Of Copernican Revolution, Fosbury Flop, Intuition, Knack, Mice and Men, etc.

[MK]

I'm glad I don't filter out much other than stupid, useless,
boring position discussions with cutely silly thread titles
to attract attention because in some unlikely threads, I
find little gems that makes reading RGB interesting and
writing posts exciting.

I'm starting a new thread here by borrowing a few quotes
from another one titled: "Reading Axel's paper on Isight".

On April 21, 2022 at 3:01:24 PM UTC-6, Axel Reichert wrote:

> Adding this complexity and mental overhead .....
> ..... this reminds me on Ptolemy's epicycles. (-;

Reading things like this really raises my hopes that first
Axel, then others will eventually come all the way around
to agree with my arguments about cube skill, equity, luck,
MET's, ER/PR, etc. calculations in gamblegammon.

Not knowing who have been following RBG since when, I
will give some background on things that I will talk about.

For so many years, I have been likening all the elaborate
calculations in gamblegammon to the extremely accurate
but completely mistaken calculations of unreal retrograde
motions of planets before the "Copernican revolution".

https://en.wikipedia.org/wiki/Copernican_Revolution

I kept advocating that such a revolution was needed in
backgammon also. For example, see this thread: "Stuck
in pre-Copernicus age of backgammon".

https://groups.google.com/g/rec.games.backgammon/c/uVhYek8QF1A/m/4vFYlD1WBgAJ

In fact, already 20 years ago, I was even called Copernicus
sarcastically, as in this post:

https://groups.google.com/g/rec.games.backgammon/c/mYKYvP459uE/m/hi9YvOvdAI4J

I hadn't minded the sarcasm that was obviously meant as
an insult thinking of the possibility that I could indeed be
called the Copernicus of the backgammon world someday...

Another analogy I also often used for the same purpose,
was the "Fosbury Flop". See:

https://groups.google.com/g/rec.games.backgammon/c/o1XT3BqSBAg/m/_BDxntJBWh0J

https://en.wikipedia.org/wiki/Fosbury_Flop

I haven't really developed a new technique in backgammon
so to speak but through my experiments playing against
the bots, I have shown that other/new approaches could
work better, even if mine doesn't prove the best one of them.

> My gut feeling says that any major improvement
> on race cube decisions will not be based on adding
> this feature or that ..... but rather on something
> fundamentally different, namely EPCs along with a
> doubling criterion matched to them.

Even though you don't seem to be taking your own advice
yet, I'm very optimistic that you eventually will. "EPCs along
with a doubling criterion matched to them" will still be an
added minor improvement, just another shovel of bullshit
in the pile, but not quite "fundamentally different".

I can't wait for the day you will liken cube skill, equity, luck,
MET's, ER/PR, etc. calculations to Ptolemy's epicycles... ;)

----------------------------------------

On April 22, 2022 at 7:32:19 AM UTC-6, peps...@gmail.com wrote:

> Even if algo X is the best when used in an automated
> botlike fashion ..... this by no means indicates that
> algo X is the best for the informal approach. I think
> Stick's method is [Keith Count + informal intuitive
> adjustments] There's no evidence that Isight beats
> this (or matches this) .....

Did I see the words "informal intuitive adjustments"?
And to say, no less than, their being better than "algos
used in an automated botlike fashion"?? Wow!

Here are some primary definitions of "intuition":
1. knowledge or belief obtained neither by reason nor
by perception
2. instinctive knowledge or belief
3. a hunch or unjustified belief

The way I hear it, this is almost music to my ears coming
from far away lands, nay, from Ptolemic planets... :)

In the past, I had talked about some top players having a
"knack" for backgammon, etc. but even I had never gone
this far. You may find this post interesting (also because
it shows I was already using the words "gamblegammon",
"botgammon", etc. many years ago):

https://groups.google.com/g/rec.games.backgammon/c/c-SmlkEIHz8/m/Xprtcu8DBwAJ

Here are some primary definitions of "knack":
1. a skilful, ingenious, or resourceful way of doing something
2. a particular talent or aptitude, esp an intuitive one

Let me elaborate a little on my past arguments on this.

I never acceptad that the bot style/strategy was the best,
perfect, optimum, etc. but argued that it was just one of
dogmatic approaches to playing backgammon, or more
specificly gamblegammon.

Since all the world-class gamblers adhere to the same
dogma, they can only be said to be "giants" in their own
"little", mentally ill universe, among themselves.

While some of those "giants" may have become strong
players through laborious study and practice, some of
them may be naturally good at playing backgammon.

While "learned giants" can't easily do so, "natural giants"
can easily adapt to playing variants of backgammon.

I had argued that the success of "natural giants" in the
"botgammon" land was by coincidence, i.e. not because
only that they can play like the gamblegammon bots.

In other words, if they are given an incentive/challenge
to play like Murat or like a Murat mutant, they can also
do that well and very likely play even better than Murat
or a Murat mutant.

If you folks remember, when we were talking about me
playing against "stick" (who may very well be one of the
"natural giants"), etc. I had offered the argument that my
playing against the bot would be more of a proof of my
being better him and the bot, instead of playing against
stick who may be almost but not as good as the bot that
he is striving to play like.

Then in the alternative, I had offered that if I had to play
against stick or another so-called gamblegammon giant,
I would expect them to play like the bots as much as they
usually can, i.e. close to their current ER/PR ratings.

Being human players more capable than bots, they may
try to adjust their play according to their opponents, by
making "PR-sacrificing moves", etc. In order to prevent
them from doing that against me and starting to play like
Murat, I had placed the restriction/condition on the bet
that if they starts to deviate from botgammon, then they
would be penalized accordingly/proportionately.

