INTRODUCTION:

The main purpose of these experiments is to "deform the cube skill dogmatism" by
poking holes in the "mythematically proven", so-called "cube skill theory"; but not
without any willingness on my part to discover, accept and learn from unexpected
empirical observations resulting from them.

Not all experiments involve "mutant cube strategies". You may find some of them
more interesting than others. Their brief descriptions below are to help you select
the ones that you may want to explore and/or replicate for yourselves.

Each experiment is further described and commented in its "abstract" file, without
repeating any of my previous arguments on the subject, made in past discussions
on rec.games.backgammon, bug-gnubg or on other forums. Similarly, any further
discussions related to my experiments or other related topics  should be done on
backgammon related public forums; and not by private correspondance with me.

I did go out of my way to document almost every line in my Python scripts in order
to make it easier for everyone to understand what they do and/or to modify them
for running their own experiments, especially for people who may be just learning
coding in computer languages in general and more specifically in Python.

All Python scripts and other content on this web page are copyrighted © 2024 by
Murat Kalinyaprak and shared under the terms of the GNU General Public License.

Unlike bot rollouts with maximum cube limits, in my experiments 9 through 13 the
scripts can recycle the cube value past the 4,096 limit multiple times, which makes
them valuable tools.

I ran my experiments in sessions of 1,000 games so that I could save them in SGF
files of manageable sizes that can be opened in a few minutes. Even though the
compressed archives are only 175-350Mb, they are not available for downloading
from this web page. Ask me for direct links if you really want them for a good use.

The various log files contain a lot more stats than what I tabulated and analysed in
my "results" spreadsheets. They are also compressed into archive files that are ony
around 75-150Kb each. You may want to download some of them to do your own,
more extensive analyses. Their contents are documented in the Python scripts.

FILES YOU CAN DOWNLOAD:

 Abstract: brief description of experiment and some comments about results.
 Python script: almost every line is documented to help others make use of it.
 Stats logs: various games and points stats, in batches of 1,000 games per line.
 Games logs: various stats for individual games, in sets of 1,000 games per file.
 Saved games: .ZIP archives for sessions of 1,000 games each, in .SGF format. 
 Results: .PDF file of tabulated stats, in groups of 10,000 games, 1,000 per line.
.

EXPERIMENT 1:

Not about mutant strategy. It was done as calibrating test to ensure that my Python
script for cubeless 2-ply auto-play worked properly and produced expected results.

EXPERIMENT 2:

Not about mutant strategy. It was done to check if the player who wins the opening
roll gains a 0.0393 ppg advantage as claimed in the summary section of web page at:
https://bkgm.com/openings/rollouts.html

EXPERIMENT 3:

Not about mutant  strategy. It was done as calibrating test to ensure that my Python
script for cubeful 2-ply auto-play worked properly and produced expected results.

EXPERIMENT 4:

Not about mutant strategy. It was done to see how much of an advantage is gained
by winning the opening roll in cubeful games.

EXPERIMENT 5:

Not about mutant strategy. It was done to contrast the cost of the opponent owning
the cube against the advantage gained by winning the opening roll in cubeful games.

EXPERIMENT 6:

Not about mutant strategy. It was done to see what would happen if the player who
wins the opening roll is simultaneously made to also own the cube in cubeful games.

EXPERIMENT 7:

Not about mutant strategy. It was done to better isolate the value of cube ownership
by making the opponent own the cube at the very beginning of all cubeful games.

EXPERIMENT 8:

Not about mutant strategy. It was done to cross-validate the previous experiment by
making the mutant always win opening rolls and own the cube in all cubeful games.

EXPERIMENT 9:

This is the first real "mutant cube strategy experiment". It's very crude and just one
notch above random cube decisions, i.e. no cube skill at all. Mutant doubles, beavers
or raccoons if its GWC is > 50%, takes if its GWC is > 0% and drops otherwise.

EXPERIMENT 10:

This is a variant of the previous experiment 9. In this one, mutant doubles if it wins
the opening roll also since that gives it a GWC > 50% as well.

EXPERIMENT 11:

This is the most telling "mutant cube strategy experiment" of them all, pitting the
much hyped and dogmatized "cube skill theory" against my "fartoffski formula"
which is based on, seemingly arbirary yet studiously selected, game stage intervals
and doubling/taking points as explained in the experiment abstract. The results are
far beyond what I could have ever expected.

EXPERIMENT 12:

This is a variant of the previous experiment 11 with 5% added to double/take points.
The difference that this small adjustment made is stunning. Total cube decisions and
points per games were reduced incredibly. Mutant came within ± 2.49% of winning
50%, i.e. being as good as GnuBG 2-ply. With this, I consider that I have more than
achieved my goal of "deforming the cube skill dogmatism".

