Hi Ian,

On the one hand, since nobody else in this forum negates, nor
even adds anything to support your arguments, I feel that I'm
debating with a spokesperson for the group, but on the other
hand I feel that our ideas don't attain their full potential.

With this thread having become too long and more about mutant
cube strategies than value of cube ownership, I will take the
opportunity to start a new thread responding to your last post,
not only here in bug-gnubg but also in rec.games.backgammon and
bgonline.org forums where you had posted in the past, for the
sake of creating more interest on the subject and hoping that
you will participate in those forums also.

-------------------------------------------------------------
*From:* MK <playbg-rgb@yahoo.com>
*Sent:* Wednesday, April 3, 2024 10:29:11 pm
*To:* Ian Shaw <Ian.Shaw@riverauto.co.uk>; GnuBg Bug <bug-gnubg@gnu.org> *Subject:* Re: Interesting question/experiment about value of cube ownership

On 4/2/2024 7:08 AM, Ian Shaw wrote:

A cube strategy against a bot that never passes:

Not never but we loosely say that since it takes at GWC > 0,
i.e. even at 0.0001%

only double when (a) you are 100% to win

I don't understand why you wouldn't double at 99%? Can you
explain this?

(b) it's the last roll of the game and you have an advantage.

Yes, this is very bad for the mutant and already happens now.

So the take point is 16.7%. Gammons complicate it, but I'm
sure you get the idea.

If you can clearly define your strategy, I would be glad to
create a script to run the experiment to see what will happen.

BTW: you are still avoiding the issue of how much the mutant
will win compared to what it would be expected to win based on
its total "cube error rate".

What win rate would you say a mutant that takes at GWC > 0.0001
even on the last roll, (which must be the biggest possible cube
error), will achieve? Any guesses by anyone..?

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

On 4/4/2024 12:01 AM, Ian Shaw wrote:

MK: I don't understand why YOU wouldn't double at 99%? Can you
explain this?

If the oppenent will still take at 100% then why risk losing 2
points 1% of the time?

I thought I answered your question about win rates previously.

A bot that always doubles, I'd expect to lose 0.3 ppg. It's
hard to search back on my phone app, so maybe that's incorrect.)

A bot that doubles immediately it's ahead, I'd expect to lose
about half that.

Those values assume the bot plays as well as gnubg for the
remainder of the game. If the opponent will make further cube
errors, then it should be a little bit more.

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

To clarify again, the mutant drops at GWC = 0% but takes at > 0%,
i.e. at 0.0001%. And you are right to assume that aside from the
above mentioned exceptions, both sides play normally at 2-ply.

I think we are miscommunicating about the mutant's "expected, i.e.
relative, win rate based on its total cube error performance rate"
but we can skip that for now and come back to it later since the
results of the experiments won't be going anywhere.

With that said, I'm elated to hear that:

1) You acknowledged that the bot becomes inadequate against even a
most primitive mutant cube strategy, (hopefully we will discuss my
more elaborate ones later also), and is obligated to adjust its
"cube skill theory",

2) You switched to a strategy of minimizing your losings instead
of maximizing your winnings, which is the exact opposite of what
the "cube skill theory" is supposed to promote

You haven't formulated a simple strategy that I could use in a
script but I decided to go ahead and run an experiment excluding
your doubling at < 100% in "last roll positions".

I searched the internet about ways to discern last roll positions
but couldn't find anything. If you can offer any suggestions, I'll
be happy to run experiments including those also.

While editing my script, I realized that I should not make your
strategy double when too good and added that in. But, since I was
using common cube routines for both players, my mutant also started
to not double when too good, which wasn't in its initial strategy.

After 1,000 games mutant won 1,411 points (56.66%) vs bot's 1,079.

You may say 1,000 games are hardly enough but I consider it enough
to get an initial impression, since there was almost no fluctuation
with the cube never going past 2, with the mutant almost always
reaching GWC > 50% and doubling early in the game and your bot never
doubling at GWC < 100%, at which the mutant dropped. There were also
a few 1-point wins.

I had read that "last roll positions" are rare but I don't have any
idea about actually how rare they are. Even so, it's possible that
they could significantly change the outcome because the mutant would
take even at 0.0001%.

After the first run, I wondered what would happen if both players
doubled even when too good and I ran that experiment also.

After 1,000 games mutant won 1,321 points (59.83%) vs bot's 887.

This is what triggered this thread's title. Could it be that, as BG
may be played on a different planet, doubling too good may be better?

Then I wondered what if your bot didn't but my mutant did double even
when too good and ran that experiment too.

After 1,000 games mutant won 1,323 points (53.28%) vs bot's 1,160.

Hmmm. Maybe two birds in the bush are indeed better than one in the hand?

Lastly, I had to run one more experiment: the reverse of the last one.

After 1,000 games mutant won 1,359 points (61.58%) vs bot's 848.

Yup. Two birds in the bush indeed seem to be better than one in the hand.

With this finding, I think I will run a variant of my "experiment 9",
with the mutant not doubling when too good and see if and/or by how
much better it will do against GnuBG's unmodified 2-ply cube skill.

What is more important for me here though is that my primitive mutant
strategy consistently won considerably more than your bot's modified
cube strategy, with so little fluctuations that I consider 4 x 1,000
trials persuasive enough that by my mutant cube strategies I destroyed
the so-called and so much hyped/dogmatized "cube skill theory".

If you think that including "last roll positions" would reverse these
results and if you can suggest a way to code it into the script, I'll
be glad to run those experiments also. But keep in mind that I can
also tweak my mutant to not take at MWC = 0.0001% in those positions.

MK

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