Johnny Luken wrote on Fri, Oct 12, 2012 08:09 PM UTC:
Jeremy,
True, the Long Leaper would probably have a higher follow on capture
probability than the Displacer, but I'd only be able to factor that in if
I was calculating 2nd move capture probability, which is an order of
magnitude more difficult problem to calculate. A piece threatened by an
LL/advancer has a higher capture evasion ability as it can move in 7
directions to avoid capture, compared to to 6 for the Displacer. Moreover
other pieces be moved behind the piece to stop the LL, which further
reduces its attack threat.
Its true that the Advancer is more flexible in where it leaves itself,
which I indeed didnt try to calculate and ignored. It might be a stronger
piece against static opposition compared to a Displacer-I imagine it could
be particularly pesky at a start of a FIDE chess game, as would a
withdrawer. This is a similar problem to the fact that a piece that can
rifle capture has the exact same value by my method as a Displacer, yet has
a much higher practical value in most game scenarios. This you could
probably calculate as "opposition counter threat", which is lower for a
rifle capturing piece as its not "at the scene of the crime" so to
speak.
What exactly do you mean by calculating the average number of captures a
piece can make? I would think this is the same as what I was doing-the
higher the average number of possible captures, then the higher the average
probability of making a single capture. There are simpler models can be
used-a D has a capture range of 1-7 on a chess board, the LL 1-6, the A
2-7, the W 1. I factored in the LLs ability to make multiple captures in my
2nd post.
Pieces that affect mobility can be calculated by the net mobility gain they
produce. The immobiliser, now that I think of it, has essentially the same
value regardless of opposition mobility, as it always reduces enemy
mobility by the same fraction. The swapper on the other hand has a value
proportional to friendly mobility. In a ultima environment its more or less
worthless, about as useful as empty space, as it only produces a queen
move, when all pieces can move like rook/queen anyway. In a FIDE chess game
it has a higher mobility gain, as the pieces are less mobile, and becomes a
stronger piece, while the I remains same in value. However the I of course
automatically produces an relative mobility gain every move, unlike a
swapper or like piece.
If the 1:2 thing holds then that obviously must be factored in aswell,
obviously piece values will be "squashed" together to some extent by
their identical movement.