Murat's "Tractatus de cubus arte" based on his "simplex flatus formulae"

[Murat K]

I thought pluralizing formula in Latin instead of Greek ;) could earn me
a tad more respect from the circle of real scientists and mathematicians
but why stop there, right...?

To get an introduction to how the idea for my "mutant cube strategy"
experiments came about, please first read this article from last January
in Google's rec.games.backgammon archive:

"Another Murat mutant cube skill experiment based on game stages"

https://groups.google.com/g/rec.games.backgammon/c/uCmiIHgDfac/m/v0Ffw0tYAAAJ

As I had said that I may do, I spent a few hours to learn Python scripting
and have been sharing the results of many experiments over the past months,
along with my scripts so that you can replicate my experiments and/or modify
them to run similar experiments of your own.

Although I had completed the last four of my experiments based on "game
stages" almost two months ago, I couldn't make time to finish updating my
web site with their results until today and I will post my summarizing
interpretation of them in a few days. But before that, I thought I would
thoroughly explain my mutant strategy formulae so that you all can better
understand the implications of those results.

Since there was no way for others to replicate my personal human-vs-bots
experimental sessions from many years ago, (which you can still see on my
web site), I thought about formulating a simple enough mutant strategy that
could be scripted to run mutant-vs-bot experiments using the GnuBG CLI.

Since my human cube strategy was based on "how much play still left in the
game", (i.e. aggressively in early stages and cautiously in late stages of
the game), the mutant would also need to play similarly. But how would the
mutant script know "how much play still left in the game"?

I came up with the idea of dividing the game into 5 stages: opening, early,
middle, late and ending; with each stage arbitrarily assigned my fartoffski
double and take points.

I envisaged that opening and ending stages would be the shortest. Early and
late stages would be longer, perhaps 2x. Middle stage would be longest, 3x.

As I had explained in the above linked article, I picked 54 as the average
rolls in a game. By coincidence, it was perfect for my purpose since it was
evenly divisible by 9. Thus, opening and ending stages would be short = 6
rolls each, (1 thru 6) and (49 thru 54). Early and late stages would be 2x
longer = 12 rolls each, (7 thru 18) and (37 thru 48). Middle stage would be
3x longest = 18 rolls, (19 thru 36).

It looks like this |------|------------|------------------|------------|------|

Since the crudest mutant cube strategy previously run by Axel doubled at MWC
>=50% and took at MWC >0%, I decided to adopt those for the most aggressive
double and take points during the opening stage. Then they would go up by 5%
during the early, middle, late and ending stages

The early version of my fartoffski formulae used in my first experiment was:

cube points = >50%, >55%, >60%, >65%, >70%
take points = >0%, >5%, >10%, >15%, >20%

The script would keep count of rolls to determine the current game stage and
would make the corresponding mutant cube decisions based on the MWC alone.

In my second experiment, I revised the numbers by 5% more conservatively as:

cube points = >55%, >60%, >65%, >70%, >75%
take points = >5%, >10%, >15%, >20%, >25%

In my latest four experiments, I improved the mutant strategy by revising the
take points to be another 10% more conservative, making it to beaver at MWC's
different than take points (2% increments) and not double when too good, as:

beaver points = >39%, >41%, >43%, >44%, >47%
too-good point = >80%

Since the jackoffski formulae had been revised (and retrofitted??) over time, I
thought I could indulge in doing the same for my fartoffski formulae and I did
experiment with different sets of beaver points like >42%, >44%, >46%, >48%, 
>50%
and >53%, >56%, >59%, >62%, >65% (3% increments) and >30%, >35%, >40%, >45%, 
>50%
(5% increments). Although the most conservative numbers seemed to produce the 
best
results, the differences were not all that decisive.

Similarly, I experimented with too-good points of >85% and >90%. Although the 
>85%
seemed to give the best results, again the differences were not all that 
decisive.

What was decisive however, is that at least in money games my fartoffski 
"simplex
flatus formulae" performed as good as the jackoffski "contortiplicatus nugacitas
formulae" against GnuBG 2-ply, 3-ply and even 4-ply within the margin of error. 
For
actual results of all my mutant cube skill experiments, please visit my web 
site:

https://www.montanaonline.net/backgammon/

In final summary, the entirety of my arbitrarily invented mutant cube skill 
formulas
consist of this:

game stages    = opening, early, middle, late, ending
roll ranges    = 1-6, 7-18, 19-36, 37-48, 49-54
cube points    = >55%, >60%, >65%, >70%, >75%
take points    = >15%, >20%, >25%, >30%, >35%
beaver points    = >39%, >41%, >43%, >44%, >47%
too-good point    = >80%

My next experiments may be to see how well my utterly simple mutant strategy 
does
in match play against bots without complicated adjustments for match scores, 
etc.

If you don't want to wait for me to do it, feel free to modify one of my scripts
to do your own experiments.

MK