Circular Circus

[MK]

After posting a response to BG-bzzt, I thought I
would spend some time keyword searching BGO.

BTW: I forgot the mention that 1-ply rollouts of
the Othello positions took about 20 minutes or
so. They go really fast. I didn't want to mislead
you guys to think that I spent a big effort...

Anyway, one of the articles I hit in BGO was from
just yesterday and its first two lines read as this:

"I also think match winning chance is an
"increasing function of match length for
"a certain PR difference.
"However, The PR itself is dependent on
"the match length.

It put a smug smirk on my face. ;) How many
times had I thought of you guys as circus dogs
chasing your tails or mathematicians/scientists
volunteering as clowns to entertain kids at county
fairs, etc. (hey why not? as long as there are no
laws against it, right?)

Instead of repeating my old arguments about
how you guys use circular logic and circular data
to prove yourselves right, I thought I would make
use of some puns like "circular circus" or such.

When I think that I may be coining a new, word,
expression or pun, I usually search for it on the
Internet to see if others had used it already.

Guess what? Doing a search for the exact words
"circular circus" found quite a few results... :(

It's in the "glossary of circus terminology" at
https://circushalloffame.com/glossary-of-circus-terminology/

There is even a web site by that name:
https://circular-circus.com/

But my usage of it would have been in a different
context than those, uniquely related to cube skill
theory, etc. in gamblegammon. :))

MK

[Frank Berger]

MK schrieb am Dienstag, 6. Juni 2023 um 11:40:33 UTC+2:

> "I also think match winning chance is an
> "increasing function of match length for
> "a certain PR difference.

If you throw a biased coin (lets say 0,52 head) you don't agree that the probability of winning betting on heads is a function of throwing the coin only once or best of 3 or best of 100?

> "However, The PR itself is dependent on
> "the match length.

I have to commit that this sentence doesn't make much sense to me, maybe some context is missing. What might be meant is that the longer the match is, the higher the probability is that the measured PR is close to the real PR. One medium error in a 1-pointer ruins your PR whereas in a 25-pointer it hasn't much influence. This is true (and rather trivial)

I'm to limited to draw from this the conclusion that this shows a circular argumentation.

[Timothy Chow]

On 6/7/2023 5:00 AM, Frank Berger wrote:
> MK schrieb am Dienstag, 6. Juni 2023 um 11:40:33 UTC+2:
>> "However, The PR itself is dependent on
>> "the match length.
> I have to commit that this sentence doesn't make much sense to me, maybe some context is missing.

The original poster said that he doesn't know his match
equity table for longer matches.

I suspect that the effect of not knowing the MET is very small
in practice. But there could be other factors, such as fatigue
or loss of concentration, that could lead players to make more
mistakes in longer matches. Or, the correlation could go in
the opposite direction---maybe a player takes longer matches
more seriously and puts in more of an effort, but regards short
matches as being frivolous and not worthy of serious attention.

---
Tim Chow

[MK]

On June 7, 2023 at 3:00:14 AM UTC-6, Frank Berger wrote:

> MK schrieb am 6. Juni 2023 um 11:40:33 UTC+2:

>> "I also think match winning chance is an
>> "increasing function of match length for
>> "a certain PR difference.

> If you throw a biased coin (lets say 0,52 head)
> you don't agree that the probability of winning
> betting on heads is a function of throwing the
> coin only once or best of 3 or best of 100?

Sure but the question is how did you determine
that the coin is 52% biased in the first place..?

Did it take you only 1 throw, 3 throws, 100 throws
to realize that it was 52% biased for for heads..?

>> "However, The PR itself is dependent on
>> "the match length.

> I have to commit that this sentence doesn't make
> much sense to me, maybe some context is missing.
> What might be meant is that the longer the match
> is, the higher the probability is that the measured
> PR is close to the real PR.

This is just the point. If the formula was correct, the
actual/estimated PRs would be accurate across all
match lengths.

> One medium error in a 1-pointer ruins your PR
> whereas in a 25-pointer it hasn't much influence.
> This is true (and rather trivial)

You are pointing out a problem with PR calculation
but why are you trivializing? Can't you face reality?

> I'm to limited to draw from this the conclusion that
> this shows a circular argumentation.

