Derek Nalls wrote on Tue, May 20, 2008 09:05 PM UTC:
Of course, I would bet anything that there are no 1:1 exchanges supported
under the standard Muller CRC model that could cause material losses. If
that were the case, yours would not be one of the three most credible CRC
models under close consideration. In fact, even your excellent Joker80
program would play poorly if stuck with using faulty CRC piece values.
Obviously, the longer the exchange, the rarer its occurrence during
gameplay. The predominance of simple 1:1 exchanges over even the least
complicated, 1:2 or 2:1 exchanges, in gameplay is large although I do not
know the stats.
In fact, there is a certain 1:2 or 2:1 exchange I am hoping to see that is
likely to support my contention that the Muller rook value should be
higher: the 1 queen for 2 rooks or 2 rooks for 1 queen exchange. Please
recall that under the standard Muller model, this is an equal exchange.
However, under asymmetrical playtesting of comparable quality to and
similar to that I used to confirm the correctness of your higher
archbishop value, I played numerous CRC games at various moderate time
controls where the player without 1 queen (yet with 2 rooks) defeated the
player without 2 rooks (yet with 1 queen). Ultimately, a key mechanism to conclusive results is that while the standard Muller model is neutral toward a 2 rook : 1 queen or 1 queen : 2 rook exchange, the special Muller model regards its 1 queen as significantly less valuable than 2 rooks of its opponent. Consequently, this contrast in valuation could be played into ... and we would see who wins.
I am actually pleased that you are a realist who shares my pessimism in
this experiment. In any case, low odds do not deter a best effort to
succeed. The main difference between us is that you calculate your
pessimism by extreme statistical methods whereas I calculate my pessimism
by moderate probabilistic methods. I remain hopeful that eventually I
will prove to you that the method Scharnagl & I developed is occasionally
productive.
