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<h4 align=center>What's the Value of a White Elephant?</h4>
Here are some thoughts on a variant I've played around with, but never
finished as I was uncertain about the balance. I thought they might
be of minor general interest, so here they are.
<P>
Sometime back, after reading the Piececlopedia article on the <a
href='../piececlopedia.dir/alfil.html'>Alfil</a>, I started thinking about
the other sort of Elephant piece, the one that moves like a Ferz or
one step forward (fWF), found in <A
HREF='../oriental.dir/burmese.html'>Sittuyin</A> (Burmese Chess) as
the Elephant, in <A HREF='../oriental.dir/thai.html'>Makruk</A> (Thai
Chess) as the Thon, and in <A HREF='../shogi.html'>Shogi</A> (Japanese
Chess) as the Silver General.
<P>
It's a simple piece, but what is it worth? A <A
HREF='../piececlopedia.dir/ferz.html'>Ferz</A> is generally accepted
to be worth about 1/2 a Knight (balancing colorboundness with a good
forward move), but how much more does that single forward move add?
I'm not as scientific about these sorts of things like Ralph Betza is,
but it does add a lot. First, an Elephant is not colorbound like a
Ferz is, and second, its forward moves are the same as a <A
HREF='../piececlopedia.dir/man.html'>Commoner's</A>. In fact, you could
look at an Elephant as 5/8's of a Commoner, which is generally considered
a Knight-valued piece and about which Ralph Betza says:
<BLOCKQUOTE>
This is a very short-range and very flexible piece that is much weaker
than a Knight in the opening, very strong in the middlegame if it can
occupy the center, and almost always wins against a Knight or Bishop
in the endgame.
</BLOCKQUOTE>
Of course, an Elephant is less flexible in the endgame where the
opposing pieces very well might not be in front of it. But on the
other hand, it has the three most useful moves of the Commoner for the
opening. So we'll assume 5/8's of a Knight is about right; roughly
two Pawns.
<P>
The next thought I had on the subject was what if I were to combine
the Alfil and the Elephant? This produced a piece that moved one or
two (jumping) diagonally or one square forward. Looking at this, I
realized that if I added a two square jump forward (yielding fWFfDA) ,
I would repeat the shape of the Elephant's move (supposedly four legs
and a trunk) on a slightly larger scale. Thus was born the 'Great
Elephant'.
<P>
Now, what's the Great Elephant's value? It attacks 10 squares on an
empty board, and it is neither colorbound nor colorchanging. The
simplest calculation would be a Knight and a quarter -- 3.75 Pawns.
The lack of colorchanging might kick it up to as much as 4 Pawns.
<P>
OK, the actual variant. Thinking about Ralph Betza's game of <A
HREF='../d.betza/chessvar/ghost.html'>Black Ghost</A>, where black is
given a piece worth less than a Pawn to balance white's first turn
advantage, I decided to give white an Elephant-based army worth a tiny
bit less than black's in order to balance white's first turn advantage.
<h4 align=center>White Elephant Chess</h4>
The rules for <B>White Elephant Chess</B> are as for <A
HREF='../ichess.html'>FIDE Chess</A>, except where stated otherwise.
<P>
White's Bishops are replaced by Elephants (fWF), and Knight's by Great
Elephant's (fWFfDA). Black's array is the usual FIDE array.
<P>
Pawns may promote to any non-Pawn, non-King piece that started the
game on either side (Elephant, Knight, Bishop, Great Elephant, Rook or
Queen).
<hr>
My suspicion (backed up unreliably by Zillions) is that white might be
a tad <STRONG>too</STRONG> weak. I tried adding the Alfil's move to
the white Queen's to produce the Queen Elephant, but that didn't seem
right, either.