PR is based on lost equity, no? And how is equity
calculated? In "Match Equity Tables" for example?
I think it's rather easy to see the circularity...

MK

[MK]

On June 7, 2023 at 7:20:34 AM UTC-6, Timothy Chow wrote:

> The original poster said that he doesn't know
> his match equity table for longer matches.
> I suspect that the effect of not knowing the
> MET is very small in practice.

And I think it can go both was also like other
factors you mentioned below.

> But there could be other factors, such as .....

Sure but finding an explanation for it doesn't
change the fact observed.

I went back and read the entire thread. Quite
interesting. It's good to see that some people
disturb the comfort of concensus in BGO, of
all places :) which seem to be official "whore
house" of gamblegammon. Maybe I'll visit the
bordello more often looking to find occasional
virgin ideas... ;)

In several posts, there were interesting remarks
that I feel like commenting on.

In your initial post, you say: "It doesn't seem
possible that winning probability can be totally
independent of match length, but I'm willing to
believe that it increases more slowly". I agree
looking at it from a different angle. 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.
(I'm just guesstimating.)

I don't know if it happens so in real life but in
theory the longer the match the higher the cube
can go, causing the "actual lengths of matches",
(measured in terms of games, not points), to
"increase more slowly" (borrowing your words).

Art Grater explains that Kaufmann created the
ELO for gamblegammon by modifying the ELO
for chess, (i.e. replacing D/400 by D times the
square root of N/2000). The problem goes back
to that. 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.

It's good to see that in another of your posts
you admit: "The conventional formula with a
square root of N doesn't seem to be very well
founded, either theoretically or empirically". :)
Better late than never but so what...? I doubt
that it will be amended. And nor for lack of will
but for lack of knowing how to.

In the same post you ask: "The 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 (because of the overestimated
"cube skill" fantasy).

In his long article where he says a lot without
saying anything new, the only thing interesting
suggestion Bob Koca makes is using 19,000
matches from other sources like dailygammon;
to which you respond by suggesting instead "a
bunch of bot-versus-bot games where random
noise is added to simulate different playing
strengths" and ask "if anyone has done that?".

If you remember, I had done something similar
and had reported on in RGB. I ran two sets of
games, one with players of equal checker skill
but very unequal cube skill, and one with players
of equal cube skill but very unaqual checker skill.
I was trying to show cube skill didn't matter as
much as checker skill but you can do a similar
experiment for your purposes.

For example, you can run cubeful and cubeless
matches between unequal players to see if the
winning probability does indeed increase more
slowly because of the cube. You an also do the
same experiment between equal players to see
if the winning probability stays the same as it
should, regardless of the cube or not.

This is all from me on this for now. I'll be very
curious to see what, if anything, will come out
of this discussion on BGO and/or here in RGB..??

MK

[Frank Berger]

MK schrieb am Mittwoch, 7. Juni 2023 um 18:36:30 UTC+2:

> This is just the point. If the formula was correct, the
> actual/estimated PRs would be accurate across all
> match lengths.

Then throwing a coin 2 times, 4 times 8, 16, 1026 etc. has alway come up with 0.5 heads? Then e.g. a 3-PR player to make an equivalent error in any subset of games. I recommend you to watch a UBC match with real time analysis. Or throw coin and count.

>Sure but the question is how did you determine
>that the coin is 52% biased in the first place..?

F: Given A then B follows because of...
MK: how can you be sure that you have an A?
A typical MK answer.

[MK]

On June 7, 2023 at 4:46:23 PM UTC-6, Frank Berger wrote:

> MK schrieb am 7. Juni 2023 um 18:36:30 UTC+2:

>> This is just the point. If the formula was correct,
>> the actual/estimated PRs would be accurate
>> across all match lengths.

> Then throwing a coin 2 times, 4 times 8, 16, 1026
> etc. has alway come up with 0.5 heads?

Frank, I'm sorry :(, but frankly :), I have difficulty in
understanding what you write and I'm doing very
badly at communicating my thoughts also... :(

So let me try again. Instead of my badly botched
sentence above, I meant to say: If the formula was
correct, estimated match winning chances based
on PR difference would be accurate, (i.e. the same
as actual winning resuls), across all match lengths.

