I had originally envisioned this variant as involving wagers, but rejected this idea because it would require an independent third party (preferably a Grandmaster) to assess the likelihood of each move and lay odds. Guessing is simpler, and results in much the same type of game play.
Before each move (including White's first move), the opponent can write down up to two guesses. Since there's no penalty for guessing, you should always make two guesses. A guess can be in one of two forms: You can guess which piece will be moved, but not guess where it will be moved; or you can guess both the piece and its destination. If you guess both the piece and its destination correctly, you earn more Zorkmids -- but if a piece/destination guess is correct as to the piece but incorrect as to the destination, you receive no Zorkmids at all. Guessing just the piece and not the destination is safer, but the rewards are smaller.
Since you're allowed to make two guesses before each of your opponent's moves, it's legal to guess the same piece twice, with two different destinations or once with a destination and once without. The two guesses are evaluated independently. You could even make the same piece/destination guess twice, if you're feeling cocky (or desperate for some cash). However, if your opponent's king is in check and there is only one legal move that will remove the check, you earn a flat 3Z: No guessing is required or allowed, and you don't earn extra for guessing the move twice.
What's interesting about this procedure, aside from the variables that are introduced during play, is that when Clairvoyant Chess is played by good players, there's an incentive to make unexpected moves so as to deprive your opponent of a few Z. Knowing you're thinking this way, your opponent may then make a "less likely" guess. That's why true clairvoyance may be as useful as a knowledge of chess tactics.
The exact value of correct guesses will probably need a little tinkering. Ideally, one would want to allow each player to gain enough Z to be able to purchase something once in every six or eight moves. Note that you must always guess the exact piece that will be moved; guessing "a knight" or "a bishop" is not allowed. Here are my preliminary suggestions:
Predicting that a particular pawn will move is worth 3Z. (No extra points for predicting which square it will move to.)
Predicting a knight or bishop move: 5Z. Predicting the move and the destination square: 9Z.
Predicting a rook move: 7Z. Predicting the move and destination: 12Z.
Predicting a king or queen move: 9Z. If the king is in check and has more than one legal escape move, but the player has no other way to remove the check except by moving the king, predicting that the king will move is worth only 1Z, and you can't make this guess twice to earn 2Z. Predicting the king's destination, however, if he has more than one legal escape square, earns the normal value for the guess. Predicting a royal piece's move and destination: 10Z for king, 15Z for queen. Castling is considered a king move, but predicting the king's destination has no extra value.
When spending your Zorkmids, the values below are suggested. When buying a piece to drop onto the board, you buy before your turn and drop immediately. The drop occurs in place of a move, and a piece cannot be dropped in such a way as to check the enemy king. When buying an extra move in a turn, you can either move the same piece twice, or move two different pieces. In either case, the second move is always the one paid for. Normally you'll prefer to move the less expensive piece second, but if the first move unblocks a piece, you may need to move the less expensive piece first. If your first move in a turn checks the enemy king, you can't buy a second move by the same piece; nor can you buy a second move that also checks the enemy king to create a double check; but you can check the king with your first move and then buy a second move that eliminates a way of removing the check (or even turns the check to a checkmate).
Buying three or more moves per turn is not allowed. You can, however, buy and drop two or more pieces per turn, or buy and drop a piece and then buy a move for it in the same turn.
Buying a new knight or bishop: 12Z. Buying a rook: 15Z. Buying a queen: 25Z.
Buying an extra move (capturing or not) for a pawn: 3Z.
An extra non-capturing move for a knight or bishop: 7Z. An extra capturing move: 15Z. (Note that since the second move in any given turn is the one that is bought, you can capture with the first move of a piece and then buy a second, non-capturing move to retreat.)
An extra non-capturing move for a rook: 9Z. An extra capturing move: 16Z.
An extra non-capturing move for a queen: 12Z. An extra capturing move: 20Z.
An extra non-capturing move for the king: 3Z if not in check, 7Z if in check, 11Z if the first move is into check and the second move is out of check, or if the first move in the turn is by another piece that leaves the king in check. An extra capturing move by the king: 9Z.
Forcing the opponent to retract a move and choose another: 8Z. Forcing retraction of a checking move: 12Z. Forcing retraction of a move that eliminates a check: 15Z. (This is only allowed if the opponent has another legal move that eliminates the check. You're not allowed to refuse a move that is the only way the opponent can remove the check.) Note that if you have enough Zorkmids, you can force two or more retractions in a single turn.
Clairvoyant Chess (c) 2001 Jim Aikin.