Here is a description of a chess variant I'll call Fresh Chess. It involves the following rule changes:
Before the game, each player secretly records the opening positions of his pieces in the first rank. He can place them anywhere, even with both bishops on the same color (as in Shuffle Chess). The second rank is always a row of pawns.
The conditions for castling are the same as in standard chess:
To castle, the king moves two or more squares towards the rook (but not onto the rook's square), and then the rook is placed on the square adjacent to the king on the opposite side.
There may be more than two possible ways to castle. For example, if you start your king on h1 and your two rooks on a1 and d1, then once the back rank is clear of intervening pieces and check, you may castle to either of two spaces (e1 or f1). If you move your central rook, you may castle to any of five spaces! On the other hand, if there are less than 2 spaces between rook and king, you can't castle.
No piece except a king may ever "undo" the previous move. If a player moves a piece from square A to square B, on that player's next turn he may not move the same piece from B to A. Threefold repetition and perpetual check thus become more difficult. This rule only applies to the prior turn - on a subsequent turn, you can move back.
A draw is worth as little as a loss: 0 points. This discourages players from giving up when a win might be possible.
Few players know that stalemate was not always considered a draw. The goal of a chess game is not checkmate; it is to kill the enemy king, but not by surprise. Stalemate is the equivalent of capturing the king without killing him - also a victory.
In the modern game, stalemate is a loophole in a winning position, a trick to avoid defeat. But why would we want that? We prefer games to end in a win, not a draw! Considering stalemate as a win makes many now-drawn endgames decisive, which is a good thing.
In a classical game, the players usually have 90 minutes for the first 40 moves, followed by 30 minutes for the rest of the game, with an addition of 30 seconds per move starting from move one. Because of this rule, players who are running low on time may make silly moves in order to reach time control, when they'll have more time. Why would we want that?
Better would be to have a single increment, for example 2 minutes per move. Each player starts with 2 minutes on the clock, and gets another 2 minutes every time he hits his button on the clock. His time accumulates, so if he only needs 1 minute for his first ten moves, he'll have 19 minutes on his clock after that. There's no longer any motive for silly moves.
Other time formats would have smaller increments: a blitz game may offer only 5 seconds per move.
The grade is a secondary measure of the quality of a chess game. As in real war, minimizing your loss of material and the time required enhance a victory. To calculate a grade, add the values of the winner's remaining pieces (with no account taken of position or the stage of the game) and divide by his number of moves:
As is clear, an early checkmate with a lot of material still on the board will be graded higher than a long drawn-out endgame.
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