So, ignoring your last question above and going
back to your previous question with 52% bias, I
had agreed with you but actually wrongly because
you wouldn't win increasingly more than 52% if
you kept tossing the coind more times.

But in gamblegammon, the same PR difference is
expected to win more at an increasing rate as the
lengths of matches increase. And the issue that
Tim raised in his BGO thread is that actual results
of the 19,000 matches showed that the stronger
player didn't win increasingly more in increasingly
longer matches, as predicted/estimated.

Your coin toss example didn't apply to the subject
on hand at all. (That's why I'm always against using
stupid coin toss, etc. examples in trying to explain
backgammon or gamblegammon :) Are we clear
thus far on this now?

>> Sure but the question is how did you determine
>> that the coin is 52% biased in the first place..?

> F: Given A then B follows because of...
> MK: how can you be sure that you have an A?
> A typical MK answer.

Let me explain this also. Originally I had quoted
two sentences. Your question with 52% bias was
in relation to the first sentence and you omitted
the second one which was the one that created
the circularity by saying: "However, The PR itself

is dependent on the match length".

So, I added back circularity to your example by
indicating to you, in a question format, that you
needed to somehow calculate/derive your 52%
from number of coin tosses, (i.e. match lengths),
instead of just pulling it out of the air. Otherwise,
there is no circularity and it's no wonder that you
don't see a circularity... I hope we are now clear
on this also?

MK

[Timothy Chow]

On 6/7/2023 2:14 PM, MK wrote:
> Art Grater explains that Kaufmann created the
> ELO for gamblegammon by modifying the ELO
> for chess, (i.e. replacing D/400 by D times the
> square root of N/2000). The problem goes back
> to that. 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.

I'm sure you raised doubts about it many years before I did,
but this is far from the first time I've expressed doubts about
it. See for example:

https://www.bgonline.org/forums/webbbs_config.pl?read=182417

---
Tim Chow

[Axel Reichert]

MK <mu...@compuplus.net> writes:

> doubling cube shortens matches

Not that much, see

https://www.bkgm.com/rgb/rgb.cgi?view+712

... but it increases the number of skillful decisions by at least 50 per
cent, so easily compensates for the smaller number of checker moves.

> For example, you can run cubeful and cubeless matches between unequal
> players to see if the winning probability does indeed increase more
> slowly because of the cube.

I have not varied the match length, but done something similar:

10 matches to 64 points, "Expert" versus "Casual player" on GNU
Backgammon. 1 batch of 10 matches cubeless, 1 batch of 10 matches
cubeful.

The expert won all 20 matches. The casual players on average won 10.2
points in the cubeful matches, but 18.3 points in the cubeless matches.

To me this seems like a cube-skillful expert gardener cutting back the
lucky branches of the wildly growing new plant.

It is easy to confirm, try it yourself.

Best regards

Axel

[Axel Reichert]

Axel Reichert <ma...@axel-reichert.de> writes:

> It is easy to confirm, try it yourself.

Another three batches, this time a money session, stopped when the
expert reached 1000 points.

1. The casual player got 321 points when played cubeless (no cube skill
involved). This is the base case.

Now two batches played with the cube:

2. When the casual checker play was combined with expert cube handling,
the casual player got 312 points, which is very similar to the base
case. As before, the size of the big win by the expert resulted only
from the checker play, since both players handled the cube expertly
(in contrast to "not at all" in case 1).

3. When the casual checker play was combined with cube handling set to
"Casual Player", the casual player reached only 103 points.

I would think that the much increased margin of the expert's win may
safely be called "cube skill".

But for sure I will be told here (not: "learn") what I did wrong.

Best regards

Axel

[MK]

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!

> I'm sure you raised doubts about it many years
> before I did, but this is far from the first time
> I've expressed doubts about it. See for example:
> https://www.bgonline.org/forums/webbbs_config.pl?read=182417

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
single number?".

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
13 respectively.

