Two philosophies exist amoung the people, I demanded to play III-COLOR-CHESS, about when the game is over and who has won. For this reason I tell you the opinion of those, who love it in another way. My view of the rules is printed bolt, but perhaps there are unthoughted possibilities, we don't know yet. Let's have part on your ideas!
1.) Only one player is the winner! Two players loose! Or the game has to be a draw! This "Highlander-Rule" (as we call it) is absolutely accepted amoung my game-partners. If this wouldn't be so, two players could agree about a coalition against the third one before they start the game. Absurd! Nothing changes if you try to find a rule for placement. (Do you imagine, how many trials and errors we have made to find practical rules?) Anyhow with the "Highlander-Rule" we created a new, animated element in chess, that I won't miss: the diplomacy! You will see what I mean.
2.) The player who checkmates one opposite king at first is the winner! This is exactly the problem: When a king is checkmated? When I checkmate it or when it is checkmate on turn? The FIDE tells us nothing about, because this question is not to be asked in 2-Chess. By example: Is the blue player allowed to move, when yellow checkmates the red player? Or is the red player checkmated (or not!), if the blue one, who is on move now, has executed his move? I think the following rule is clever to produce a maximum of diplomatic thrill:
2a.) A king is checkmated, if it is checkmated on move! If therefore red creates a situation with the yellow king in checkmate, the blue player is still on move to avert this checkmate, if he can (by capturing the yellow mategiving piece or by interrupting the dangerous line).
Think about, in the star-variant a yellow piece is taken off in a way, it checks the red king and a blue piece does it simultaniously, too. If now the red player would be on turn, he is checkmated and yellow is the winner. But he is not. Blue is on turn, he can possibly negate the checkmate against red and even win. Here is a position in the star-variant, you can setup and have a look, because its difficult to read in mind. (Did you download the tinkers model yet?)
If now the yellow bishop moves Ig3-Ih2+, so red would be checkmated and yellow wins. The blue rook on IIIg1 checks too, but blue was not the first one to check, because he was not "on move". But now the blue player is on move with QIIIh2:Ih2 and checkmates red in fact, because the blue queen is covered from the yellow rook. Blue has won, red and yellow have loosen in common.
2b.) The alternative view: "A king is checkmated, if I checkmate it!" shortens the games indeed, because attacks against the turning direction are getting very dangerous. But this seems not to be fair, because the supposed checkmated player, who is not on move, cannot defend against the check.
2c.) A third possibility could be: "Never attack a king from both opponents!" Only the first to come can win. But why we should forbid such wonderful moves like in the example?
In our playing circles we tested a lot of different win and loose conditions, even some, I don't explain here (ever heart about the governor-principle?...). In the moment I prefer variant 2a absolutely. The criterion for checkmate is devided in two aspects: one part is the active: the first to checkmate an opposite king is the winner!, the other is the passive a king is checkmated, if it is checkmated on move! But this problem is a very hard one, and I cannot say that this is the only truth. Perhaps you have some better ideas. Lets give these variants as much as time for evolution, the FIDE-Chess had!
3.) For the star-variant matters: Never move a piece from one opponent boardthird part directly to the other opponent boardthird part! At that the pieces have to go the detour over the own boardthird part in two moves. This rule depends to the geometry of the game arrangement. These forbidden moves would break symmetry. By example the bishops would change their square colours...
4.) For the star-variant matters: If a pawn moves from the forth to the fifth rank, it can decide on witch opponents third part it continues the game! But this decision is uninversible, cause pawns never walk backwards. Please notice, you open a file against the other opponent by such a pawn move. Sometimes two opponent pawns meet on the boardthird part of the third opponent moving in the same direction. These pawns can capture each other from the back logicaly. Indeed that never happens to them in FIDE-Chess.
There are no more new rules for the star-variant. All well known FIDE-Chess-rules maintain: the double-step of the pawns out of their ground position, en-passant-capturing, promotion on the last rank, casteling... For that reason the arised postions are mostely well known, too, but the reciprocal actions inner these chesspictures are much more complex. Action and reaction are not so clear separated as they are in 2-Chess. 3-COLOR-CHESS plays non linear logical problems with the human brains, a little like fuzzy-logic. It is crazy! For our strength in Chess (ELO ~1700) it is nearly impossible to extrapolate more than one move into the future. That depends on some unusual effects not known from 2-Chess. I sum them up to the conception of diplomacy. This enrichment in Chess is really wonderful. In spite of the natural chess determinism, STAR-III-COLOR-CHESS is so damned chaotical sometimes... But to have this adventure, you have to play the game.
First there are two possible directions for attacking - in direction of moves or contrary to this. Moves against the turning direction are very dangerous for both opponents, because the not shared in player moves first (b.e. red checks blue, yellow attacks the blue queen, blue has to move his king out of the check, red is doing something, yellow captures the blue queen). Sometimes you have to help a weak opponent instead of loose with him, so you have to bind your forces on the opponents defend. If I attack an opponent's piece, I protect it against the other opponent. If you change a piece, the not concerned player keeps free from injury. You can use these effects in full cognizance to get space for attacks or to build malicios traps.
By the way, it is no object, who captures how many pieces from whom. But the loss of material has a psychological aspect - you try to revenge yourself... and make the third player overwhelming by this. So every decision about capturing is a kind of diplomacy, too.
It can be a successful opening strategy, to avoid conflicts with your opponents, keep your position closed but good developed and look for chances on both flanks against both opponents (b.e. all-around defenses from indian, french or sicilian structures), late short or long casteling (or even noone)... But if all three opponents prefer this style, the game can last a little longer without a Chess-clock. We had nearly all well known opening strategies on our III-COLOR-CHESS-BOARDS, and nobody really knows what's right or wrong.
The middle game is tactical motivated, the same way as it is in 2-Chess, but the consequences are much more unconceivable. The third player always disturb the plans in a way. At some time or other you have to change pieces. Then the diplomacy commands the both involved players in a way to unite against the third one to capture one of his pieces and balance the forces. Two weak players are stronger then one strong player is! Sometimes a weak player will be underrated. This may be his big chance. If two men struggle, the third one will profit by this! Maybe now you think: By this way there will be a balancing in the game. But people make risky decisions, they fail, they make mistakes... We never had a draw playing the star-variant yet.
If there are only few pieces left on the boards, we come to the endgame. Now you can see, who has understood the game of 3-Chess. Most times two stronger players attack the weakest more or less blindly and hope to checkmate first. Without a doubt it is better to remember the knowledge from FIDE-Chess endgames and carry on in diplomacy. An apparent attack from the own board may force one opponent to make "bad moves". Endgame knowledge is experience. But we had only a few endgames yet in III-COLOR-CHESS, so for me it is a book with seven seals.
It is a brandnew aspect in Chess, that one player in the star-variant is not allowed give up alone! If two players decide together to give it up, the third one is the winner, for sure. But one weak player alone can still be the weigher. And at all: we have had little wonders! So the common resign is a question of diplomacy.
Initiative describes in Chess, who depresses on the other one. In III-COLOR-CHESS this notion has to be differentiated. In most cases the initiative is shared to each other in unbalanced parts. It is better to increase the pressure against both opponents instead of execution against one of them. Sooner or later every defense will be destroyed by itself against two opponents.
By the way: In our game circles it is not forbidden to talk about the game while we are playing. So you can have influence on the game by psychology. While one player thinks about his next move, the two others lie like the devil. In this way you get a real party game of Chess. Don't calculate with the moves of the others, they will do something different for sure. But always have a look at the game between your opponents! Don't give one of them a good chance by mistake. The "tempo" gets a diplomatic character in this variant, too.
I told you, a draw never happened yet, because our games ended always by a player's "mistake". So you can see in the example game. It shows some important aspects of III-COLOR-CHESS, I've told you about in this chapter. Please build your own game with the (downloads and tinker-sheets) to realize the game dynamics before you try it with your friends. By the way you will learn quickly to manage the coordinate system and diagrams.
3.) For the triangel-variant matters: Every move (exepted pawn-capturing - look at rule 4.) has to be legal on all boards. (This rule prevents queens, rooks and bishops in jumping over other pieces!) If one piece is captured, the particular phantom-piece on the other board disappears, too, because it is the same piece.
4.) For the triangle-variant matters: If a pawn captures a piece, then this move may (not has to) be a legal capturing only on one board. On the other board the pawn has to be moved, as if it has captured a piece. (With this rule you get well known opening positions.)
You need no more new rules for the triangle-variant. With this you get another attractive concept for III-COLOR-CHESS. If you like tactics, you will enjoy to know, that you can calculate some moves into the future in this variant. The diplomatic calculus is still working (because you can attack against the move direction), but by far not in such a high scale as it is in the star-variant. Past games have shown that it seems to be good to break the symmetry early and not to imitate the opponent's moves. This makes the decision for moves more difficult for your opponents.
The star-variant is an OR-connection of three chessboards. By crossing the middle a piece can only attack one or the other opponent. The triangle-variant is an AND-connection, because the piece attacks both opponents by crossing the middle. With the triangle-variant the two dimensions of FIDE-Chess maintain, but the star-variant works in three dimensions.
At the start of the game you can have a consense about which variant you will play, for sure. But in our playing circle we have developed a special mode to fix the variant that will be played. As long as the players move only on their own board third, the variants don't differ from each other. Just if a piece crosses the middle, both variants are separated. That's why we think, the following simple rule is clever:
5.) The first player who moves a piece over the middle fixes the variant that will be played. If he attacks one opponent, we play the star-variant. If he attacks both opponents on the contrary, we play the triangel-variant.
By playing these two variants, the dualism becomes obvious. While I still think about, how to give up alone in the star-variant, it is most simple in the triangle-variant: put two boards away and play further on the only interesting board. But I prefer not to give up and play until one player is checkmated. While a draw nearly never happens in the star-variant, the triangle-variant is very draw suspected. In the star-variant you often don't know, which one of the many nice moves you do the best, in the triangle-variant you easy get into zugzwang...
You see, both variants are the two sides of one coin. If you think, there has to be a way to put these two variants together to a hybrid, then please remember the FIDE-Chess! Mother nature has realised many kinds of dualisms, it seems to be a natural law. One of the most known one, Albert Einstein has found in energy and matter (E = m x c²). The most obvious one exist between men and women. Which III-COLOR-VARIANT you prefer is a question of taste.