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Here's how I think two move chess could work, so that the game doesn't end instantly:
1. Each player has two moves per turn
2. If your first move puts the opponents king in check, your turn is over (possible checks are not automatically checkmate)
3. Your king can only move once per turn (this includes castling) (makes checkmating in a lost endgame simpler and doable) The king is allowed to move either of the 2 moves.
4. You are allowed to move a pinned piece from king as long as your second move absolves the resulting check. (this means it will be harder to deliver checkmate in this variant)
5. Checkmate results from you being unable to move your king out of check by the second move. (remember, you can only move your king once per turn)
6. Once the first move is made, you cannot take it back.
7. If the first move is made and the player is unable to absolve any resulting check, that player is now checkmated and loses
8. You cannot move your king into a check (i.e. you cannot move your king into a check and then block the check for your second move-- inter-move checks are only possible with pinned pieces).
9. Due to the previous rule, normal rules involving castling apply. (if your king cannot move through check to castle)
10. If it is a player's turn and there are no legal moves on the first turn, the game results in stalemate.
11. Players must make 2 moves each turn, even if the second move forces stalemate.
12. All other chess rules apply
Give it a try, it results in a dynamic, instantly crazy game of chess. Let me know if you think any other rules should apply (such as allowing white only one move to start the game).