Single Comment

This discussion is wonderful, about 3 levels up from excellent. 
I'll try to reply to everything at once... 

Michael Nelson 'inverse relationship between the geometric move 
length and the ratio of the mobility of a rider', but isn't that 
ratio already accounted for by the probability that the 
destination square is on the board? 

'Clearly this suggests that the Rook has an advantage over short 
Rooks', why didn't I think of that? I may be wrong, but at first 
sight this looks like a brilliant thought! Maybe it is K 
interdiction; I wonder how you'd quantify that? 

'This suggests that the Wazir loses more value from its poor 
forwardness', continues and concludes a compelling and powerful 
sequence of logic. Then there follows a plaintive plea for some 
mathematical type to get interested and find a way to quantify it. 
Where have I heard that plea before?, I ask myself with a wry 
grin, and mentally give myself 3 points for the rare use of the 
word 'wry'. 

Robert Shimmin 'PV = M + 0.043 FP'. This also looks like something 
brilliant. You urgently need to run your numbers for the 
Knightrider! I was surprised that the Bishop had such a high '% 
from forking'; never thought of it as a great forker because when 
Bf1-c4, the square a6 is not newly attacked; but perhaps I forgot 
that Bc4xf7+ also attacking g8 is a kind of fork that I have 
played a million times -- the B forks 2 forward when it captures 
forward! 

Nelson 'WmR ... WcR' my feeling is that when a piece captures as A 
but moves as B, if A and B have nearly equal values then the 
composite piece is roughly equal to the average, but when A and B 
are vastly different, the composite is notably weaker than the 
average. Does it matter whether capture or move is stronger? I 
think not much difference if any, because mobility lets the piece 
with weak attack get more easily into position to use its weak 
attack; but this opinion is largely untested. 

Lawson (Hello!) mentions the levelling effect; Shimmin talks about having

tried to calculate it! Wow! I made a great many calculations that 
did not work out, and the failures contributed to learning. I 
disagree that a top Amazon suffers no worse than a top Q from 
levelling; say it suffers a bit more, because sometimes Q can get 
out of trouble by sacrificing self for R+N+positional advantage, 
but Amazon needs more and thus is more difficult for that kind of 
sacrifice. 

'Which may mean the mobility calculation works as well as it does 
because a lot of its errors very nearly cancel out.' Yes, it may 
mean that. The mobility calc seems to work but there's an 
arbitrary magic number in there, the results are approximate, how 
can you have full faith in this methodology? Someday there will be 
something better, but until then my flawed mobility calc is the 
best we have. Bummer. 

'135-point advantage at strength 4 and a 260-point advantage at 
strength 5' -- makes me feel good, worth of advantage varies by 
strength of player, as predicted. 

Several '[multi-move calculation]' I think the idea is very 
interesting that the mmove cal might intrinsically compensate for 
many of the value adjustments that we struggle with.