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In Ralph Betza's article on the <a href='http://www.chessvariants.com/piececlopedia.dir/ideal-and-practical-values-3.html'>Rider Problem</a>, he indicates that the multiplier for a rider is roughly inversely propoertional to the geometric length of the base move. So the Rook is worth 3 times the Wazir (move lenght=1.000), the Bishop is worth 2 times the Ferz (move length=1.414), and so on. He gives 1.5 for the Nightrider, making it exactly equal to the Rook (where the Rook is 4.5 pawns rather than 5, see Ralph's articles on piece values).
Since the geometric move length of the Mao's move and the Knight's move are the same, the same muliplier applies. So if the Mao is worth 2/3 of a Knight, the Maorider is equal to the Knight.
Mike, the value depends at least in part on how big the board is. On an
8x8 board a Maorider is worth comparatively less than on a 10x10 board.
If you use Betza's modification of empty board mobility (found
<a href='../d.betza/pieceval/betterway.html'>here</a>) for an 8x8 board,
you can calculate a value of a Maorider. If I read it correctly, it would
be 0.68275 the value of a Nightrider. Now a Nightrider is generally
accepted to be worth a Rook and Betza follows Spielmann in assigning the
Rook a value of 4.5 Pawns, yielding about 3.07 Pawns for a Maorider, or
right in the Bishop/Knight ballpark.
<p>
Of course, Ralph has expressed doubts about these values from time to time.
However, given that the Maorider is awkward in the opening, and limited in
the endgame (I don't <em>think</em> K + NN vs K is a win, never mind K +
nNnN vs K), the value seems OK to me.
Cross-post with Mike Nelson! It's interesting that referencing different
parts of Ralph's work we got basically the same answer. It implies that
he's consistent at the very least
Robert Shimmin wrote on Tue, Jan 28, 2003 04:01 PM EST:K + NN vs K cannot possibly be a win, because there are no positions in which a king and nightrider can checkmate a bare king. To be able to checkmate the bare king (with the assistance of the friendly king) it is at least necessary that a piece attack two orthogonally adjacent squares.
Point well taken, Peter. I had assumed an 8x8 board. On a larger board I would expect the Maorider to be stronger than the Knight, but still equal to the Bishop, which is also stronger than the Knight on a larger board. As an aside, I think the Moarider (based on the Moa, which moves one diagonally, then one orthogonally) is worth very slightly more than the Maorider because it is easier to develop.
The British Chess Variant Society's
<a href='http://www.bcvs.ukf.net/gvcm.htm'>A Guide to Variant Chess: All
the King's Men</a> calls a Mao + Moa a Moo. This would result in, I guess,
a Moo-rider. (Somehow I have an image of a large flightless bird wearing
an ugly jacket and holding a little red book.)
Using Betza's 'magic number', the probabity of at least one of two adjacent squares being open is quite close to 90%, so the moorider/outrigger should be worth 90% of the Nightrider--perhaps a weak Rook rather than a strong Bishop.
Anonymous wrote on Tue, Jan 28, 2003 09:32 PM EST:'(Somehow I have an image of a large flightless bird wearing an ugly jacket and holding a little red book.)' Yeah, or in the case of a maomoarider, a guy in an ugly jacket holding a little red book riding a saddled-up flightless bird. Anyway, after some experiments I have found that the maorider is too blockable to be terribly interesting, but that the maomoarider is too unblockable for my taste. So I'm currently experimenting with a set of augmented mao/moa riders: horseman = maorider plus ferz; equestrian = moarider plus wazir; caballero = maorider plus wazir; postilion = moarider plus ferz. Of course, others are possible, but so far I've not tried combining mao-moa riders with dabbaba or alfil. These should be in between bishop and rook in strength and the added one-step moves should give them enough added mobility to bring their rider powers into play more effectively. We'll see.
Regarding the Moo-rider, I am not clear on one thing: is it optionally either a Mao-rider or Moa-rider on any given turn, or do you get to choose either the moa-path or mao-path between each touch-down point on a single move? I get the image of a cow on a motorcycle.
You could call it 'Maa-rider'! So, if your game includes moariders, maoriders, mooriders, and maariders, you'd better not make any typos in the rules, and you would have to provide handicaps for dyslexic players. ;-)
Hey, you could set the rules to music! 'You say moarider and I say maorider. You say moorider and I say maarider. Moarider, maorider, moorider, maarider, Let's call the whole thing off!'
In my game Holywar, the Mao+Moa was called a Squire, because it was like a Knight but weaker.
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