From: Benjamin Good ANDREW CMU EDU>
Date: 16 apr 1997
Subject: relative value of pieces
awhile ago i did some analyzing of pieces to help compare them. i
originally sent my email write-up of my result to colin adams, in case
he was interested in using any of the info for his book on tenjiku
shogi. he thought the rest of the shogi-l readers might be interested,
so here it is (slightly edited of course):
my method was to make diagrams of how many moves it took them to reach
every square on an empty board. since some pieces reach certain
distances more effectively than others, i came up w/ 3 #'s for each
piece:
average number of moves to reach any square within a 5x5 area w/ the
piece in the center.
ditto for a 9x9 board and a 15x15 board.
of course i realize that this is not an absolute system for determining
the value of pieces. the GGn, FEg, and FK would all have identical #s.
the Ln would lose to the FK on the chu shogi board. the VGn would lose
to the RGn on a large board. the chess knight and xianqi knight would
be indentical. and of course the board is never actually empty. but i
think the system still has its uses, esp for the more 'awkward' pieces.
first i compared the chess knight and the phoenix. i thought the
phoenix was a pretty awkward piece, and that if you ignored it's
promotion possibilities, it was worse than the knight. but i read
somewhere that it was better. and i think it is, in fact, it seems
pretty obvious to me now, so i'm not sure why i thought that. probably
because as a chess player i was very used to using the knight, whereas
the phoenix is still a relatively new piece for me.
the numbers for the knight and phoenix are:
knight phoenix
15x15: 3.5 3.5
9x9: 2.5 2.4
5x5: 2.17 1.66
these definitely support the phoenix, esp since it is significantly
better for close-in manuervering, which i think it is more likey to do
in tenjiku shogi, esp if it used in defense of the king. of course,
since the numbers average out to 3.5 for the large board, it means that
the phoenix must be worse at accurately travelling larger distances
(which means that if you had a chess knight in tenjiku shogi, it would
be better at promoting than the phoenix).
just for the sake of comparison, i also have numbers for:
free king dragon king dragon horse rook
15x15: 1.75 1.86 2.13 1.88
9x9: 1.6 1.75 1.9 1.8
5x5: 1.33 1.66 1.5 1.66
finally i did the heavenly tetrarchs. i think it's worth mentioning
that the HTr is almost colorbound, the only way it can flip is to move
exactly 3 squares to the left of the right. this and the fact that it
can't move to any adjacent square make it tough to get around. it turns
out that a HTr in the center of an empty 15x15 board can get to any
empty square in 3 moves or less w/ one exception: it takes a minumum of
4 to reach the square directly in front of it. so the HTr's numbers
turn out to be not too bad, but the important thing to note is that
often the route to certain squares is very roundabout, particularly
those that are relatively close. the result is that the HTr's mobility
will be highly dependent on the number of pieces around it; in a crowded
sitution the HTr may be fairly difficult to get around.
compensating for that tho, is the HTr's igui power. this means that the
number of moves it takes to reach a certain square may not be important,
only the number of moves it needs to make a capture on a certain square.
in this respect the numbers for the HTr are significantly better:
HTr movement HTr capturing
15x15: 2.23 1.94
9x9: 2.23 1.7
5x5: 2.08 1.41
so that's it. in his book colin has made a table classifying the
pieces, admittedly quite similar the wayne schmittenberger table in the
gfhodges manual on chu shogi, and one of the uncertainties is where to
put the HTr on the table. i don't know if my analysis helps at all or
not (i sure don't know where to put it).
that's it. i anyone finds any errors in my numbers, let me know, the
calculations weren't double-checked.
later,
ben