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"... :)

MK

===========================================
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
players
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
---------------------------------------------------------
1 1.6
3 1.6
5 2.1
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
slightly more.
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.
===========================================

[MK]

On June 8, 2023 at 7:12:31 AM UTC-6, Axel Reichert wrote:

> MK <mu...@compuplus.net> writes:

>> doubling cube shortens matches

> Not that much, see
> https://www.bkgm.com/rgb/rgb.cgi?view+712

The stats there show average number of games
in matches to be 24-48% less than match lengths.

If they were meaningful, I would say that they are
a little more than what you call "not that much" but
without comparing to average games in cubeless
matches, they are useless in telling how much the
cube shortens matches.

> ... but it increases the number of skillful
> decisions by at least 50 per cent,

Who says?

> so easily compensates for the smaller
> number of checker moves.

Number of moves isn't relevant to this subject.

>> For example, you can run cubeful and cubeless
>> matches between unequal players to see if the
>> winning probability does indeed increase more
>> slowly because of the cube.

> I have not varied the match length, but done
> something similar:

Right off the bat, this means that what you did was
irrelevant to this discussion but let's hear it anyway.

> 10 matches to 64 points, "Expert" versus "Casual
> player" on GNU Backgammon. 1 batch of 10
> matches cubeless, 1 batch of 10 matches cubeful.

Eliminating the cube, i.e. "isolating the cube" isn't
the same thing as "isolating the cube skill"..!

Thus only cubeful play can be used to isolate and
demontrate cube skill vs no cube skill.

> The casual players on average won 10.2 points
> in the cubeful matches, but 18.3 points in the
> cubeless matches.

So, you're not "isolating cube skill" in the cubeful
matches either.

> To me this seems like a cube-skillful expert
> gardener cutting back the lucky branches

To me it seems you are comparing oranges to
apples and pears at the same and arriving at
some wishful conclusions... :(

> It is easy to confirm, try it yourself.

How do you mean? Duplicate your meaningless
experiment to arrive at the same results?? No,
thanks. I'll take your word for it... ;)

MK

[MK]

On June 8, 2023 at 11:50:09 AM UTC-6, Axel Reichert wrote:

> Axel Reichert <ma...@axel-reichert.de> writes:

> I would think that the much increased
> margin of the expert's win may safely
> be called "cube skill".

Okay, this is better.

> But for sure I will be told here (not:
> "learn") what I did wrong.

Not but I don't understand is what were
you trying to prove at the expense of
derailing/hikacking this thread?

Even as I call it "bullshit", I never argued
that there wasn't any cube skill at all.

I have and I continue to argue that it is
way too exaggerated and misassessed
by the bots because of some jackoffski
formula, circular MET's, etc.

So, really, what have you accomplished??

MK

[Timothy Chow]

On 6/8/2023 11:10 PM, MK wrote:
> 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?

The reason I wasn't clear is that I didn't---and still
don't---have well-developed ideas of my own on the subject.

> 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.

In chess, they maintain separate Elo ratings for classical,
rapid, and blitz, because people have made the judgment call
that the different time controls make enough of a difference
to call it a different game.

Are you suggesting, perhaps, that if we were to maintain
separate Elo ratings for different match lengths, then for
cubeless backgammon, players' Elo ratings would be pretty
much the same for all match lengths, but that with the cube,
their Elo ratings might not correlate very well? Player A
might be significantly better against Player B in a 5-point
match, but significantly worse in an 11-point match?

---
Tim Chow

[Axel Reichert]

Axel Reichert <ma...@axel-reichert.de> writes:

> Another three batches, this time a money session, stopped when the
> expert reached 1000 points.
>
> 1. The casual player got 321 points when played cubeless (no cube skill
> involved). This is the base case.
>
> Now two batches played with the cube:
>
> 2. When the casual checker play was combined with expert cube handling,
> the casual player got 312 points, which is very similar to the base
> case. As before, the size of the big win by the expert resulted only
> from the checker play, since both players handled the cube expertly
> (in contrast to "not at all" in case 1).
>
> 3. When the casual checker play was combined with cube handling set to
> "Casual Player", the casual player reached only 103 points.
>
> I would think that the much increased margin of the expert's win may
> safely be called "cube skill".

And in order to get a result as bad as in case 3, you need to set the
checker play to have a noise of about 0.1 (casual player has a noise of
0.05). With this noise used in a cubeless session or with expert cube
handling in a cubeful session, you will get roughly the same defeat
(1000 points for the expert, 100 point for the clueless).

