Draft:Entanglement Chess

Entanglement Chess (originally known as Haft Schroedinger Chess) is a chess variant where all the pieces start in a quantum superposition, with all pieces being "entangled" with each other a la quantum entanglement. Each player starts with the standard chess army composition (8 pawns, 2 rooks, 2 bishops, 2 knights, 1 queen, 1 king), but the starting positions are not set. However, this game doesn't not contain any hidden information - instead, the pieces actually do not have locations until they are observed (in this case, by making moves). This game originally existed as a thought experiment, as the rules are prohibitively difficult to implement on a physical board. However, multiple people have created software implementations.

Rules

Other than the rules of entanglement and superposition that will be described later, there are only 3 divergences from the rules of conventional chess, all of which enable the entanglement mechanics. 1) Castling is not permitted 2) En passant is not possible 3) When pawns reach the back rank, they promote, but the player does not declare what the pawn promotes to. Instead, the promoted pawn's identity will be determined by any subsequent moves and entanglements it develops.

The main difference between Entanglement Chess and conventional chess is that in Entanglement Chess, pieces do not have a known identity until they are determined during gameplay. The game is based around the notion that whatever identity a piece ultimately has, it would have been able to have been for the entire game. That is to say, if a piece ultimately turns out to be a rook, if the piece had been a rook from turn 1, the game would appear to be legal according to the rules of chess, including the "rules" about piece count.

Since pieces can have multiple possible identities, piece identities in Entanglement Chess are shown via various symbols that can freely overlap each other. For instance, a piece shown with a circle, square, and plus could be a pawn, rook, or king, but no other piece.

The following diagram will show how waveform collapse and entanglement works.

In the above diagram the moves 1) a2a5 h7h4 2) b2b5 g7g4 3) c2c5 have been played. These all are moves that could only be made by a rook or queen. In the case of white, this means that collectively, the three moved pieces represent 2 rooks and a queen. As such, all of white's remaining pieces can no longer be a rook nor queen as, even though the specific identities of the moved pieces are unaccounted for, it is known that no other rooks or queens can exist among white's pieces. Black, on the other hand, has either moved 2 rooks, or 1 rook and 1 queen, and thus black's remaining pieces retain all possible identities.

White's pieces on a5 b5 and c5 are currently strongly entangled, as collectively they are 2 rooks and 1 queen. If a5 were to make a diagonal move, it would be revealed as a queen and the other two pieces would be revealed as rooks. The same goes for if either of the other two pieces were to make diagonal movements.

Also of note are the pieces on a7,b7,b7,g2,h2. These pieces can no longer be kings. This is because, regardless of whether the moved pieces turn out to be rooks or queens, these pieces ended their turn while threatened, which a king is unable to do.

This diagram also subtly shows other forms of entanglement. To provide one example, the piece on d7 is entangled with the piece on b5. The piece on b5 can either be a rook or a queen. If b5 is a queen, d7 is attacked. If b5 is a rook, d7 is not attacked. Given that black ended turn in this position, it cannot be true that b5 is a queen and d7 is a king, or else black would have illegally ended turn in check. Thus, b5 and d7 are now entangled - if b5 is later found to be a queen, d7 will no longer be able to be a king. Conversely, if d7 is found to be a king, b5 will be revealed as a rook.

Thus, all pieces of the same color are entangled with each other via piece count entanglement, and pieces are entangled with opponent's pieces via check entanglement.