Drek Nalls:
| They definitely mean something ... although exactly how much is not 
| easily known or quantified (measured) mathematically.
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. The only thing you proved
with reasonable confidence (say 95%) is that two Rooks are not 1.66 Pawn
weaker than a Queen. So if Q=950, then R > 392. Well, no one claimed
anything different. What we want to see is if Q-RR scores 50% (R=475) or
62% (R=525). That difference just can't be seen with two games. Play 100.
There is no shortcut. Even perfect play doesn't help. We do have perfect
play for all 6-men positions. Can you derive piece values from that, even
end-game piece values???

| Statistically, when dealing with speed chess games populated 
| exclusively with virtually random moves ... YES, I can understand and 
| agree with you requiring a minimum of 100 games.  However, what you 
| are doing is at the opposite extreme from what I am doing via my 
| playtesting method.
Where do you get this nonsense? This is approximately master-level play.
Fact is that results from playing opening-type positions (with 35 pieces
or more) are stochastic quantity at any level of play we are likely to see
the next few million years. And even if they weren't, so that you could
answer the question 'who wins' through a 35-men tablebase, you would
still have to make some average over all positions (weighted by relevance)
with a certain material composition to extract piece values. And if you
would do that by sampling, the resukt would again be a sochastic quantity.
And if you would do it by exhaustive enumeration, you would have no idea
which weights to use.
And if you are sampling a stochastic quantity, the error will be AT LEAST
as large as the statistical error. Errors from other sources could add to
that. But if you have two games, you will have at least 32% error in the
result percentage. Doesnt 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 yesr per move, fine. But you will still
need 100 games.

| Nonetheless, games played at 100 minutes per move (for example) have 
| a much greater probability of correctly determining which player has 
| a definite, significant advantage than games played at 10 seconds per 
| move (for example).
Why do I get the suspicion that you are just making up this nonsense? Can
you show me even one example where you have shown that a certain material
advantage would be more than 3-sigma different for games at 100 min / move
than for games at 1 sec/move? Show us the games, then. Be aware that this
would require at least 100 games at aech time control. That seems to make
it a safe guess that you did not do that for 100 min/move.
 On the other hand, in stead of just making things up, I have actually
done such tests, not with 100 games per TC, but with 432, and for the
faster even with 1728 games per TC. And there was no difference beyond the
expected and unavoidable statistical fluctuations corresponding to those
numbers of games, between playing 15 sec or 5 minutes. 
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. (Provided ou have the same number of games).
If you think it would be different for extremely long TC, show us
statistically sound proof.

I might comment on the rest of your long posting later, but have to go
now...