The difference between 0.05 noise and 0.1 noise is HUGE, even "Beginner"
has only 0.06 noise. Imagine every checker play on average being a
whopper.

Axel

[Axel Reichert]

MK <mu...@compuplus.net> writes:

> On June 8, 2023 at 7:12:31 AM UTC-6, Axel Reichert wrote:
>

[Cube use]

>> ... but it increases the number of skillful
>> decisions by at least 50 per cent,
>
> Who says?

Easy to see:

Imagine the cube staying in the middle for the whole game. Then
obviously the number of decisions has doubled ("every roll is a cube
decision"). If the cube is turned at first opportunity (and then maybe
used later or not, does not matter), then only the cube owner has an
additional cube decision, which amounts to 50 per cent more decisions.

Axel

[MK]

On June 9, 2023 at 7:14:39 AM UTC-6, Timothy Chow wrote:

> On 6/8/2023 11:10 PM, MK wrote:

>> 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?

> The reason I wasn't clear is that I didn't---and still
> don't---have well-developed ideas of my own on
> the subject.

Ah, okay. No problem. Keep contributing if/when you
come up with new ideas, well-developed or not.

>> 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.

> Are you suggesting, perhaps, that if we were to
> maintain separate Elo ratings for different match
> lengths, then for cubeless backgammon, players'
> Elo ratings would be pretty much the same for all
> match lengths, but that with the cube, their Elo
> ratings might not correlate very well?

Yes, I am suggesting that it would be so but I am not
suggesting that it should be done so. I am confident
that given a sufficient amount of emprical data, any
competent mathematician can derive a single formula
that would work for all bacgammon/gamblegammon
matches of all lengths. It would help if the data is as
unbiased as possible but "understanding the data" is
the more imprtant.

What I meant above is that any such attempted rating
formula, (which we should stop referring to as "ELO"),
would better tolerate biased data in backgammon than
in gamblegammon because there is less "amount of"
and less "fluctuation of" luck without the doubling cube.

See my "Where there is no luck, there is no cube skill"
thread"

https://groups.google.com/g/rec.games.backgammon/c/TD3K--EK1cc/m/zGWh9J-FAgAJ

Thus, in gamblegammon, calculating the probability of
winning becomes calculating the probability of getting
lucky, because luck increases faster than skill as match
length increases.

I could see that cube magnified luck the moment I was
introduced to it and I categorically objected to an "ELO"
adapted from chess, (a game of skill), to backgammon,
(already a game of luck without the doubling cube and
even more so with it in gamblegammon), especially also
because of more than one arbitrary constant in the formula.

Soon after, in 1998, I had initiated discussions about it
and proposed a simple dynamic brackets system (that
we can discuss separately if there is an interest). What I
quoted from Jim Williams was from one of my threads
titled: "FIBS formula question/comment"

https://groups.google.com/g/rec.games.backgammon/c/2fCYjYSo9Ts/m/9EAZxznAFm8J

Another one of my threads on the same subject, from
around the same time is: "Rating system suggestions"

https://groups.google.com/g/rec.games.backgammon/c/qJ8T-0lJKz4/m/M61_5MEmvT4J

Many articles from these threads, (as from many others),
are individually, (thus improperly), quoted at "bkgm.com",
etc. without links to the threads they are taken from, which
leads to a loss of context. Anyone who can spare the time
may want to read the entire threads, as they contain many
other valuable posts from other, people, (even if they may
be less respected by the "incestuous circle").

Since I didn't believe in "fixing" the FIBS ELO at the time, I
didn't pay much attention to things like what Jim Williams
had written. What a novel idea his "effective match length"
was. Unfortunately, nobody else had picked up on it either
(his usage of the expressions was the first and only time
in RBG in all those 25 years). It is almost exactly what I was
trying to explain here a few days ago, (i.e. cube shortens
matches).

Since then, mentalli ill gambler mathematicians blamed it
on the inferior quality of the empirical data that was taken
from FIBS, maintaining that the formula would be accurate
if applied to "perfectly" played matches between bots. 25
years later, Bob Koca wonders if it may works better using
data taken from "cleaner sources like Gailygammon". What
if it does not? Will he, et al., shove it up their stuffy noses?