Along with that, I have explicitly expressed in unrelated
contexts, numerous times, that my beating the bots didn't
mean that I was the greatest backgammon player on the
planet but it just meant that the bots weren't as strong as
I am and that other stronger human players could beat me
by playing like humans instead of playing like bots.

Think about it folks. All this shows that I must be the most
"humble zeppelin" you will ever meet in RGB... ;)

The bitter reality of nature is that most of you here don't
have the brains to understand what I'm talking about and
of the few who can, most are god fearing primates... :( So,
I just have to wait for some intelligent, heathen life forms
to catch up to me... :)

MK

[Axel Reichert]

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

> through my experiments playing against the bots, I have shown that
> other/new approaches could work better

If you are referring to our "mutant" discussion: You just found a way
that ends up as a Petersburg paradox and thus makes quantification more
difficult in a real live session, but still possible in an analytical
way. This cube strategy is vastly inferior.

> I can't wait for the day you will liken cube skill, equity, luck,
> MET's, ER/PR, etc. calculations to Ptolemy's epicycles

It is very likely that you cannot. At least I do not suggest to hold
your breath. (-:

> Did I see the words "informal intuitive adjustments"? And to say, no
> less than, their being better than "algos used in an automated botlike
> fashion"?? Wow!

Do not mix things up. Racing double algorithms such as my Isight method
are crutches for mere humans. Every bot uses much better tuned neural
nets that should be close to perfection for races (which can be handled
analytically in a recursive way).

> my beating the bots didn't mean that I was the greatest backgammon
> player on the planet but it just meant that the bots weren't as strong
> as I am

My suggestion is that you do 100 1-point matches against the bot of your
choice and report the results. This will prevent two strategies:

1. Normal checker play, but mutant cube strategy to jack the cube up
and fabricate a Petersburg paradox, which drowns the signal in the
noise.

2. Normal cube strategy, but mutant checker play aiming at ultra-deep
backgames or primes in the opponent's outfield (which the neural
nets have seldomly seen and thus might get wrong) will result in a
similar effect, because then the bot will use a "mutant" cube
strategy.

My prediction is you will get trounced. Good luck!

Axel

P. S.: Both strategies are no argument against the doubling cube. The
first is an argument against beavers. The second in my opinion is not
even an argument for your imagined "AlphaGammon", because I expect that,
left on their own, bots "from scratch" will not see these positions
frequently enough. Rather my guess is that something similar to recent
"physics-based/augmented/guided deep neural networks" is the way to
go. Which calls for (heresy!) hand-coded, hard-wired features ...

[peps...@gmail.com]

On Sunday, April 24, 2022 at 8:53:16 AM UTC+1, Axel Reichert wrote:
... The
> first is an argument against beavers. ...

I have a somewhat idiosyncratic argument against beavers.
If we ignore the rare Kauder paradox positions, a beaver functions (among other things)
as a sharp rebuke of the opponent's play -- "Your double was so inaccurate! It's actually
a beaver!"
Well, that's fine -- nothing wrong with criticism, or holding an opposite opinion to someone.
But then surely the cuber has got the right to defend her own view (if she hasn't changed it).
And she should be able to reply -- "No, it's your beaver that is wrong!"
So it seems that she should be able to raccoon. Therefore I don't think it can be justified
to allow beavers without allowing raccoons (although I'm sure some places do have
beavers-without-raccoons [but I think they're wrong].)
I think the argument can end there. I don't think you can (validly) extend my argument
to say we need to allow otters, x 16 whatever that's called etc. etc.
The argument can finish when both sides have made their point. My point is that once the beaver attack
has been made, the cuber deserves a right of reply.
And, if you accept my argument that you must allow raccoons if you allow beavers (but not everyone
does accept that), then it seems we're allowing a massive escalation of the stakes, beyond what the
players would have been ready for, particularly if we also have automatic doubles.

I've made the point before that I think that beavers-without-allowing-raccoons is wrong.
A possible rebuttal is that "Well, if beavering is wrong, prove it by winning more money!"
But, of course, the randomness in the game doesn't allow such a demo.
The beavered player might have positive equity but you can't necessarily show that in practice.

Paul

[Axel Reichert]

"peps...@gmail.com" <peps...@gmail.com> writes:

> a beaver functions (among other things) as a sharp rebuke of the
> opponent's play -- "Your double was so inaccurate!

Yes. A double allows only the player on roll (who is "on the brink of
the unknown") to raise the stakes, while a beaver allows both players to
"comment" on the same position (in case of further critters, multiple
times).

This is a significant difference (also from a procedural point of view,
the beavering player is not on roll) to a simple take and redoubling on
next turn: Except when neither player could move, the position will be a
different one.

The exception gives me the idea that it could be interesting to think
about an "eternal beaver" position similar to

https://www.bkgm.com/rgb/rgb.cgi?view+366

that might be both a correct double and a correct beaver. Then the
stakes would explode even more rapidly ...

> particularly if we also have automatic doubles.

Just a highly volatile equivalent of multiplying the stakes with
1.25. No need for this.

> The beavered player might have positive equity but you can't
> necessarily show that in practice.

... because of the possibility of a Petersburg paradox. Enough reasons
to get rid of it.

Best regards

Axel

[peps...@gmail.com]

The article you link to is indeed interesting but very well-known.
It shows (or claims to show) the concept of a position without a well-defined equity.
This is very different to the other (more common but still rare) situation where double and beaver
are both correct. That is the Kauder paradox.
In the position you link to, beavering would be a massive mistake -- clearly the player on roll has a big advantage.
The position is problematic in that the stakes are likely to get out of control if players try to maximise their equity.
But there are no beavers in your position.
When I said "The beavered player might have positive equity but you can't necessarily show that in practice.", I meant
to refer to the small-samples problem rather than the St Petersburg paradox. But the St Petersburg paradox might
be another good point.
In other words, unless players agree to play a huge number of games from the same position, just because a cube action
has worked in practice doesn't make it right (as we all know).