Experiment 13:

I actually started my experiments with this one, wanting to establish a base line for
no cube skill at all by making mutant randomly double/beave/raccoon, randomly
take and never drop. After seing the cube go to 2^54, i.e. 18,014,398,509,481,984,
by the 14,417th game, I realized that I would need to run millions of trials and so,
I abandoned the experiment after 30,000 games. It was fun and interesting to see
how high the cube can go in one game, if not arbitrarily limited to 1,024 or 4,096.

EXPERIMENT 14-a:

This is a more elaborate version of the Experiment 12 with more conservative take
points and newly added beaver points and a too-good point. In addition, this time
the mutant played against GnuBG 3-ply cube skill instead of 2-ply as in all previous
experiments but astonishingly the results are almost the same as Experiment 12.

EXPERIMENT 14-b:

While Experiment 14-a was running, I wondered how the same mutant would do
against GnuBG 4-ply cube skill and started a session of 1,000 games on my other
computer. The intervals for five stages of game, double points, take points, beaver
points and the too good point are all the same as in Experiment 14-a. Again, quite
astonishingly the mutant fared even better against GnuBG 4-ply. I only ran 1,000
games because even that many trials took more than four days on my older spare
computer. Yet, I think it's enough to give an idea considering the minimal amount
luck fluctuations. But, please don't take my word for anything. Run as many trials
as it would take to convince yourselves. After all, that's why I'm sharing my scripts.

EXPERIMENT 14-c:

After Experiments 14-a and 14-b, I noticed that there was almost a "glass ceiling"
at 47.50% that none of my mutant strategies had been able to surpass. I decided
to try some more tweak and ran 10,000 games with very conservative double and
beaver points. I also increased the too-good point to GWC > 0.85 which produced
slightly better results. Then I ran 10,000 more games with double points reverted
and more spread out beaver points. I set the too-good point higher at GWC > 0.9
but none of my tweaks produced in any noticeable changes in results, neither for
the better nor for the worse, which I found rather puzzling.

EXPERIMENT 14-d:

I wanted to see if my tweaked mutant would now perform better against GnuBG
2-ply in 20,000 games. The results weren't any better than against GnuBG 3-ply
nor even against GnuBG 4-ply. In fact, the results of my last six experiments were
all within less than 2% of each other, even though their formulae and/or their bot
opponent cube skill levels were quite different. This observation led me to run the
next Experiment 15 by making GnuBG 2-ply cube skill play against GnuBG 3-ply
cube skill to see if indeed there wasn't easily detectable skill differences between
various cube decision ply levels in GbuBG.

EXPERIMENT 15:

After 20,000 games played as described at the end of Experiment 14-d, GnuBG
3-ply cube won 23,426 points (50.26%) vs. GnuBG 2-ply cube's 23,179 points
(49.74%), with checker play set to 2-ply for both sides. Only 0.52% difference
between 2-ply cube and 3-ply cube after 20,000 games? Really??

I am sure you guys can interpret these stats better than I can but to me it looks
like GnuBG is cheating against itself... ;)

This will probably be my last experiment for now. With my new computer 5 times
faster than my old one, I may just run more trials for some previous experiments
in order to get more accurate results, at least until I may come up with new ideas
for more experiments. Let me know if you come up with any suggestions.

CONCLUSIONS:

Since none of the gamblegammon bots that ever existed had been trained through
cubeful and/or "matchful", (a term I coined), self-play, I have been arguing since the
days of Jellyfish and Snowie that cubeful equities (extrapolated using formulas) and
matchful equities (extrapolated using tables) were inaccurate of unknown amounts;
and I kept suggesting that empirical evidence from double-blind tests were needed.

After doing my own experiments of long sessions of money games against GnuBG
and XG at their strongest skill level, I have become even more convinced and began
to propose specific bot-vs-bot experiments (for consistentcy in repeated decisions),
for testing various "mutant cube strategies" against the established cube strategy.

Initially, I would have been happy to just demonstrate that "mutant cube strategies"
could win more than what would be expexted from their cube error rates. I believe
that this became obvious even through the few half-baked experiments that others
have done but nobody would and/or could talk about it. Instead, everyone focused
on whether any mutant cube strategies could win more than 50%, which obviously
wasn't possible especially considering how crude, (almost random), those were.

In the end, I decided to do my own experiments and just put the results out there,
along with my scripts, so that if others didn't trust my results, they could run their
own experiments. To my delight, the results of my Experiments 9 and 10, and then
even more the results of my Experiments 11 and 12 actually came much closer to
winning 50% than I could have ever imagined possible. Then my experiments 14-a,
14-b, 14-c and 14-d have conclusively shown my revised mutant strategies to be as
good as GnuBG 4-ply cube within an acceptable margin of error.

Based on those results, there is no doubt that my mutant cube strategies will win
disproportionately more than what would be expected from their cube error rates,
thus even more decisively prove that the overly hyped and dogmatized "cube skill
theory" is just a pile of horse-muffins indeed; even if no addicted gamblegammon
players admit it. Perhaps "time" will help you all reconcile with the bitter reality...