Re: Interesting question/experiment about value of cube ownership

[Bug reports for and general discussion about GNU Backgammon.]

If the mutant strategy is always to take, then gnubg GAINS when Mutant takes a 
D/P because that increases the points GnuBg wins.


Currently, gnubg is assuming it is playing against a player using it's own cube 
strategy. It could be reprogrammed to take advantage of knowing that it's 
opponent would never pass.


From: MK 
Sent: Friday, March 29, 2024 2:28:09 AM
To: Ian Shaw ; GnuBg Bug 
Subject: Re: Interesting question/experiment about value of cube ownership

On 3/19/2024 3:54 AM, Ian Shaw wrote:

> MK "Those numbers are based on how the bot would play against itself.
> If you accept the bot's decisions as best/perfect and if you try to
> play just like bot, assuming that your opponent will also try to play
> just like the bot, of course you wouldn't/shouldn't double."

> Agreed. Against a worse player, you can take with fewer winning chances.
> If your opponent will give up enough equity in errors to overcome the
> error of the bad take (and your own subsequent errors), then you should
> still come out ahead.

I hope you are realizing that you are agreeing with the bot, not with me.
What you quoted from me above was in response to your previously saying:

"I wouldn’t double.  As shown by the rollouts, I'd be giving
"up 0.36 points per game, on average. Even if I knew you would
"roll 66, I would still take, because the equity of -0.276 * 2
"is still better than giving up a whole 1.000 point.

Would you drop if you knew that the mutant would roll 77? You wouldn't.
(Just exaggerating to make a point, while reminiscing how Jellyfish was
not only rolling 77's but shamelessly playing them to escape 6-primes:)

Once the mutant conditionally pre-doubles, (i.e. if rules allow it, in
case it wins the opening roll), you will become hostage to its strategy,
or in better sounding words, you will be dancing to its tune... ;)

Reaching a D/P later won't help you either because the mutant will not
drop and will force you to keep playing until the last roll, perhaps
trading the cube more times back and forth.

Letting the bot play for both side after the "opening double" actually
defeats the purpose of the experiment but since there is no "separately
existing, fully functional mutant bot (that would play like me;)" to
make it play against GnuBG 2-ply, this is the only way we can do it and
it's better than nothing.

So, this way the really "semi-mutant" play will lose but it still will
not lose more than what would be expected from the cube error rate that
the mutant incurs from this "opening double". This alone is enough to
prove that the currently dogmatized "cube skill theory" is a jarful of
cow chip cookies...

MK

Re: Interesting question/experiment about value of cube ownership

[Bug reports for and general discussion about GNU Backgammon.]

I'm glad we agree on the basic 25% take point. Do you also agree on the the 
theoretical 20% take point for perfect cube efficiency?

As far as I know, the only part of cube theory not calculated mathematically is 
the estimate made for cube efficiency. But it's a long time since I read 
Janowski so I may be wrong on that.

(I think you are using "gamble gammon" as a pejorative. I suspect that every 
time you do so, you lose credibility with anyone likely to read this. You may 
wish to take this into account, bearing in mind that most backgammon with the 
cube isn't played for money.)


Regards,

Ian Shaw


From: MK 
Sent: Friday, March 29, 2024 4:34:39 AM
To: Ian Shaw ; GnuBg Bug 
Subject: Re: Interesting question/experiment about value of cube ownership

On 3/19/2024 7:44 AM, Ian Shaw wrote:

> I don’t "divinely believe" in the current cube theory. I understand
> the maths behind it. If you have found errors in the maths, then I
> would be glad to re-evaluate.

> Let's find out where you disagree by starting from the beginning.
> What is your analysis of the basic 25% takepoint calculation?


I'm not questioning whether a simple doubling theory, (assuming it
can be called a "theory"), can be applied in simple game where you
can calculate that 25% accurately and consistently.

I'm questioning whether some doubling strategy can be applied in
gamblegammon, based on a jumble of incomplete/inaccurate empirical
statistics and mathematical calculation formulas that were several
times retrofitted to produce some expected results, and call it a
"cube skill theory".

In RGB, some mathematicians had argued that it could be called a
"theory" because it was mathematically proven, which can not be
because the so-called "cube skill" is not a purely mathematical
proposition.

In a game involving luck like gamblegammon, (more luck than skill
in my personal opinion), the proposition is necessarily statistical,
empirical one and thus needs to be empirically proven.

You say "let's start from the beginning". Yes, let's do so indeed.

TD-Gammon v.1 was empirically trained through self-play of cubeless
"money games", including gammons but not backgammons, and perhaps
not enough trials. That's it. That's your beginning...

To that, you use all kinds of "maths and mirrors" to add backgammon
rates, cubeful equity formulas, cubeful matchful equity tables, etc.
to "estimate" your winning chances, in order to apply to it what you
a "basic 25% take point". And I'm questioning sanity of all this, in
fact I'm arguing that it's all a pile of cow pies.

Shortcuts was taken in the days of TD-Gammon because of not having
enough CPU power, which is no longer true. Yet, there is no signs
of any willingness out there to create cubefully, matcfully trained
better gamblegammon bots.

It's easier to destroy a falsely claimed "theory" by poking holes in
it than to prove a proposition so that you can call it a theory, and
this is what I'm trying to accomplish with my experiments.

Since I can't single-handedly create a better bot, I'm trying what
I can do to create a need for, thus an incentive for the creation of
such a bot, "from scratch".

My "fartoffski mutant cube strategy", (based on arbitrary stages of
game and double/take points), in my experiments 11 and 12 came within
margin of error of beating GnuBG 2-ply. Folks, it's time for better
gamblegammon bots...

MK