25 years later, you are still asking if anyone has done any
bot-vs-bot experiments... Why weren't they done? Perhaps
for fear of discovering the ugly reality that you all couldn't
face? How much more time is needed to see one inch of
progress made?

After standing back for a few days, it is sad to see that no
new articles were posted on this, neither in BGO nor RBG.
I wonder if some of you may at times feel as I do, failing
to making an iota of difference with all that we write here?
No matter, personally I enjoy rational debate just for the
sake of it. So, let's pick up from your last post in BGO:

https://www.bgonline.org/forums/webbbs_config.pl?read=210853

Have you thought any more about whether you agree with
Kaufmann's derivation even with the said assumptions?

Your having written: "I'm mainly concerned that gammons
and the cube could change things significantly" made me
realise that I didn't know for sure if TD-Gammon v.1 was
trained playing "1-pointers", (no gammon or backgammon
wins), or "single games", (with gammon and backgammon
wins). Well, it was neither. It played "single games" with
gammons but without backgammons. Sheesh! I am sure
we will talk about the implications of this later... :(

But on the bright side, what you wrote gave me hope that
you may sooner than later accept the fact that the cube
magnifies luck without adding even a compensating, (let
alone exceeding), amount of skill to gamblegammon.

I can undestand the timid statements and the baby
steps. It's okay. Just keep walking. Come to papa... ;)

MK

[MK]

On June 12, 2023 at 5:51:50 AM UTC-6, Axel Reichert wrote:

> .....

> The difference between 0.05 noise and 0.1

> noise is HUGE, even "Beginner" has only.....

I'm not trying to ignore you and would like to
discuss these kinds of subjects with you but
I honestly don't understand what exactly are
you trying to prove...?

I stopped doing even my experiments setting
the error level to maximum 1.0, as a substitute
for true random play, because it really doesn't
make sense to make a bot, that I argue is biased,
play against itself regardless how much noise is
added, (especially not even knowing how exactly
it is done), because any amount of bias is bias
and it is likely to keep compounding with longer
trials.

I'm not all that familiar with the command line
functions as you may be. I suspect it would be
fairly easy to send random cube decisions but
I don't know if it is possible to query the bot for
all legal moves and picl/send a random checker
decision? If you know how to do this, why don't
you have whatever levels of the "biased bot"
play against random cube and checker play?
That would be so much more meaningful. Too
bad the Noo-BG team won't add even the most
technically trivial yet eXtremely useful features
to their cheating, err, teaching ;) bot...?

MK

[MK]

On June 12, 2023 at 5:56:59 AM UTC-6, Axel Reichert wrote:

> MK <mu...@compuplus.net> writes:

>> On June 8, 2023 at 7:12:31 AM UTC-6, Axel Reichert wrote:

>>> ... but it increases the number of skillful
>>> decisions by at least 50 per cent,

>> Who says?

> Imagine the cube staying in the middle for
> the whole game. Then obviously the number
> of decisions has doubled

I was questioning your statement "skillful
decisions". Now that you dropped the word
"skillful", I will only object to the percentage.

> If the cube is turned .... then only the cube

> owner has an additional cube decision,
> which amounts to 50 per cent more decisions.

Since you corrected yourself that even the
non-skillful cube decisions woud increase
by less than 50%, I will leave this here well
alone, as I see no real benefit in dwelling on
it beyond this. Thanks for clarifying. Let's
discuss more exciting things...

MK

[Axel Reichert]

MK <mu...@compuplus.net> writes:

> On June 12, 2023 at 5:51:50 AM UTC-6, Axel Reichert wrote:
>
>> .....
>> The difference between 0.05 noise and 0.1
>> noise is HUGE, even "Beginner" has only.....
>
> I'm not trying to ignore you and would like to
> discuss these kinds of subjects with you but
> I honestly don't understand what exactly are
> you trying to prove...?

Imagine you are a casual player (0.05 noise for both checkers and
cube). If you then enhance your cube handling to expert it will
compensate roughly your checker play deteriorating from casual player to
0.1 noise (almost clueless). This is cube skill.

