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White Elephant Chess

By Peter Aronson

Introduction

          White Elephant Chess is a set of games, each of which is a form of Chess with Different Armies, where some of White's pieces are replaced with pieces that move like some sort of Elephant piece or another.

          White Elephant Chess was inspired by Ralph Betza's game of Black Ghost, 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. (For those not familiar with the English idom, a white elephant is a "property requiring much care and expense, but yielding little profit", making the game's name a sort of weak pun.) It didn't work out quite that way (see below).

          Why Elephants? Because I like them.

General Rules

          The rules of all forms of White Elephant Chess are identical to those of FIDE Chess, except where noted below. In any version of White Elephant Chess, a Pawn may promote to any piece (other than a Pawn or a King) that started the game on the board.

White Elephant Chess I

          This is White Elephant Chess for beginners and casual players. Black has the usual FIDE army, while White's Bishops are replaced by Elephants, and White's Knights by Great Elephants.

Elephants

           Sometime back, after reading the Piececlopedia article on the Alfil, I started thinking about the other sort of Elephant piece, the one that moves like a Ferz or one step forward like a Wazir (fWF), found in Sittuyin (Burmese Chess) as the Elephant, in Makruk (Thai Chess) as the Thon, and in Shogi (Japanese Chess) as the Silver General. 








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          It's a simple piece, but what is it worth? A Ferz 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 Commoner's. 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:
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.
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. And that forwardness is important, as according to Betza's calculations, the forward move of a Wazir is worth 0.6 of of its total added move to another piece. That gives us a value of 0.8 of a Knight (0.5N + 0.6 * 0.5N) for the Elephant, which will call 3/4 of a Knight for convenience (and besides with these calculations 0.05 either way doesn't mean much).

Great Elephants

          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 Dabbabah jump forward (yielding FAfWfD) , 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". 








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          Now, what's the Great Elephant's value? It attacks 10 squares on an empty board, and it is neither colorbound nor colorchanging. Since it's a doubled version of the Elephant, the simplest approach to valuing it is to assume it is worth twice what an Elephant is worth, or 1.5 Knights, which is 4.5 Pawns. Now, 4.5 Pawns is either the value of a Rook or just a bit below, depending on who you listen to, but Rookish in any case.

White Elephant Chess II

          This is White Elephant Chess for more advanced players. You see, if you do the math for the White Elephant I army, you will see that it is 0.5 Knights too strong. However, its starting position is slightly awkward and its pieces not necessarily easy to use. But once a player has mastered the Elephant and the Great Elephant, they are ready to play using the White Elephant Chess II army: Black has the usual FIDE army, while White's Bishops are replaced by Elephants, Knights by Great Elephants, and the white Queen by a War Elephant.

The War Elephant

          To produce a slightly weaker Queen for the Elephant Army, I combined the Alfil Rider (a piece that can make repeated Alfil jumps in the same direction) with the ever useful Rook (RAA). The resulting piece is both slightly awkward and dangerous, just like a proper War Elephant. 








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          If the Elephant is 0.75 of a Knight, and the Great Elephant is 1.5 Knights, then the White Elephants are about 0.5 of a Knight too strong (the exact amount depending on your opinion of the relative values of the Knight and Bishop). Replacing the Queen with the War Elephant, Rook + Alfil Rider, should be about the proper balance, since a Rook + Alfil would be a full 0.5 of a Knight 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 Alfil Rider over the Alfil ought to just balance things.

White Elephant Chess III

          This was supposed to be an intermediate form of White Elephant Chess, with an army partway between the White Elephant I and White Elephant II armies in strength for people who like to split the difference, however, it didn't turn out that way. The proposed Queen for this army -- the Tiger -- instead of being about halfway between a Queen and a War Elephant, is almost as strong as a Queen, I suspect. But it looks interesting, so I'll include it.

          In White Elephant Chess III Black has the usual FIDE army, while White's Bishops are replaced by Elephants, Knights by Great Elephants, and the white Queen by a Tiger.

The Tiger

          Thinking back to Jörg Knappen's army for Chess with Different Armies, the Seeping Shifters, I was reminded of those interesting pieces, the Slip Rook and the Slip Bishop. Slip pieces travel on the odd-numbered squares away from their starting square, taking a step, and if that square is empty, they can then leap two squares to the third square, and if that square is empty, leap two more squares to the fifth square, etc. Slip pieces are a special form of Bent Riders, but ones without any actual bend! The Tiger is a regular Rook combined with a Slip Bishop. 








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          My original thought was that a Tiger would be intermediate in value between a Queen and a War Elephant, and it is, but alas, far, far closer to a Queen than otherwise. I calculated the mobility of the Slip Bishop using this method of Ralph Betza's, and compared it to the mobility of the regular Bishop as calculated using the same magic number (0.6875 as it happens), and it turned out that a Slip Bishop has slightly over 90% of a Bishop's mobility, which makes it doubtful in my mind that a Tiger is worth very much less than a Queen.

White Elephant Chess IV

          This was my second attempt to construct intermediate form of White Elephant Chess with an army partway between the White Elephant I and White Elephant II armies. It is based on the untested but intuitively reasonable assumption that about 0.75 of a Bishop's contribution to a Queen's value is the two forward moves. I use this to construct a new Queen equivalent -- the Mammoth.

          In White Elephant Chess IV Black has the usual FIDE army, while White's Bishops are replaced by Elephants, Knights by Great Elephants, and the white Queen by a Mammoth.

The Mammoth

          A Mammoth is simply an Elephant (sort-of (*)) writ large: a Rook plus the forward moves of a Bishop (RfB). Mammoths charge forward wonderfully, but are not as good at backing up (rather like large trucks). Mammoths are very vulnerable to being immobilized by pea shooters, but fortunately for them, there aren't any of those in this game. ((*) A piece that was an Elephant writ large -- BfR would be interesting, but not very Queen-like.) 








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          The value of a Mammoth is a simple matter. If you assume, as I have, that 75% of the value of the Bishop lies in its forward moves, then an RfB (Rook + 0.75B) would be about halfway in value between RAA (Rook + 0.5B) and RB (Rook + 1.0B). If my assumption is wrong, then this is all moonshine of course.

Notes

          This variant's design is heavily dependent on Ralph Betza's work on estimating the values of Chess pieces. Now, Ralph has been known to doubt his own work at time (although I have always found it helpful), but I figure such metrics are like computer documentation (and some other things): when they are good, they're wonderful, and when they're bad they're still much better than nothing.

Computer Play

          I have written an implementation of all four forms of White Elephant Chess for Zillions of Games. You can download it here:

Written by Peter Aronson.
WWW page created: June 19th, 2002.