Re: Interesting question/experiment about value of cube ownership

[MK]

On 3/19/2024 7:37 AM, Ian Shaw wrote:

> > MK: This is why I am doing my various experiments. One of which
> > that I had previously mentioned in this very thread involves a
> > "mutant cubestrategy" of doubling at GWC > 50% and taking at
> > GWC > 0%. In that experiment of 20,000 money games, the mutant
> > won 40.80% of total points against GnuBG 2-ply. Since winning the
> > opening roll gives the player GWC > 50%, I ran a variant of the
> > above experiment making the mutant also double if it wins the
> > opening roll. This time, after 20,000 money games the mutant won
> > 45.77% of total points.

> These sound similar enough that I'll combine them.  Overall, the
> mutant strategy if doubling as soon as you had an advantage lost
> 0.1343 points per game. Always doubling immediately lost 0.36 ppg.
> So, not doubling until you are winning appears to be a better
> strategy than always doubling. But, as you expected, the mutant
> strategy isn't as good as the current cube algorithm, which loses
> 0 ppg.

I think you misunderstood the whole thing. You need to compare the
first mutant strategy to the bot playing against itself straight.
The mutant is expected to lose. The fact that it didn't lose too
badly is a separate point by itself.

Then you need to compare mutant's variant strategy of doubling at
once to bot's regular play against itself with the only difference
of doubling at once. Now we are comparing mutant variant against
mutant and bot variant against bot.

In the case of the bot, doubling at once causes the variant bot to
lose points. However, in the case of the mutant, doubling at once
causes the variant mutant ti win more points, not compared to the
bot but compared to the mutant itself!

I can imagine how difficult it may be for some of you guys to stick
your heads out of the box and try to understand what I'm trying to
demonstrate. I'm not saying that the above crude mutant cube strategy
is better than the 2-ply bot but that if it was the only way people
played gamblegammon on a different planet, then doubling as soon as
winning the opening roll would be the correct cube action that wins
more points than not doubling. I hope this is clear now, because I
don't know how else I can explain this.

> However, I don’t think 40000 trials is enough. Your strategy has
> huge variance. Have you calculated the statistical significance
> as suggested by one of the earlier responders? I recall that he
> suggested a similar experiment with lower variance to reduce the
> required number of trials, but you didn't want to try it.  I can't
> find that post at the moment, so I don’t know how many trials he
> calculated, but since your cube can get very high you would
> inevitably need more trials.

You must be thinking of the first experiment that I had mention, in
which the mutant would double/take/drop totally randomly. In that
the cube has gone astronomically high and I abandoned it after only
30,000 games since I realized that even a million trials may not be
enough, let alone a few hundred thousands that was suggested to me.

In the above experiment the variance is surely big but I wouldn't
say huge. I agree that 20,000 trials for each mutant variant is
barely enough to give a glimpse of the possible results. With my
now shared scripts, nothing prevents anyone to run as many trials
as they consider enough. (I may do some more myself also if I find
the time for it). My preliminary results may be considered well
enough indicators to justify pursuing the experiment further with
more trials.

MK