Derek Nalls wrote on Tue, May 13, 2008 02:39 AM UTC:
'Of course, that is easily quantified. The entire mathematical field of
statistics is designed to precisely quantify such things, through
confidence levels and uncertainty intervals.'
No, it is not easily quantified. Some things of numerical importance
as well as geometric importance that we try to understand or prove
in the study of chess variants are NOT covered or addressed by statistics.
I wish our field of interest was that simple (relatively speaking) and
approachable but it is far more complicated and interdisciplinary.
All you talk about is statistics. Is this because statistics is all you
know well?
___________
'That difference just can't be seen with two games. Play 100.
There is no shortcut.'
I agree. Not with only 2 games.
However ...
With only 4 games, IF they were ALL victories or defeats for the player
using a given piece values model, I could tell you with confidence
that there is at least a 15/16 chance the given piece values model is
stronger or weaker, respectively, than the piece values model used by
its opponent. [Otherwise, the results are inconclusive and useless.]
Furthermore, based upon the average number of moves per game
required for victory or defeat compared to the established average
number of moves in a long, close game, I could probably, correctly
estimate whether one model was a little or a lot stronger or weaker,
respectively, than the other model. Thus, I will not play 100 games
because there is no pressing, rational need to reduce the 'chance of
random good-bad luck' to the ridiculously-low value of
'the inverse of (base 2 to exponent 100)'.
Is there anything about the odds associated with 'flipping a coin'
that is beyond your ability to understand? This is a fundamental
mathematical concept applicable without reservation to symmetrical
playtesting. In any case, it is a legitimate 'shortcut' that I can and
will use freely.
________________
'Even perfect play doesn't help. We do have perfect play for all 6-men
positions.'
I meant perfect play throughout an entire game of a CRC variant
involving 40 pieces initially. That is why I used the word 'impossible'
with reference to state-of-the-art computer technology.
_______________________________________________________
'This is approximately master-level play.'
Well, if you are getting master-level play from Joker80 with speed
chess games, then I am surely getting a superior level of play from
SMIRF with much longer times and deeper plies per move. You see,
I used the term 'virtually random moves' appropriately in a
comparative context based upon my experience.
_____________________________________________
'Doesn't matter if you play at an hour per move, a week per move,
a year per move, 100 year per move. The error will remain >=32%.
So if you want to play 100 years per move, fine. But you will still
need 100 games.'
Of course, it matters a lot. If the program is well-written, then the
longer it runs per move, the more plies it completes per move
and consequently, the better the moves it makes. Hence,
the entire game played will progressively approach the ideal of
perfect play ... even though this finite goal is impossible to attain.
Incisive, intelligent, resourceful moves must NOT to be confused with
or dismissed as purely random moves. Although I could humbly limit
myself to applying only statistical methods, I am totally justified,
in this case, in more aggressively using the 'probabilities associated
with N coin flips ALL with the same result' as an incomplete, minimum
value before even taking the playing strength of SMIRF at extremely-long
time controls into account to estimate a complete, maximum value.
______________________________________________________________
'The advantage that a player has in terms of winning probability is the
same at any TC I ever tried, and can thus equally reliably be determined
with games of any duration.'
You are obviously lacking completely in the prerequisite patience and
determination to have EVER consistently used long enough time controls
to see any benefit whatsoever in doing so. If you had ever done so,
then you would realize (as everyone else who has done so realizes)
that the quality of the moves improves and even if the winning probability
has not changed much numerically in your experience, the figure you
obtain is more reliable.
[I cannot prove to you that this 'invisible' benefit exists
statistically. Instead, it is an important concept that you need to
understand in its own terms. This is essential to what most playtesters do, with the notable exception of you. If you want to understand what I do and why, then you must come to grips with this reality.]
