Okay folks, I think I have a properly working script
for a mutant that randomly doubles and/or takes but
never drops, against Noo-BG World-Class cube skill,
with both sides set to World-Class checker skill.

It can recycle the 4,096 cube limit multiple times
In my first session of 100 games the cube got as
high as 2^34 = 17,179,869,184

I will share my script and preliminary results with
you all, as soon as I get some guesses from you guys
about what percentage of the games the mutant will
win and how many points each side will win, after a
long enough session that you may deem as significant.

It runs really fast. It took me about 15 minutes to
run 100 games with a total of 5,788 moves, with the
longest game lasting 133 moves. So, we can expect to
run 10,000 games in about 24 hours.

I did go out of my way to document it with lots of
comments to make easier for anyone to run it as is
or to modify it to run their own experiments, even
people who may be just learning coding in general
and specifically in Python.

So, let me hear your predictions. Don't be shy now. ;)

MK

On 1/27/2024 7:06 PM, MK wrote:

> So, let me hear your predictions. Don't be shy now. ;)

Don't you guys feel bad here. They don't know in the
Noo-BG group either. ;) :(

Since I posted the above, I really got into improving my
scripts and coming up with more mutant experiment ideas.

Currently I'm running five different scripts, with some
done and some still going. Then I'll do yet two or three
more different ones.

Below is what I just posted to Noo-BG group about a new
experiment based on an old idea of mine.

I wonder if the resident math PHD's of RGB will be able
to better answer the questions at the bottom?

MK

I'm chugging along with my mutant cube skill experiments
as I can spare time, saving all games, which I will share
on my web site, when I'm done, along with my scripts.

While doing the double at > 50% experiment, I remembered
an old question I had asked in RGB about a year ago: What
if the winner of the opening roll is allowed pre-double?

See thread:
https://groups.google.com/g/rec.games.backgammon/c/BVEnaqGM6dg/m/2c685q4DAAAJ

When you evaluate the opening position in GnuBG, this is
what you get:

=========================================================
Position ID: 4HPwATDgc/ABMA
Match ID: cAkAAAAAAAAA

Evaluator: Contact
Win W(g) W(bg) L(g) L(bg) Equity Cubeful
static: 52.1 15.4 0.8 13.0 0.8 +0.067 +0.084
1 ply: 52.7 14.8 0.9 12.9 0.5 +0.076 +0.098
2 ply: 52.5 14.9 0.7 12.5 0.5 +0.076 +0.099

Cube analysis
2-ply cubeless equity +0.076
52.5 14.9 0.7 - 47.5 12.5 0.5
Cubeful equities:
1. No double +0.099
2. Double, pass +1.000 (+0.901)
3. Double, take -0.171 (-0.270)
Proper cube action: No double, take (23.0%)
=========================================================

I have created a Python script to intervene if the human
player wins the opening roll, to set the cube at 2 owned
by the bot, and then to execute "end game" command, for
the bot to play for both sides at the same checker and
cube skill settings.

So, you know the equity gained by winning the opening
roll and the equity lost by making the cube error at
the same time, before the first move. Can anyone tell
me what I will be expecting to see after, let's say,
10,000 games, in terms of which side will win/lose by
what percentage?

BTW: I already know. ;) I'm asking to see how confident
are you in GnuBG's equity and/or error calculations and
how competent are you to make mathematical predictions?

MK

MK <playbg-rgb@yahoo.com> writes:

> I have a properly working script for a mutant that randomly doubles
> and/or takes but never drops, against Noo-BG World-Class cube skill,
> with both sides set to World-Class checker skill.

Good!

> It can recycle the 4,096 cube limit multiple times In my first session
> of 100 games the cube got as high as 2^34 = 17,179,869,184

Welcome to St. Petersburg! I assume that you also allowed beavers,
possibly unlimited?

> guesses from you guys about what percentage of the games the mutant
> will win and how many points each side will win

The percentage will be below 50 %, probably below 40 %. The points won
will be essentially large random numbers due to the Petersburg
paradox. And also this will not stabilize if you run longer sessions,
but only get worse.

Axel

On 2/8/2024 1:38 AM, Axel Reichert wrote:

> MK <playbg-rgb@yahoo.com> writes:

>> ... mutant that randomly doubles and/or takes but never drops,

>> It can recycle the 4,096 cube limit multiple times In my first
>> session of 100 games the cube got as high as 2^34 = 17,179,869,184

> Welcome to St. Petersburg! I assume that you also allowed beavers,
> possibly unlimited?

Only 2 consecutive beavers, (Noo-BG default setting), but with
cube recycling beyond the 4096 limit and games lasting longer
due to mutant not dropping, beaver-raccoon sequences happened
enough time to end up in Petropavlovsk, Kamchatskly... :)

>> guesses from you guys about what percentage of the games the
>> mutant will win and how many points each side will win

> The percentage will be below 50 %, probably below 40 %.

If you are talking about the number of games won/lost, I didn't
count since that doesn't matter at all in money games, where the
object is to win more points (money) than games, by demonstrating
better "cube skill".

>> The points won will be essentially large random numbers due to
>> the Petersburg paradox.

The equities aren't undefined, if that's what you are getting at,
but humanly incomprehensible because of astronomical cube values.

When I posted about this in Noo-BG group, I was told I may need
to run hundreds of thousand or even a million games, in order to
get meaningful results but now I'm thinking if ten million will
be enough.

I run my experiments in chunks of 1,000 games so that I can save
them in reasonable sgf file sizes. For this experiment, I ran
30,000 games with mutant winning 549,877,108,651 against bot's
55,937,020,736, i.e. 90.7666365% in one batch and 80,937,311
against bot's 18,014,435,569,901,100, i.e. 0.0000004%

This is not an experiment I originally intended to do bot done
anyway just out of curiosity. Mutant winning as little as 2-3%
would help my argument but there is no practical way to finish
this experiment. I'm a potato counter. I don't trust math and
mirrors extrapolations. Thus, I will abandon this experiment
and won't spend anymore time on it.

It was fun and interesting to see how high the cube could go in
a single game if it wasn't arbitrarily limited at 1,024 or 4,096.

>> And also this will not stabilize if you run longer sessions,
>> but only get worse.

I don't agree but maybe I don't understand what you mean? I'd
argue that it will eventually stabilize but I have no idea of
how long of a session may be needed for that to happen.

I'm continuing with my other experiments and truly enjoying the
process. In fact, while doing the ones I originally wanted to
do, I came up with new ideas and have been squeezing them in
as well. Stay tuned. I think we all will learn from them...

MK