> I suspect it would be fairly easy to send random cube decisions but I
> don't know if it is possible to query the bot for all legal moves and
> picl/send a random checker decision?

Yes.

> If you know how to do this,

Yes.

> why don't you have whatever levels of the "biased bot" play against
> random cube and checker play?

Because "I honestly don't understand what exactly are you trying to
prove". Define precisely what checker/cube skill I should pair against
which. Maybe I can detect a slight trace of meaning in the setup and
might do it.

Axel

[MK]

On June 22, 2023 at 3:31:56 PM UTC-6, Axel Reichert wrote:

> MK <mu...@compuplus.net> writes:

>> why don't you have whatever levels of the
>> "biased bot" play against random cube
>> and checker play?

> Because "I honestly don't understand what
> exactly are you trying to prove".

Fair enough. I may be the one failing to make
my point clear. I will try better.

> Define precisely what checker/cube skill I
> should pair against which. Maybe I can
> detect a slight trace of meaning in the
> setup and might do it.

This side discussion with you branched out
from my suggestion to Tim:

"For example, you can run cubeful and
"cubeless matches between unequal
"players to see if the winning probability
"does indeed increase more slowly
"because of the cube.

I thought your experiments were irrelevant
to that issue. Here is what I suggest you do:

Have Noo-BG "beginner" play against "4-ply"
a large number, (1,000? 10,000?), of 1, 5, 13,
25 point matches, each first cubeless then
again cubeful.

Personally, I would go with shorter cubeless
1, 3, 7, 13 point matches but it may be even
better to do both sets of lengths.

Also, I would try fewer, (i.e. 1,000) matches of
more varied lengths first, to see if I am on the
right track; then run more, (i.e. another 9,000).

Since we don't know the ELO/ER/PR of the
"beginner" and "4-ply" beforehand, we'll do
our calculations using the resulting values.

For "4-ply", ER will be zero. For "beginner"s ER,
I think the manual says 26 to 35. Let's say 30.

For converting to ELO, I happened on this bit:

1 PR = 33 Elo (according to eXtreme Gammon)
1 ER = 26 Elo (according to Stick)

Let's say 30 as a number in the middle also.

For winning probability, we will of course use:

1-(1/(10^((ELOdiff)*SQRT(ML)/2000)+1))

After 1,000 cubeless matches, if "beginner"s
ER is 30, for example, and the ELO difference
is 30*30=900, we will calculate his probabilities
of winning for each cubeless match length and
compare to his actual winnings.

If Noo-BG's assessment of errors is accurate,
after 1,000 cubeful matches, "beginner"s ER
and ELO difference should also be 30 and 900.
Again, will calculate his probabilities of winning
for each cubeful match length and compare to
his actual winnings.

The goal is to see how does the probabilities of
winning increase as the match lengths increase,
and how the actual number of wins compare to
the predicted numbers.

If the difference is small enough to call it "hand
waving", you gamblegammon mathematicians
may be able to live with it happyly ever after. If
it is big enough to call the formula "bullshit", I
will be happily vindicated ever after.

This experiment will be useful in another way
also. By modifying the formula and applying to
our results, we can calculate "effective match
lengths" for all cubeless and cubeful declared
match lengths. For this, 1-point matches have
a special usefulness. Even if it's awkward to
call them "matches", they are so theoretically
and technically. What's unique about them is
that a cubeless 1-pointer is the same as a
cubeful 1-pointer, with the same "effective
match length".

In this aspect of the experiment, we don't know
what to expect other than my prediction that
"effective match lengths" for cufeful matches
will increase at a slower rate than for cubeless
matches.

If this comes true, then it will also vindicate my
argument that the "cube magnifies luck", rather
than skill, at an "increasing rate", as the match
length increases, (thus, reversely, it will cause
the "effective match length" to increase at a
"decreasing rate"), thus proving the so-called
"cube skill theory" a pile of "bullshit" also!

Let me know if I were able explain it all clearly
this time? And if you will do the experiment?

(Once you create the script or utility, I would
be glad to do some of the grunt work on my
computer but you may not trust the results as
much as you would if you do it all yourself).

MK