Progressive chess is a chess variant in which players, rather than just making one move per turn, play progressively longer series of moves. The game starts with white making one move, then black makes two consecutive moves, white replies with three, black makes four and so on.
There are two main varieties of progressive chess: Italian progressive chess and Scottish progressive chess (otherwise known as Scotch chess). The two have the following rules in common:
A check must be escaped from on the first move of a series--if this cannot be done, it is checkmate and the game is lost.
En passant captures of pawns are allowed if the pawn in question moved two squares in one move, but no further, at some point during the last turn , but the capture must be made on the first move of a series.
If ten consecutive turns are played with no captures and no pawn moves, then the game is declared a draw unless one of the players can force a checkmate (this is the progressive chess equivalent of the fifty move rule in orthodox chess).
If at any stage a player has no legal moves but is not in check, the game is a draw by progressive stalemate.
Italian and Scottish progressive chess are distinguished by rules on when a player is allowed to give check:
Scottish progressive chess: check may be given on any move of a series, but a check ends the series--all further moves that would otherwise be allowed are forfeited. This has no effect on the other player's next series--he will receive as many moves as he would have had the other player played his full series.
Italian progressive chess: a check may only be given on the last move of a full series (for example, on move six, a check can only be given on the sixth move)--giving a check at any other point in a series is illegal. In particular, if the only way to escape a check is to give check on the first move of the series, then the game is lost by the player in check by "progressive checkmate".
Progressive chess, like orthodox chess, is notated with algebraic notation. However, the numbering of moves is handled slightly differently. Rather than one white and one black move being given under each move number (leading to notation in orthodox chess like 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6), each move by each player is given its own move number (leading to notation in progressive chess like 1.e4 2.e5 Nf6 3.Bc4 Qh5 Qxf7#). In this way, the move number is equal to the number of moves in a series available to a player on that turn.
There is another form of progressive chess, English progressive chess, which makes quite a significant change to the rules: within each turn, no piece may be moved twice until every other piece which has a legal move has moved once; no piece may move three times until every other piece which can has moved twice; and so on. These restrictions do not carry over from one move to the next--so the opening 1.e4 2.e6 f6 3.e5 Nf3 Bc4 is legal (white's e-pawn may move again because its moves are on different turns), but the sequence 1.e4 2.e6 f6 3.e5 Ba6 Bxb7 is not (the bishop has made two moves, but there are many other white pieces which have not moved on that turn). There is no en passant capture under English rules, and rules on checks follow the Scottish rules.
Progressive chess can be combined with other variants; for example, when circe is played as a game, it is usually progressively.