Paul

[Timothy Chow]

On 4/24/2022 3:53 AM, Axel Reichert wrote:

> 1. Normal checker play, but mutant cube strategy to jack the cube up
> and fabricate a Petersburg paradox, which drowns the signal in the
> noise.

[...]

> P. S.: Both strategies are no argument against the doubling cube. The
> first is an argument against beavers.

If one is trying to argue that backgammon ought to be a game of skill
rather than a gambling game, then one really doesn't need to work that
hard to argue against beavers. Beavers were pretty clearly invented
by gamblers. They're still disallowed in tournament games.

---
Tim Chow

[Axel Reichert]

"peps...@gmail.com" <peps...@gmail.com> writes:

> The article you link to is indeed interesting but very well-known. It
> shows (or claims to show) the concept of a position without a
> well-defined equity.

[...]

> In the position you link to, beavering would be a massive mistake --
> clearly the player on roll has a big advantage.

I know all this. I was hypothesizing about a position that has similar
properties to the first, but still is a Kauder paradox. But after the
first "Double, Beaver" the Kauder paradox becomes impossible, if I
understand correctly (because the gammons have been "activated"). So no
subsequent "Redouble, Beaver" could be correct anymore.

Forget about the idea, my bad.

Best regards

Axel

[Axel Reichert]

Timothy Chow <tchow...@yahoo.com> writes:

> Beavers were pretty clearly invented by gamblers.

Is there more known about the history?

Best regards

Axel

[Timothy Chow]

On 4/24/2022 9:29 AM, Axel Reichert wrote:
> Timothy Chow <tchow...@yahoo.com> writes:
>
>> Beavers were pretty clearly invented by gamblers.
>
> Is there more known about the history?

Some standard links for the history of the doubling cube are:

http://www.chicagopoint.com/bgdoubling.html
https://bkgm.com/articles/Morawski/30sUnderstandingOfDoubling.html

Neither web page mentions beavers specifically. But asking for
a reference for the claim that beavers were invented by gamblers
is akin to tacking "[citation needed]" on to "Prostitution is one
of the oldest professions."

---
Tim Chow

[Axel Reichert]

Timothy Chow <tchow...@yahoo.com> writes:

> On 4/24/2022 9:29 AM, Axel Reichert wrote:
>> Timothy Chow <tchow...@yahoo.com> writes:
>>
>>> Beavers were pretty clearly invented by gamblers.
>> Is there more known about the history?
>
> Some standard links for the history of the doubling cube are:
>
> http://www.chicagopoint.com/bgdoubling.html

This I have read.

> https://bkgm.com/articles/Morawski/30sUnderstandingOfDoubling.html

This one not, thanks for the pointer. Quite interesting.

> tacking "[citation needed]" on to "Prostitution is one
> of the oldest professions."

(-:

[MK]

On April 24, 2022 at 1:53:16 AM UTC-6, Axel Reichert wrote:

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

>> through my experiments playing against the bots, I have
>> shown that other/new approaches could work better

> If you are referring to our "mutant" discussion: You just
> found a way that ends up as a Petersburg paradox and
> thus makes quantification more difficult in a real live
> session, but still possible in an analytical way. This cube
> strategy is vastly inferior.

You have no justification to make this last ass-ertion. The
"mutant experiment" I had suggested was in an attempt to
simply poke a hole, raise a shadow of doubt in what you
guys dare call "cube skill theory".

I know it's not fair. It's easy to destroy than to construct.
But when what you constructed is a pile of horseshit, the
first step towards correcting it is to destrot it.

I had no intentions of finding a way to make it end up in a
Petersburg paradox. I didn't even know what a Petersburg
paradox was nor even am I sure if I know now nor even if
I give a shit about a Petersburg paradox.

The "Murat murtant" to double at MWC>50% and take at
MWC>0% was just "a" Murat mutant, the minimum I did
settle for just not lose the chance of making you do the
experiment.

Your experiment as I had proposed it, ended after the first
set of real life games. After that it was "smoke and math"
or "maths and mirrors"... You did something completely
different which was in trying to but which failed to take
anything away from the results of that first set of data,
even as it was not statistically meaningful, it poked a
hole in your bullshit "cube skill theory".

>> Did I see the words "informal intuitive adjustments"?
>> And to say, no less than, their being better than "algos
>> used in an automated botlike fashion"?? Wow!

> Do not mix things up. Racing double algorithms such as
> my Isight method are crutches for mere humans.

I wasn't talking about your method. I was talking about
"intuitive" and "botlike" in general...!

>> my beating the bots didn't mean that I was the greatest
>> backgammon player on the planet but it just meant that
>> the bots weren't as strong as I am

> My suggestion is that you do 100 1-point matches against
> the bot of your choice and report the results.

I have already done this many many times over the years.
Have you looked at my backgammon website or youtube
videos?

> 1. Normal checker play, but mutant cube strategy to jack
> the cube up and fabricate a Petersburg paradox, which
> drowns the signal in the noise.

The "Murat mutant" that you used in your experiment is not
Murat! Let's call it "murat-mutant-a". It was a way for me to
make you to prove it to yourself that the "cube skill theory"
is fancyfully elaborate bullshit. You demonstrated that. I
don't give a rat's ass about Petersburg paradox, etc.

> 2. Normal cube strategy, but mutant checker play aiming
> at ultra-deep backgames or primes in the opponent's
> outfield (which the neural nets have seldomly seen and
> thus might get wrong) will result in a similar effect, because
> then the bot will use a "mutant" cube strategy.

