What are the rules of Quantum Chess? The game Quantum Chess, as seen in the video where Paul Rudd defeats Hawking, has no "set of rules" written down. You either have to do the in-game tutorial, watch a video on the game and pick them up.

So what are the rules of Quantum Chess?

This refers to the game (currently only available on steam) created by Chris Cantwell.
The board and pieces


Quantum chess is played on a regular 8x8 chess board with standard pieces.
Pieces have rings around them, filled in with colour. These rings show the probability that the piece is in that square.


Modifications to existing chess rules


A player is not required to move their king out of check and the game concludes when there is a 100% probability that one of the kings has been taken. As a result there is no checkmate.
All promotions result in a queen as of 10/8/17, since underpromoting has not been implemented into the game.


Movement


All pieces move as usual in normal circumstances.
On any given turn, the player can make one quantum move instead of a normal move.


Quantum moves


Quantum moves are notated with the ^ symbol. (e.g: N^d4)
When quantum moving a piece, it can make up to two normal moves.
The probability of the piece moving is equal to the probability that the piece has not moved, resulting in a superposition of multiple board states.
A quantum move cannot be used to take a piece.
Pawns cannot make quantum moves.




Superposition


When any quantum move is made, that piece exists in multiple places simultaneously. This is represented by multiple copies of the piece displayed, with appropriate meters to show the probability of finding the piece in that square. There is only one piece, but it can exist in one of multiple places.
If a piece "takes" one of the copies of another piece in superposition and has  100% probability of being available to take it, the piece is taken if it was in that square. Since there is a probability of the piece being in other squares, those copies of the piece remain, however there is now a chance that the piece has already been taken and is no longer on the board.





If a piece "takes" one of the copies of another piece in superposition and it is not certain that the piece was available to take it, a measurement occurs. A measured piece will collapse onto one square using a random selection. The probability of it collapsing onto a particular square is the same as the probability that is was moved there. All pieces that are entangled with the measured piece will also be measured and may have their outcome influenced by the measurement of the piece(s) that they are entangled with.





A pawn can be put into superposition if it takes a piece which is in superposition. If the piece was there, the pawn could take it. If not, moving diagonally was an illegal move. The probability of the pawn being on the new square is the same as the probability that a piece was there to be taken.





A pawn can also be superimposed by moving two spaces forward, through a square which may contain a piece. This results in entanglement.




Entanglement


Entanglement occurs when a piece attempts to move through an instance of a piece in superposition. The probability of the moved piece existing in its new square is the same as the probability that the obstruction was not there to block it.
If a piece is entangled with another piece and is measured, both pieces are affected by the results of the measurement accordingly.




Special circumstances

The following "rules" are combinations of rules from above, however they are worth mentioning as useful tactics:



Quantum Trading


It is possible to trade probabilities of pieces, leading to complex trading. For example, it is possible to trade knights in a way which leaves one player with a 2/3 chance of having a knight, and the other with a 1/3 chance of having a knight. The first player is more likely to have benefited from this trade, however it is uncertain until measured.


Schrödinger's King


If the king is in superposition and one of the instances is taken, the probability that that player has lost is equal to the probability that the king was in that square. Since it is not certain that they have lost, play continues.
This means that it is possible for a player to win a game with a probability that they have already lost by fully capturing the opposing king.




Ghost capture


This is a result of a pawn taking a piece in superposition. If there is one other state of the taken piece still on the board and a piece attacking it, ghost capture can take place. If the attacking piece must move through the square where the pawn would be if it hadn't moved in order to attack the superimposed piece, two outcomes can occur:


The measurement confirms that the piece had not moved, so an attack is impossible and the opposing player gains "half a piece".
The measurement shows that the piece has moved and has already been taken, so the opposing player loses "half a piece".





Quantum Castling


If there is a probability that a piece is between the king and rook, the probability of castling is equal to the probability that the piece was not there. A measurement may take place if two pieces end up on the same square.
If there is a probability that the rook may have moved, castling can occur with the probability that the rook is available to castle. The king and rook are now entangled since the castling move depends on whether the rook was on the correct square.


Double Castling


After a quantum castle, the king can castle the other way if the rook is available, with the probability of castling being the probability that the king is there.


In this example, both sides have castled both ways: