Chess is the fundamental game for two persons - how can anyone get the crazy idea, searching for a chessgame for three players?... In this way many chess-players react, when they hear from this problem the first time. But the intention is not so misleading at all, you will see here soon. Of course, I'm not the first person, who published a solution for this puzzle. In the beginning it was only an absurd problem, but later I recognized, that it is the most exciting project, I ever have worked about. I'm still working on it! In this manner: How to play chess for three?
My sighted goal is to find a threehanded chessgame, that is located at the FIDE-chess exclusively. Only in this case (if in any case at all) it might have the chance to become accepted by chess-masters. That's why I expect a great deal from the game, that I have to find, by example:
1. Every player needs 8 Pawns, 1 King, 1 Queen, 2 Rooks, 2 Bishops and 2 Knights.
2. The chessmen have to keep their specific movements from the FIDE-chessgame.
3. The available room to play has to be increased by 32 squares (half a chessboard).
4. The quadratic form of boards and squares may be unchanged.
To tell it one word: The symmetrie and the rules of FIDE-chess have to be maintained (if possible) unlimited in my threehanded chess-variant! Or you can say that chess for 2 players has to be a special case of the threehanded chessgame, I like to find.
But in which way the partly ostensibly inconsistant characteristics may be arranged in harmony? It needed some years to crack the nut. Finally I was rewarded with two dualistic variants - the Star-III-COLOR and the Triangle-III-COLOR. Sorry, but now you have to think with me, because it is not easy to explain the facts.
From the time, we learned how to play chess, we know the rule of setting up the pieces: white queen on white square, black queen on black square. In the beginning of the game the queens stay in opposition on squares of their own colour. This chess-rule manifests a symmetry, which scientists declares as CP-invariance. C is for charge, P is for parity, invariance signifies unchangeableness. CP-invariance means following for our chessgame: If I change all colours of squares and chessmen (all white gets black, all black gets white) in the setup and watch the result in a mirror, then I see my original chessgame there. This symmetrie is often found in physics to desribe particals and their anti-particles (b.e. electrons and positrons). They are in proportion to each other as the white half of the chessboard to the black half. If you like so, playing chess is a simulation of a quantum-mechanical process of domitation between matter and anti-matter.
Let's decide first: If there are three persons (A, B and C) who want to play chess with each other simulteaneously, they can play three normal games at the same time: Player A with white against player B with black, B with white against C with black, and C with white against A with black. This variant was created 1882 by a frenchman named Demonchy. If you set up three boards (on a round table) by producing a same-sided triangel in the middle and sit down in one of the niches, righthanded a white, lefthanded a black position, you can begin immediately. The direction of moves is left way around (anti-clockwise) per definition.
This variant does not offend against the CP-invariance, but in a way it isn't a real threehanded chessgame. You see immedialely, that these three chessgames are not combinated with each other. Each one stands for its own and hasn't anything to do with both of the others. You might have played the three games after another. The question maintains: In which way you can combine these three games with each other? Or better: How you can make a threehanded chessgame out of it?