gnohmon wrote on Thu, Jun 13, 2002 04:23 AM UTC:Values are different in Shogi, where the drops and 6th-rank limited promotion rules change all values. After I sought out and visited the Shogi equivalent of the Nihon Ki-In (but decided not t play because of my limited shogi experience -- the exercize of finding it on the map and actually finding my way to a remote region of Tokyo was quite rewarding enough!), I downloaded the supremely weak shogi master program from the home of the underdogs, and played quite a bit; and my impression is that (1) having more Pawns is good, but not specific number of Pawns is worth anything; (2) fR == ffN; Gold == Silver == 2 of the previous; R == B == 2 of the previous (although R versus B may often be decisive). But in a 'normal' game, what's a Silver worth? My ancient researches seemed to indicate that adding the forward move+capture of Wazir to something else is worth nearly half as much as adding a whole Wazir; and that adding the sideways moves is worth most of the remaining half-Wazir. For the Ferz, I forget. It's written down somewhere but of course forwards is worth more than half. Thus, the basic estimate for the Silver General is roughly 3/4 of a Knight, and the basic estimat for the Gold General is somewhat more than 3/4 of a Knight. If the simplest possible estimates of the values are taken, then your Elephant may possibly be worth 3/4 N and your Great Elephant may possibly be worth 1.5 N, which is roughly the value of a Rook. According to the shock-troop theory, the combination of weak FfW which have no jumping move and the strong fWfDWA which does have jumping, this combination interferes with the harmonious development of the army; but Philidor's shock-troop theory, although it contains some truth, is not the final word. Morphy showed how one can cause great damage to the opponent by developing the Rook-valued pieces, and his example must be kept in mind when you are playing an army that includes HFD or Great Elephants as R-valued pieces. If the Great Elephant is Rookish in value, then it is logical that splicing equine genes into the Greater Elephant must produce a Q-valued piece; using this in the same army would be consistent but it would be overkill. If my guesses about the elaphantine values are somewhat near correct, then why does your playtesting seem to hint that the army is too weak? In my experience, the unreliable values produced by my pseudoscientific guesses are actually more reliable than playtesting. The most common problem with playtesting is that if you don't know how to use a piece to best advantage, it seems weaker than it really is. Learning to use every possible piece is difficult and time-consuming.
While I am certainly willing to believe in the inaccuracy of playtesting
as
a means of determining the value of pieces (unless, of course, there are
a
great number of games played by strong players), still, I have some
trouble
thinking of the Great Elephant as a Rook-equivalent piece.
<p>
And I wonder. While almost 1/2 the value of the Wazir might come from
its
forward move, does that mean that that forward move necessarily adds 1/2
of the value of a Wazir to a piece, like the Ferz, which already has
considerable forward movement? In the Great Elephant's case, the fWfD
component adds two forward moves to a piece that has four already -- it
seems to me that there ought to be some principle of diminishing returns
here. There is also the strange issue of directional colorboundness;
that
the Elephants are colorbound when moving backwards but not when moving
forwards.
gnohmon wrote on Fri, Jun 14, 2002 03:27 AM UTC:'I have some trouble thinking of the Great Elephant as a Rook-equivalent piece.' It has two full atoms, half of another, and a quarter of another; this puts it already in the Rookish range, though maybe a bit weak. The partial atoms are the forward parts, which must boost it to full Rookitude. You have inspired me to write Captain Spalding Chess, of which the most important feature is that one may find an Elephant in one's Pajama.
<blockquote><i>
It has two full atoms, half of another, and a quarter of another; this puts
it already in the Rookish range, though maybe a bit weak. The partial atoms
are the forward parts, which must boost it to full Rookitude.
</i></blockquote>
Well, as I count it, it has two full atoms, and the quarter of <em>two</em>
others. Now, I am certainly willing to accept that 0.5 of the value of the
W is due to its forward move, but what I am less convinced of, I guess, is
whether the W forward move by itself <strong>adds</strong> that much to of
the value of the W to another piece that already has forward moves. It's
at least an interesting question, I think.
<p>
If the Elephant is 0.75 N, and the Great Elephant is 1.5 N, then the White
Elephants are about 0.5 N too strong (the exact amount depending on your
opinion of the relative values of the N and B). If that's the case, maybe
the Queen should be replaced by the War Elephant, Rook + Alfil Rider (RAA)
-- this should be about the proper balance, since a Rook + Alfil would
be a full 0.5 N weaker than a Queen, but since the Great Elephants are a
tiny bit weaker than Rooks, maybe, and there's the Bishop differential,
the extra strength of the AA over the A ought to just balance things.
<p>
<hr>
Captain Spalding Chess!? -- Marxist!
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