For every turn, play your move and also announce to your opponent what your next move will be. (The move you just played would have been announced the previous turn, so any thinking you did this turn would have been about what to announce, not the move played.)
Both players could play like this, or just one player, as a handicap. The opponent gets a sense of what their opponent is about to do next, before they do it, and can "react" ahead of time. Note that the announced next move must be played regardless of the opponent's "reaction" a half move earlier. This is a huge handicap (when done only by one player), not dissimilar to the experience of villains facing Spider-Man's precognition.
If both players do this, then the game simply becomes normal chess with moves shifted in time by one move. For the rest of this discussion, we assume that only one player is doing this, as a handicap.
The announcement of the next move does not have to announce whether or not it will be a capture. If the destination square was occupied (intending capture) but is now empty, simply move to the destination square. The villain punches into thin air because the Spider-Man had dodged ahead of time.
Suppose the next turn comes around and the previously announced move is not possible. (We probably need a restriction that the announced move needs to be possible in some line of play.)
If the announced move has become not possible is because it would leave the player's own king in check, then the player loses (or can lose). Equivalently, let king capture be legal.
If it is a ranged piece whose movement is blocked, the piece should go as far as possible toward the previously announced destination square. This will typically be a capture. Two-square pawn advance moves might become just one square.
Not sure what to do if the announced move was a one-square pawn advance that is now completely blocked.
Not sure what to do if it was a pawn capture of a square now empty, or en passant capture did not become possible. Things would be simpler if pawns captured the same direction they move.
Not sure what to do if the announced piece has been captured. Some of these cases might be straightforward if passing were permitted.Even though stalemate is mostly eliminated with king capture being legal, it is theoretically possible. Not sure what to do about it.
Design a chess variant in which announcements don't have these problems.
Announce the next move and a backup move if the first move is not possible. If neither move is possible, the player loses.
Announcement could be done not every move but only when the opponent invokes the privilege, with some limit on frequency. Spidey sense can only be turned on occasionally.
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