In three-player chess every player play against every other player. All three players have differently coloured pieces. The three colours on this site are white, red and black.
This page describes the general rules of three-player chess. It does not cover the shape of the board and the movement of the pieces because there are many possibilities (see: Three-player chess variants). Here we illustrate the rules on an 8x8 standard chessboard, but those are also valid on all kind of boards.
All other rules not mentioned here can be found at: Rules of Chess.
White moves first, then Red, then Black, and this move sequence repeats. This move order is always counterclockwise.
A player is in check when there is another player who, were to move, could take the first player's king. It is forbidden to make a move resulting being in check, even when the other player who could take the king is not the next player.
The game ends when the next player in the move order cannot make a valid move. If the player is also in check (so checkmated), then this player loses and gets 0 points. The player who could capture the king wins and gets 1 point. The third player gets 1/2 points. If in a checkmate position both opponents could take the king, the winner is who comes first in the move order (because that player could take the king first).
Red checkmated White.
White is checkmated. Black wins as Black checked White.
Red checked White, but Black comes next. If Black does not move the rook, then White comes next and loses from Red. If however Black moves away the rook (or into the check line), then White is saved this time.
White is checkmated by Black. The white king cannot capture the queen as then it were in check by the red bishop. If the move order were different, then the red bishop could take the queen, but in this order the game ended before that.
White is checkmated. The king is in check by both other players, but Red is the winner because red comes next after White.
It seems that both Red and White are checkmated by Black. However, White comes first after Black, and cannot make a legal move. Therefore White loses the game immediately, and Red survives.
Even when we adhere to the check-rule, positions can arise when the king could be captured. Look at the following board:
If Red moves away the bishop, White becomes checked. However after Red, Black comes, who is able to take the king without White having any chance to move it away. In such situations Black wins automatically (after Red moves away the bishop).
In a hopeless situation a player can resign the game, but resigning in a three-player game is not so simple. Here when someone is going to lose it is generally not obvious who will be the winner. Resigning is discouraged as for the other two players the game can be still interesting. Even when we resign we have to tell which player we resign for (who we think the winner is). This have to be accepted by the third (non-winning) player.
The game can also end in a draw similarly to standard chess. When a draw happens all three players get 1/2 points. The fifty-move rule applies to fifty rounds, so fifty times three moves at all.