David Pritchard's Encyclopedia of Chess Variants lists 31 distinct versions of three-player chess, the earliest of which dates back to 1765. All feature different attempts to solve the two basic problems of the three-handed game: what's the shape of the board, and what do you have to do in order to defeat both opponents?
On the first count, the simplest idea is just to extend the normal board to accommodate another set of pieces, as, for example, in the 1843 version by Tesche shown in the lowest diagram. But there is no way of doing this to produce perfect three-way symmetry. Squares into triangles won't go. You may, as Tesche claimed he had done, produce a game with more of less equal chances for the three players, but they still occupy different terrains at the start.
You can get round the problem by using hexagons instead of squares, as Sigmund Wellisch did in his 1912 "Three-Handed Hexagonal Chess". Hexagons, however, make life hell for bishops, because there are no real diagonals. You need either three quasi-bishops to cover the whole board on pseudo- diagonals, or, as Wellisch preferred, to eliminate bishops from the game altogether. If you like hexagons and don't want to lose your bishops, there's a 1964 three-handed hexagonal game, invented by Joe Baxter, played on a 217-hexagon board with 19 men on each side.
If you want symmetry, but consider hexagons too outlandish, you can arrange your three sides at 120 angles to each other, but then face the problem of what to do with the space in the middle. Henry J Self, in 1895 (middle diagram), did nothing with it at all. On reaching the no-man's-land in the middle, a player just continues round its edge. "In my game," Self proudly announced, "the pieces of any one of the players have not the slightest advantage so far as position goes over either of the remaining players." On the other hand, once you have sent your pieces into battle against one opponent, it's a very long trip to get them back to fight the other.
Rassmussen's new game gets round that problem with an elegant diamond array serving as crossroads in the centre of the battlefield. You still have to decide whether to turn left or right on reaching the middle, but the route back is not so arduous. Similar attempts to design neat traffic intersections in the centre were designed by Coqueret and Waider, both in 1837.
But how do you decide who has won? The problem with three-handed chess that nobody has truly solved is to concoct a set of rules that prevents two players ganging up on the third, then fighting each other for the gold and silver medals. Self tried to encourage aggressive play by rewarding any player who checkmated another with the return of any of his captured pieces. Other variants, such as Tesche's, do not eliminate a checkmated (or stalemated) player, but merely freeze his participation in the game until such time as the checkmate is lifted. The eventual winner must leave both his opponent's checkmated simultaneously. Since forces used in a checkmate are liable to be needed sooner or later elsewhere, this can prolong a game almost indefinitely.
But will Ches 3 catch on? Over the past 25 years, Allegiance Chess, Chesser, Dreier-Schach, En Garde, Interface, Mad Threeparty Chess, Neutral-Zone Chess, Three-Man Chess, Three-Player Chess, Tri-Chess, Trio Chess, Triscacsia and Trischa are only a few of the proprietary three-player chess games that sank almost without trace soon after their launch.
We have also seen Four-Handed Dice Chess, Four-Handed Round Chess (played on a circular board), Decimal Four-Handed Chess (on a ten-by-ten board), Russian Four-Handed Chess, Forchess, Partnership Chess, Double Chess and a host of other chess deviations for four players.
The trouble is that the good old ancient game of chess for two seems to have the potential to create quite enough complexity, and certainly sufficient acrimony among its participants, to satisfy all our needs. And even if chess is not the perfect game, it has established itself too well as the principal intellectual board game in Western society. As the history of such games shown, when a mutated three-handed version evolves alongside the established species, it does not tend to survive.
Sets of Ches 3 will soon be available at prices between pounds 30 and pounds 70. David Pritchard's `The Encyclopedia of Chess Variants' may be obtained from: Games & Puzzles Publications, PO Box 20, Godalming, Surrey, for pounds 21.99 including postage.