I don't need to do any of these because I have already shown
that I can beat the best of the bots consistently by playing
like Murat, without even feeling a need to resort to ultra-deep
backgames, etc. Take a look at my published experiments
before you ask more from me.

> My prediction is you will get trounced. Good luck!

Do you want to bet?

> P. S.: Both strategies are no argument against the doubling
> cube. The first is an argument against beavers.

Beavers, raccoons, rats, bats, etc. are all part of what is called
"cube skill". Are you denying this? Then go ahead and propose
to redefine the rules and the meaning of cube skill, and see
what kind of response you will get from the gamblegammon
community.

> The second in my opinion is not even an argument for your
> imagined "AlphaGammon", because I expect that, left on
> their own, bots "from scratch" will not see these positions
> frequently enough.

What positions are you referring to? I'm referring to positions
as early as after the opening rolls. I predict that alpha-zero
type bg bots will start cubing very early and will never stop
until the games will almost always end up as cubeless games
played out to the end. They will humiliate any current bots or
worl-class gambler humans.

MK

[MK]

On April 24, 2022 at 2:51:08 AM UTC-6, peps...@gmail.com wrote:

> I've made the point before that I think that beavers-
> without-allowing-raccoons is wrong.

Without quoting more from your post (that people can
more read from), I will say that not only I agree with you
on this but I disagree with you about all the critters that
follow raccoons. They should all be allowed. Or, in the
alternative, a mathematical proof needs to offered that
the so-called cube skill stops at raccoons or even before
that at beavers.

In the "Murat mutant" experiment, I'm not sure how Axel
actually handled this. If mutant doubled at MWC>50%
wrongly according the bot and the bot beavers, then the
mutant has the right to argue that it doubled correctly
and since its MWC is still >50%, it should be allowed to
raccoon.

Same goes for mutant beavering at MWC>0% incorrectly
according to the bot but correctly according to the mutant.
Mutant wouldn't mind the bot raccooning its incorrect
beaver... ;)

Come out of your deep denial already folks. Sooner the
better. :)

MK

[MK]

On April 24, 2022 at 4:08:49 AM UTC-6, Axel Reichert wrote:

> ... because of the possibility of a Petersburg paradox.
> Enough reasons to get rid of it.

I agree completely. To hell with beavers, raccoons, and
other mentally ill gambler creatures. Get rid of them all!

MK

[Axel Reichert]

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

> On April 24, 2022 at 1:53:16 AM UTC-6, Axel Reichert wrote:
>

>> [Mutant] cube strategy is vastly inferior.

>
> You have no justification to make this last ass-ertion.

I do, I did the maths. Feel free to point to any errors in my
derivation.

> Your experiment as I had proposed it, ended after the first set of
> real life games. After that it was "smoke and math" or "maths and
> mirrors"...

Which numbers are wrong? In which lines are errors?

> Have you looked at my backgammon website

Yes. It was the starting point of my mutant experiment.

> The "Murat mutant" that you used in your experiment is not Murat!
> Let's call it "murat-mutant-a". It was a way for me to make you to
> prove it to yourself that the "cube skill theory" is fancyfully
> elaborate bullshit. You demonstrated that.

To remind you (quoting here):

By the way, in 10000 games with 1 beaver allowed, double > 0.5 and
take > 0.0 the mutant lost 62117 against gnubg's 84870.

So the session results are pretty clear and thus cannot be misused to
demonstrate your claim. Likewise my math cannot be misused to
demonstrate your claim, because according to you it is "smoke".
However, if you believe so, you should point to any errors in my
derivation. Not understanding the math does not count as argument.

I would rather say that both the session and the math that built upon it
(showing the mutant strategy is expected to lose 0.7 cube-normalized
points per game in the long run against GNU Backgammon) are pretty
strong arguments AGAINST your claim.

> I don't give a rat's ass about Petersburg paradox, etc.

The paradox will just happen and ignore your decision to ignore it.

> Take a look at my published experiments before you ask more from me.

I did so. The money sessions were done with beavers and raccoons, so
suffer from the Petersburg paradox (you bring home a lucky game with
lots of critters and protect your lead from then on). The matches
obviously cannot suffer from the Petersburg paradox, so a different
explanation is needed: In almost all matches (and I checked all your
published 5-point matches, 15-point matches, and 25-point matches) that
you won you were considerably luckier than GNU Backgammon.

Do a 100 games money session without beavers, and do 100 1-point
matches.

Axel

[Axel Reichert]

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

> critters that follow raccoons. They should all be allowed. Or, in the
> alternative, a mathematical proof needs to offered that the so-called
> cube skill stops at raccoons or even before that at beavers.

Done. Doubles: Usually fine. Beyond that: Easily a Petersburg paradox.

> In the "Murat mutant" experiment, I'm not sure how Axel actually
> handled this.

I allowed only beavers, because I just needed a distribution about these
cube actions. The rest was done analytically. Raccoons etc. can for all
practical purposes be catered for by introducing an exponent: 0 = no
beavers, 1 = beavers, 2 = raccoons, etc.

Best regards

Axel

[MK]

On April 30, 2022 at 7:26:58 AM UTC-6, Axel Reichert wrote:

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

>> You have no justification to make this last ass-ertion.

> I do, I did the maths. Feel free to point to any errors in
> my derivation.

Not being a mathematician, I may not be able to do that.
Even if a mathematician couldn't point to any errors in
your calculations, what would that prove? Can you as a
mathematician point to any errors in Ptolemic epicycle
calculations? I hope your answer is "no".

Any inaccuracies in their predictions were discovered
only after observing the facts and then they were further
fine-tuned (by adding more epicycles). That's all you guys
are doing by defending and improving on your fallacious
theories.

