Re: Request for help or advice for cube skill experiment using Gnubg

[MK]

On 9/18/2022 2:43 PM, Joseph Heled wrote:

> My 2 cents, for a few years now, is that you can't measure luck
> unless the two opponents are of exactly the same strength.

You're not replying to what I wrote. You're telling me what you
feel like telling me but even so it's not quite true, which we
can discuss separately.

> With two equally skilled players, the luckier will always win.
> [luck = sum over all throws of (expected equity - equity after
> roll)] With non-equal players luck is always on the side of the
> stronger player, because better moves reduce opponent luck. A
> good move, by definition, gives less lucky rolls for the opponent.

This is the dogmatic theoretical fallacy that we have heard only
a thousand times already. If you make your "non-equal opponents"
100% skill (let's say Gnubg 4-ply for the sake of the argument)
and 0% skill (i.e. random play), luck can only help and will help
the random player win more than 0%.

The cubeless part of the experiment I suggested would help find
that what percent the random player will win due to luck alone,
since he has zero skill. In other words, skill won't even come
into the equation until after that number which we don't know.

All of your current calculations are off by that amount until
you adjust your formulas to allow for it.

> I can show this easily with games that I actually "solved",
> that is, games for which a perfect player exists.

Yes, please do. Start a new thread for it if you wish.

> I can't prove it for Backgammon, but I believe the general
> argument holds in an two player game.

Well, there you go. You already admit that your proof failed
before you started. This has been a chronic problem of the
math phd's in RGB. They have resorted to all kinds of imaginary
"coin-toss football" games and such to offer proofs that don't
apply to backgammon.

After all that said, let's go back to what I was trying to
"measure": whether the introduction of the cube increases or
decreases the luck factor in backgammon.

I'm sure you will understand if you read what I wrote again
carefully but let me try to illustrate to help anyway.

Let's say the 0% skilled random player wins 10% against the
100% skilled perfect player in a series of cubeless games.

In a series of cubeful games of the same length, if the 0%
checker skill wins 5%, then we can say that the cube adds
more skill to BG and decreases the luck factor, but if he
wins 15%, then we can say that the cube increases the luck
factor in BG.

Until now, all I could offer were my personal experiments
against the bots that the cube increases the luck factor,
which were countered by purely divine revelations that it
decreases the luck factor.

The purpose of the experiment I proposed is to settle this
debate.

MK


> On Mon, 19 Sept 2022 at 08:06, <playbg-rgb@yahoo.com 
<mailto:playbg-rgb@yahoo.com>> wrote:

>     If only the predefined setting is selected, then in the eval.c a few
>     lines of code will be added for cube and for checker decisions.
>
>     For cube, after determining what kind of cube access the "mutant"
>     has, it will flip a coin and make a random decision. Nothing else.
>
>     For checker, after the filling of the legal moves array, the "mutant"
>     will randomly play an entry from the array. Nothing else.
>
>     For now I'll just give one example of usefulness per feature. I think
>     I have been the only one who argued for years that cube magnifies
>     luck against everyone else who claimed the opposite. With this, we
>     can settle the debate by making "grandmaster" play 10,000 cubeless
>     games against "mutant" random and see how much pure luck wins.
>
>     Then we can let them play 10,000 cubeful games with both playing
>     at "grandmaster" cube skill level. The difference between the two
>     results will indicate whether the "mutant" will win more or less with
>     the cube than without the cube.