The Time Thief explained OVERRULED BY V2 SORRY

The Time Thief moves like a Queen.

The Time Thief can be captured by other pieces. But the Time Thief itself cannot capture other pieces in a normal way.

However, the Time Thief has a special way of postponed capture:
If an enemy piece is in reach of the Time Thief, and does a move, the Time Thief can as response revert the entire move and then capture the piece.

In this diagram, the black Rook is in reach of the white Time Thief. Suppose Black plays Rf2.

As response, the white Time Thief can revert Black's previous move. So it would move the black Rook back from f2 to f7. And then it can capture the black Rook on f7. As a result this would be the position:

The Time Thief must do this capture on the very next turn, or the right to do so is lost!

The Time Thief cannot revert a move after being captured itself:

After Rxh3, the Time Thief is off the board, and has no powers to revert that move and capture the Rook.

If the Time Thief reverts a move, it reverts all aspects and everything what happened with that move. It really turns back time.

In this diagram, Black might play Rxi7. The Time Thief can revert that move and capture the Rook on f7, but that also means that the Queen comes back on the board on i7 : the Queen is restored by the Time Thief.
After Rxi7 TTxf7:

In the following diagram, Black has just played pawn f7-f5:

Before f7-f5 was played, the Rook was in reach of the Time Thief. but the Rook did not make any move. So the Time Thief cannot capture the Rook.
The pawn did move, but did not come from a square in reach of the Time Thief. So the Time Thief can also not capture the pawn.

Conditional check is the situation, that a King is in check, but the Time Thief is able to restore the King after the King is captured (see also "Limited Time Thief" at the bottom of this post).

In this position, with White to move, the white King is in check. But it is conditional check: after Nxe1 the King can be restored with TTxf3. It is legal to leave your King in conditional check, but only if you would be able to restore the King safely(*) after the King would be captured.

(*) Safely means: after restoring the King, the King is not in check or again only in conditional check.

So in the previous position, it is legal if White plays ixj7. But then after a King capture, it is obligatory to actually safely restore the King.

In this position, it is also conditional check. But the Time Thief is pinned. It is illegal for White to play ixj7 here. After Nxe1 TTxf3, the King would be in check from the black Bishop.

Suggestion:
If such an illegal move is made, because a position is complex and it is difficult to understand if the conditional check is legal or not, allow the King to be taken. Let the game continue with ixj7 Nxe1 TTxf3 Bxe1 and declare the game lost for White.

In other words: If a player loses his or her King, because the illegality of a conditional check has not been seen, than that player loses the game.

In this diagram, White has no legal move and it is stalemate. It is not mate, because the check is only conditional.

If the White player now fails to recognize this and plays e.g. Ne3, I can suggest to allow the game to continue with Qxj1 TTxj2 Rxj1. But then White loses the game, instead of recognizing and claiming the Stalemate.

If it was Black's move in the same position, let's look at Rxd1 and see what happens:

White is now stuck in an illegal/unresolvable conditional check position. We consider this mate.

In this diagram, Black is in check and White is in conditional check. Black cannot play Nxe1. After Nxe1, White would be obligated to restore his King, but meanwhile the white pieces still give check. Black must first get out of check before playing Nxe1.

A King in reach of an enemy Time Thief, is not yet in check.

White to move here. With any move by the White King, White would put himself in check, because it allows that the black Time Thief will capture the white King. This position would be Stalemate, as White has clearly no legal moves left.

The same position with black to move: Ke4#!

Black is only in conditional check (Kxe4 TTxd4), White is mate and Black wins.

Limited Time Thief
It is possible to agree with your opponent, prior to your game, that the Time Thief cannot restore the King, and that there is no such thing as conditional check. By doing so, the Time Thief would become substantially weaker, and from certain positions, the outcome of the game might be very different due to this limitation. Without this prior agreement, the default abilities of the Time Thief include restoring a King and conditional check.

Confusing...

That is the whole idea of conditonal check. Black is allowed to move in a conditional check. Black's King is protected by the fact that, should the White King take the Black King, the black Time Thief can restore the Black King.

I wish to take one more look at the concept of conditional check. I am copying the earlier rules and below add one comment.

"

Conditional check is the situation, that a King is in check, but the Time Thief is able to restore the King after the King is captured (see also "Limited Time Thief" at the bottom of this post).

In this position, with White to move, the white King is in check. But it is conditional check: after Nxe1 the King can be restored with TTxf3. It is legal to leave your King in conditional check, but only if you would be able to restore the King safely(*) after the King would be captured.

(*) Safely means: after restoring the King, the King is not in check or again only in conditional check.

So in the previous position, it is legal if White plays ixj7. But then after a King capture, it is obligatory to actually safely restore the King.

In this position, it is also conditional check. But the Time Thief is pinned. It is illegal for White to play ixj7 here. After Nxe1 TTxf3, the King would be in check from the black Bishop.

Suggestion:
If such an illegal move is made, because a position is complex and it is difficult to understand if the conditional check is legal or not, allow the King to be taken. Let the game continue with ixj7 Nxe1 TTxf3 Bxe1 and declare the game lost for White.

In other words: If a player loses his or her King, because the illegality of a conditional check has not been seen, than that player loses the game.

In this diagram, White has no legal move and it is stalemate. It is not mate, because the check is only conditional.

If the White player now fails to recognize this and plays e.g. Ne3, I can suggest to allow the game to continue with Qxj1 TTxj2 Rxj1. But then White loses the game, instead of recognizing and claiming the Stalemate.

If it was Black's move in the same position, let's look at Rxd1 and see what happens:

White is now stuck in an illegal/unresolvable conditional check position. We consider this mate.

In this diagram, Black is in check and White is in conditional check. Black cannot play Nxe1. After Nxe1, White would be obligated to restore his King, but meanwhile the white pieces still give check. Black must first get out of check before playing Nxe1.

"

I think that these rules are not good. Not logically consistent and not finalized.

Without the concept of conditional check, the words mate and stalemate are very well defined. And the conditions under which one player wins or both players draw, are very clear.

But while trying to introduce "conditional check", these winning / drawing conditions have become messed-up. And this is demonstrated by the most tricky diagram where I claim that White can claim "stalemate".

Conclusion

For now, what I above call "limited Time Thief" must the official one. If there exists a version of the Time Thief that can revert King capture, it's current status is at best under construction.