>> Your experiment as I had proposed it, ended after the
>> first set of real life games. After that it was "smoke and
>> math" or "maths and mirrors"...

> Which numbers are wrong? In which lines are errors?

You first ran 1,000 games. Then 5,000 without beavers,
3,000 with beavers and 3,000 with raccoons. Later on in
discussion we all kept talking about 10,000 games but I
never understood if that was a subset of the total of the
above numbers of if was a new/different set of games.

When you started the experiment, you admitted that you
didn't really understan Markov chains. Then you went on
to derive 5 billion (or more?) games from that 10,000. Is
there even a point in looking for errors in such a Mickey
Mouse experiment?

>> The "Murat mutant" that you used in your experiment is
>> not Murat! Let's call it "murat-mutant-a".

Or maybe even just "mutant-a" for efficiency from now on.
If we conduct more experiments later with combinations
like doubling at 55% and taking at 5%, doubling at 45% and
taking at 15%, etc. we can call those "mutant-b", "mutant-c",
"mutant-d", etc.

>> It was a way for me to make you to prove it to yourself
>> that the "cube skill theory" is fancyfully elaborate bullshit.
>> You demonstrated that.

> To remind you (quoting here):
> By the way, in 10000 games with 1 beaver allowed, double > 0.5
> and take > 0.0 the mutant lost 62117 against gnubg's 84870.

Okay, so, that's 57% for Gnubg vs 43% for mutant-a. I would
say that this is an incredible for such crude monkey wrench.

One bad thing about your experiment was that you didn't
offer a prediction on the outcome but I won't dwell on this
since I haven't offer one either. Basically, I just wanted to
the experiment and analyse the results later.

I don't know about Gnubg but XG does retroactively calculate
what would have been the predicted win rate based on the
actual error rates accrued at the end of the session. We could
do that with your set of games but you weren't able to provide
even a smaller subset of them.

Any mutant doesn't need to win more than 50% in order to
debunk your "cube skill theory" because, again, a mutant's
goal is not to replace it with another "theory" but just to poke
a hole in it as a first step, to establish a need to run more
experiments. For that, a mutant's winning more than what it
was expected to win, i.e. even a low 20% actual win vs even
a lower 10% expected win, is enough.

It's not to late go back run another 10,000 games and this
time save the games for further analysis. Your script already
exists and as I remember it only took some hours to run it.
In fact, we should run several such set. If you provide your
software, I'll be willing to run them if nobody else volunteers.

> I would rather say that both the session and the math that
> built upon it (showing the mutant strategy is expected to
> lose 0.7 cube-normalized points per game in the long run
> against GNU Backgammon) are pretty strong arguments
> AGAINST your claim.

Can you please clarify what was my claim or how you had
understood it? This is a crudest possible monkey wrench
experiment relatively easy to repeat even more than once.
Your 0.7 points lost by mutant argument is meaningless by
itself, even if we assume that you sampled and/or derived
enough games, because the purpose was to show that the
bot's calculations of cube skill were wrong, i.e. wouldn't be
able to accurately predict an actual win rate by the mutant.

Come on folks, if you still can't understand this, maybe we
should go find more meaningless ways to waste our times.

>> Take a look at my published experiments

> I did so. The money sessions were done with beavers and
> raccoons, so suffer from the Petersburg paradox (you bring
> home a lucky game with lots of critters and protect your
> lead from then on).

In time, I did better overcoming that tendency to try not to
lose what I had gained. But you can do better than that by
excluding 5 games each with the biggest wins for me and
the bot, for example, as a response to your above allegation.
You will see that I will still win way more than expected from
my error rates but just not by as much.

> The matches obviously cannot suffer from the Petersburg
> paradox, so a different explanation is needed: In almost all
> matches (and I checked all your published 5-point matches,
> 15-point matches, and 25-point matches) that you won you
> were considerably luckier than GNU Backgammon.

That's the results of the fallacious luck calculations by the bot.
My errors rates are huge because of all the big PR-sacrificing
moves that I make by not playing like the bot would. Thus, any
dice rolls that the bot would consider lucky for itself, are not
really lucky for me because I don't make the move that makes
the most out of that "lucky roll". So, my calculated luck mostly
goes to waste and I win more by skill than luck. If you people
will insist in being in denial of this, all I end up doing is going
around you in circles... :(

> Do a 100 games money session without beavers, and do
> 100 1-point matches.

What would be the point of this? To reduce lucky high cubes?

I am the one who argues that cube magnifies luck, remember?

MK

[Axel Reichert]

MK <mu...@compuplus.net> writes:
>
> You first ran 1,000 games. Then 5,000 without beavers,
> 3,000 with beavers and 3,000 with raccoons. Later on in
> discussion we all kept talking about 10,000 games but I
> never understood if that was a subset of the total of the
> above numbers of if was a new/different set of games.

O. K., fair point, since I kept adding incrementally to my
session. Overall, I had 10000 games (with beavers, but no raccoons
allowed).

I did some independent short sessions with raccoons, but later found
out two things:

1. They are not needed, since it is trivial to factor them
in. "Mutant-a" doubles above 50 %, so it will kind of automatically
raccoon if beavered.

2. GNU Backgammon has a cube limit of 4096, so allowing raccoons made it
far more likely to have a game violating this limit and thus skew the
results of the session.

So no need to allow raccoons, just assume automatic ones.

> When you started the experiment, you admitted that you didn't really
> understan Markov chains. Then you went on to derive 5 billion (or
> more?) games from that 10,000.

Some people are able to learn. (-:

The Markov chain stuff was just helpful to confirm my gut feeling
about beavers and beyond leading to Petersburg paradoxa. It is not
needed for my (analytical) argument, but it served to turn my head into
the right direction.

