> 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
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
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
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. :)
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