cuts away the luck.
Ha ha! :) How funny. If shortening matches and games
"cuts away the luck", why don't you make championship
matches 15-points instead of 25-points? Or even why
not 7-points? 3-points? 1-points? If that's still too boring
for you, you can skip playing altogether and just roll dice
or better yet toss a coin to determine the winner. ;)
2. Imperfect human players might squander more
equity getting cube decisions wrong than checker plays.
You weigh humans using bots as scales but you have
never made any efforts to check if your scales are not
imperfect, inacurate themselves.
As a last comment, let me say that despite all the harsh
words I use in citicizing you, I still hold you special from
others because you are the only one open minded and
willing enough to conduct experiments. It's obvious that
you are doing them not to discover, learn something new
but to prove that your gambling addiction is actually an
exercise in skill competition, in order to comfort your
sick mind. Still, it's better than nothing. So, I do openly
thank you for that.
MK
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