That is how research often works. (-:

> Is there even a point in looking for errors in such a Mickey Mouse
> experiment?

"If in doubt or without clue, insult"? Where are your Donald Duck
experiments? I have a to-do list for you at the end of this posting ...

> If we conduct more experiments later with combinations like doubling
> at 55% and taking at 5%, doubling at 45% and taking at 15%, etc. we
> can call those "mutant-b", "mutant-c", "mutant-d", etc.

"We"? Not me, I am happy with the results of my research. Go ahead if
you feel more is needed.

> a mutant's goal is not to replace it with another "theory" but just to
> poke a hole in it as a first step

[...]

> Can you please clarify what was my claim or how you had understood it?
> This is a crudest possible monkey wrench experiment

If you only would know your claim yourself ...

Candidate 1: Cube theory does not matter

Easily disproved by rolling a dice for doubling decisions: 1, 2, 3 =
Double, 4, 5, 6 = Hold. Likewise for taking decisions: 1, 2 = Beaver,
3, 4 = Take, 5, 6 = Pass. If cube skill does not exist, this should
give the same results as GNU Backgammon playing itself. It does not, I
did this, but was of course insulted by you for carrying out this
"meaningless experiment".

Candidate 2: Mutant cube handling is better than the bot's

Disproved by my 10000 games session and my subsequent analytical
work. The latter was necessary due to beavers and beyond yielding a
Petersburg paradox, which does not occur without beavers. Try a long
session with only doubles, but no beavers to convince yourself.

Candidate 3: Mutant checker play is better than the bot's

Disproved by doing 100 1-point matches. Your job (I cannot
algorithmically mimic your brain ...), not mine.

> That's the results of the fallacious luck calculations by the bot.

And here we go in epicycles again ...

>> Do a 100 games money session without beavers, and do
>> 100 1-point matches.
>
> What would be the point of this? To reduce lucky high cubes?

No. The first task serves to reject candidate 2 (no real need to, I did
something equivalent), the second task serves to reject candidat 3.

> I am the one who argues that cube magnifies luck, remember?

Sigh. There is is cube skill, see candidate 1, but there is the
Petersburg paradox with beavers and beyond. So the "skill maximum" is
with doubles only.

Axel

[MK]

On May 1, 2022 at 2:07:51 AM UTC-6, Axel Reichert wrote:

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

> O. K., fair point, since I kept adding incrementally
> to my session. Overall, I had 10000 games (with
> beavers, but no raccoons allowed).
> I did some independent short sessions with
> raccoons, but later found out two things:

> 1. They are not needed, since it is trivial to factor
> them in. "Mutant-a" doubles above 50 %, so it will
> kind of automatically raccoon if beavered.

As I purposefully avoided learning them, I don't know
about cube action points/windows. Here is an honest
question: from what you say, will I be right to understand
that Gnubg will never double with its MVC < 50% and will
also never beaver with its MVC < 50%?

> 2. GNU Backgammon has a cube limit of 4096, so
> allowing raccoons made it far more likely to have a
> game violating this limit and thus skew the results
> of the session.

No. It's you who skewed the results by not allowing!

> So no need to allow raccoons, just assume automatic
> ones.

If your answers to my above questions are both "yes".

>> When you started the experiment, you admitted that you
>> didn't really understan Markov chains. Then you went on
>> to derive 5 billion (or more?) games from that 10,000.

> Some people are able to learn. (-:

Yet, just a couple of weeks ago you made statements
about graphs and Markov chains in a different context
that indicated that you still didn't understand either.

> The Markov chain stuff was just helpful to confirm my gut
> feeling about beavers and beyond leading to Petersburg

> paradox. It is not needed for my (analytical) argument, but

> it served to turn my head into the right direction.

> That is how research often works. (-:

Cube going sky high doesn't mean Petersburg Paradox.

I searched RBG for the words and found that it was only
mentioned once by Wong and once by Zare in 2001, in
referring to the infamous position with both players on
the bar against 5-point boards.

How many times did that happen in your experiment?

Also, you never did (or never said that you did the "sanity
check" suggested by Chow.

>> Is there even a point in looking for errors in such a
>> Mickey Mouse experiment?

> "If in doubt or without clue, insult"? Where are your
> Donald Duck experiments?

I shared quite a few thousands of games on my web
site and on Youtube.

More importantly, I don't need to offer an alternative
experiment in order to find fault with yours. As I said
before, it's easier to destroy than to build. Life isn't fair.

>> If we conduct more experiments later with combinations
>> like doubling at 55% and taking at 5%, doubling at 45%
>> and taking at 15%, etc. we can call those "mutant-b",
>> "mutant-c", "mutant-d", etc.

> "We"? Not me, I am happy with the results of my research.
> Go ahead if you feel more is needed.

Of course, there is always more needed. One problem
with indogtrained believers like you is that you easily
conclude that you know enough to know. :(

For my initial purpose, your results are more than good
enough for me also. Your experiment blew a bazooka
hole in the "cube skill therory" when a bullet hole would
have been enough for me to start with before reaching
for bigger guns. :)

>> Can you please clarify what was my claim or how you
>> had understood it?

> If you only would know your claim yourself ...

I do but regardless, it's more important for you to know
what you have done and why. I'm just checking.

> Candidate 1: Cube theory does not matter

> Easily disproved by rolling a dice for doubling decisions:
> 1, 2, 3 = Double, 4, 5, 6 = Hold. Likewise for taking decisions:
> 1, 2 = Beaver, 3, 4 = Take, 5, 6 = Pass. If cube skill does not
> exist, this should give the same results as GNU Backgammon
> playing itself. It does not, I did this, but was of course insulted
> by you for carrying out this "meaningless experiment".

I can only remember/find your mentioning this (also as
an example of German law) but nothing about what I
had said nor about what was the results of your test?

I loosely say that the cube skill is bullshit without being
specific that I don't mean zero skill because any actual
cube skill (most often towards the ends of games) is just
a fraction of what you guys hype up.

In addition, random cube doesn't need to win more than
50% in order to debunk the so-called "cube skill theory"
which is measured by units of "cube errors", which are
based on equity calculations, which are based on MET's,
which are based of some Jackoff-ski formulas, etc...

Can you tell me what would your gut feeling be about
the total cube error rate that would result from your
above random cube play example...?!

Then we can see if the actual win% through random cube
play is within the margin of error of the predicted win% as
calculated by Gnubg...

> Candidate 2: Mutant cube handling is better than the bot's

> Disproved by my 10000 games session and my subsequent
> analytical work. The latter was necessary due to beavers
> and beyond yielding a Petersburg paradox, which does not
> occur without beavers.

Once more again, once again, again, I never argued that a
"maniac strategy" such as double at MWC > 50% take at
MWC > 0% would beat Gnubg more than 50% of the time.

Actually, your first run was based on doubling at MWC > 50%
take as Gnubg does. You last said that you were still running
the double at MWC > 50% take at MWC > 0% experiment but
I don't think you ever reported the results of that one.

At the risk of hurting your feelings again, I must say that your
experiment was garbage. :( But, if you insist otherwise, I'll be
happy to use your results to benefit my argument. ;)

I don't understand why are you so obsessed with Petersburg
Paradox which doesn't apply here. Are you trying to soften
the fact that you have proven the so-called "cube skill" to be
only partially but not totally bullshit?

Do you think you can tear of a page from a book and call
the rest still good?

I think you deserve the honors of being the one to go tell
Zare et al. that they can take all those pretentious high-math
papers they wrote about beavers, raccoons, etc. and shove
them in their rear pockets! ;)

> Try a long session with only doubles, but no beavers to
> convince yourself.

To convince myself of what? I'm trying to convince you
that the cube skill is almost totally bullshit, including but
not limited to beavers, raccoons, etc.

Even without them, the mutant will win more than Gnubg
will predict it can based on its total error rate. You don't
get this, do you? Or you are in denial in order to not lose
the meaning of your life... :(

> Candidate 3: Mutant checker play is better than the bot's

> Disproved by doing 100 1-point matches. Your job (I
> cannot algorithmically mimic your brain ...), not mine.

What mutant? What checker play? What are you talking
about?

It's true that I argue that if there is continuity in backgammon,
then there must be "strategy" in its real meaning and that
will mean more than only one best/perfect/optimum play
is possible.

But that has nothing to do with what I'm trying to do here,
which is to debunk the "cube skill theory" as bullshit.

> Sigh. There is is cube skill, see candidate 1, but there is
> the Petersburg paradox with beavers and beyond. So the
> "skill maximum" is with doubles only.

All of your 3 "candidates" are strawmen arguments that
you are resort to as damage control...

Contrary to how I may be coming across about it, I really
commend you for having done something that nobody
else dared to or was willing to do. I don't know how long
it will take all of the mentally ill gambler mathematicians
to accept the significance of your results but you are the
one who did it! You deserve my sincere praise.

If you agree to do more experiments with me, not as Tonto
but my pardner, I'll be willing to share a Nobel with you. :)

MK

PS: I will read the entire two main threads about your mutant
experiment and post a summary about what was intended,
what was done, what the results should mean, etc. from my
perspective.

[MK]

On April 30, 2022 at 7:26:58 AM UTC-6, Axel Reichert wrote:

> In almost all matches (and I checked all your published
> 5-point matches, 15-point matches, and 25-point matches) that
> you won you were considerably luckier than GNU Backgammon.

As an afterthought, this reminded me of a very old and
short thread of only two posts; mine and Zare's reply to
it (which may have been the first and only time?:) Here
it is:

https://groups.google.com/g/rec.games.backgammon/c/o4qnefr7XeU/m/oVZ4DeF0rcsJ

This relates to what you are saying about the cube in
match play but in the context of jacking up the cube.

Can you imagine me getting always as lucky as the
bots says while I'm jacking up the cube... ;)

MK

[Timothy Chow]

On 4/30/2022 9:26 AM, Axel Reichert wrote:
> In almost all matches (and I checked all your
> published 5-point matches, 15-point matches, and 25-point matches) that
> you won you were considerably luckier than GNU Backgammon.

This fact by itself doesn't mean much. Take any single match between
any players, and with high probability the winner will also have
the higher luck rating.

I recall that someone took a bunch of Murat's money games and calculated
the total luck over all games of both players, and the luck was about
the same for both players.

One could do the same calculation for his matches, but to be meaningful,
the luck would have to be measured in terms of MWC rather than EMG.

---
Tim Chow

[peps...@gmail.com]

I once beat XG in a match where XG was luckier according to EMG.
I couldn't understand how I beat XG while being unlucky until Stick explained it to me
when I set up a thread here.
Stick stuck to the point at hand, without using my confusion as a stick to beat me with.

Paul

[Axel Reichert]

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

> On May 1, 2022 at 2:07:51 AM UTC-6, Axel Reichert wrote:
>
> will I be right to understand that Gnubg will never double with its
> MVC < 50% and will also never beaver with its MVC < 50%?

As a crude first approximation, yes.

>> 2. GNU Backgammon has a cube limit of 4096, so
>> allowing raccoons made it far more likely to have a
>> game violating this limit and thus skew the results
>> of the session.
>
> No. It's you who skewed the results by not allowing!

No, but to understand that, you would need to accept or learn some math,
and I am pessimistic of you doing either. (-:

> Cube going sky high doesn't mean Petersburg Paradox.

True, it is a necessary, but not sufficient condition. But I checked the
sufficient one (divergent geometrical series) and showed it holds true
when beavers are allowed and a mutant cube strategy is used.

> Do you think you can tear of a page from a book and call
> the rest still good?

Yes, roughly.

>> Candidate 3: Mutant checker play is better than the bot's
>>
>> Disproved by doing 100 1-point matches. Your job (I
>> cannot algorithmically mimic your brain ...), not mine.
>
> What mutant? What checker play? What are you talking
> about?

I ask YOU to do this: Play 100 matches to 1 point and report the
results. This will eliminate candidate 3.

Axel

[MK]

On May 8, 2022 at 8:10:36 AM UTC-6, Axel Reichert wrote:

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

>> will I be right to understand that Gnubg will never double with
>> its MVC < 50% and will also never beaver with its MVC < 50%?

> As a crude first approximation, yes.

This is not a good enough answer. Actually it's a bad/wrong
answer because we already know that half of the answer is
"no". When mutant doubles at MWC > 50%, Gnubg's MWC
is < 50% yet it beavers! In fact, apparently a correct beaver
can be at as low as MWC 20%. You are flunking very badly. :(

I don't know the answer to the second part of the question
and I was hoping that you or some other cube experts would
give a more "mathematical" answer. If/when Gnubg doubles
at MWC < 50%, with its MWC being > 50% the mutant would
also beaver, which is against your assumption. Furthermore,
then you would need to answer if Gnubg would raccoon?!

Frankly, I'm disppointed that your thinking isn't deep enough. :(

>>> 2. GNU Backgammon has a cube limit of 4096, so allowing
>>> raccoons made it far more likely to have a game violating
>>> this limit and thus skew the results of the session.

>> No. It's you who skewed the results by not allowing!

> No, but to understand that, you would need to accept or
> learn some math, and I am pessimistic of you doing either. (-:

"A game violating the 4096 limit" is a nonsensical expression.
I understand that when the limit is reached, the cube is "stuck"
so to speak, but in a long enough session it will apply to both
players equally. Not allowing raccons just because if this was
wrong and defeated the purpose of your experiment beyond
simply skewing it.

>> Cube going sky high doesn't mean Petersburg Paradox.

> True, it is a necessary, but not sufficient condition.

Your accepting this is great progress. Now you need to go
back and reword your statements without using the words
Petersburg Paradox, in plain language so that everyone can
understand it. Would you please do this?

> But I checked the sufficient one (divergent geometrical series)
> and showed it holds true when beavers are allowed and a
> mutant cube strategy is used.

You just negated what you said in your previous sentence. I
never expected that this would be a quick and simple process.
I understand that self-deception kicks in to protect you from
the potential trauma of losing half the meaning of your life by
accepting the reality of the cube skill being bullshit...

>> Do you think you can tear of a page from a book and call
>> the rest still good?

> Yes, roughly.

Another evasive answer. It may not be true even if the tore one
page in a several hundred pages long book but the book of the
"cube skill theory" sureli isn't that long. What? Three pages? Or
four, five? You tore a bing chunk of it.

Now it's time to retract those "mathematical papers" about the
beavers, raccoons, etc. and tear out those pages from all of the
books published by gamblegammon giants, and then publish
corrections/amendments to the remaining contents of them.

>>> Candidate 3: Mutant checker play is better than the bot's
>>> Disproved by doing 100 1-point matches. Your job (I
>>> cannot algorithmically mimic your brain ...), not mine.

>> What mutant? What checker play? What are you talking
>> about?

> I ask YOU to do this: Play 100 matches to 1 point and report
> the results. This will eliminate candidate 3.

But I never made such a claim. The closest I may have come
such a claim could be my saying that some lack of cube skill
can be overcome/compensated by better checker play. But
even so, the experiment would need to include cube skill also.

Plus, we don't have a checker play mutant. You can't make me
play to prove anything, especially when I can't even play 100%
consistently like a mutant bot could. Now, you can propose
that we create a "Murat checker only bot" instead of a "Gnubg
checker only mutant" but I have no idea how could we ever do
that...??

No matter, such an experiment would have no value at all in a
debate about whether the "cube skill theory" is bullshit or not.

I see that we both do (but I think more often you) respond to
arguments selectively but I'm not going to make you wrong
for that. It may be just how discussions narrow down to an
end but I think we both need to (at least I will try) summarize
these "mutant experiment" threads by revisiting important
details that we may have dropped along the way.

MK

[Axel Reichert]

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

[lots of vague/irrelevant stuff]

There is no value for me in continuing a fruitless discussion. In case
an interesting idea from you comes up, I will happily (and perhaps even
gratefully) pick it up, but otherwise spend my time in genuine research
rather than sophistry.

Good luck.

Axel

[MK]

On May 9, 2022 at 4:32:18 AM UTC-6, Axel Reichert wrote:

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

> [lots of vague/irrelevant stuff]

I feel your pain... :(

> There is no value for me in continuing a fruitless discussion.

I diagree. It bore fruit alright but you didn't like the taste
and couldn't digest. I see more fruit on the tree waiting
to ripen yet... ;)

> In case an interesting idea from you comes up, I will happily
> (and perhaps even gratefully) pick it up, but otherwise spend
> my time in genuine research rather than sophistry.

Your reaction is unfortunate. Considering everything, we
were doing well. These were perhaps the longest running
(five and a half months to date) threads in RGB history...

The subject/s were more than just interesting, they were
indeed absorbing. You helped me open a Pandora's box.
What you found in there was not what you expected but
so much the better and I assure you that there lots more
in there to "discover".

I don't think your mind will find peace until you ask and
answer all questions that did/will cross your mind about
this subject. I think/hope you will not surrender yet.

MK