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A chess engine builds a Zobrist key by XORing pseudorandom values assigned to the position’s active features: which pieces occupy which squares, whose turn it is, castling rights, and en-passant availability. Because XOR reverses itself when the same value is applied again, the engine can update the key as a move changes the position instead of rebuilding it from scratch. The key lets a transposition table look up previously searched positions, but it is a compact signature—not proof that two positions are identical.
What a Zobrist key represents
A Zobrist key is a fixed-width fingerprint of relevant chess state. It is not a complete board encoding: many possible positions are represented by values drawn from a finite set of keys, so two distinct positions can theoretically share one.
The key must represent more than the visible arrangement of pieces. A typical chess position hash includes:
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- Each piece type on each square.
- The side to move.
- Castling rights.
- En-passant availability, usually represented by the file on which an en-passant capture is possible.
These details matter because positions that look alike on the board can have different legal moves or game states. Omitting state that affects play can cause an engine to treat distinct positions as equivalent.
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How the key is constructed
Assign reproducible values to features
At initialization, an engine generates pseudorandom bit strings for the position features it tracks. In one common scheme described by the Chess Programming Wiki, there are 781 values: 12 piece types × 64 squares, one side-to-move value, four castling-right values, and eight en-passant-file values. This is a conventional count, not a required constant; some implementations encode the 16 possible castling-right combinations directly instead of using four separate values.
Engines often use a local pseudorandom generator so that the values are reproducible across platforms. Stable keys are useful when other data, such as an opening book, is indexed by position.
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XOR the active values
Start with a zero key and XOR the value for each feature that applies. For example, the initial key combines the values for all pieces on their starting squares, the side to move, the current castling rights, and any applicable en-passant state.
XOR is useful because applying the same value twice cancels it: x ^ y ^ y = x. This property makes it straightforward to add or remove a feature from the key. The approach is a form of tabulation hashing: feature values are looked up and combined with XOR.
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How a move updates the key
Rather than scan the whole board after every move, an engine updates only the feature values affected by that move. For a white knight moving from b1 to c3 and capturing a black bishop, the update XORs out the white knight on b1, XORs out the captured bishop on c3, XORs in the white knight on c3, and toggles the side-to-move value.
Other moves must account for every changed feature, not just piece locations:
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- Captures: remove the captured piece’s piece-square value.
- Castling-right changes: XOR out the old rights value and in the new one when a king or rook move, or a relevant capture, changes those rights.
- En passant: update the en-passant state when a move creates or removes an en-passant opportunity; an en-passant capture also removes the captured pawn from its actual square.
- Promotions: replace the pawn’s piece-square value with the promoted piece’s value on the destination square.
- Side to move: toggle the side value after each legal move.
Because XOR is its own inverse, unmaking a move can restore the previous key by applying the same changed feature values again. The engine’s make and unmake logic must keep the key synchronized with its board and other state.
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How engines use the key in a transposition table
Different move orders can reach the same position. A transposition table stores information from positions already searched so the engine can avoid repeating work. An entry may contain a key signature, a best or refutation move, search depth, score, bound type, and age.
- Choose a table slot. The engine reduces the position key to an index, often with modulo or by masking low bits when the table size is a power of two.
- Probe the entry. It checks the stored signature against the queried key information. The exact amount stored varies by implementation.
- Decide whether the result is usable. A sufficiently deep entry with an exact score or a suitable lower or upper bound may support an alpha-beta cutoff.
- Order moves when a cutoff is unavailable. The stored move can still be tried earlier, potentially improving search ordering.
The table cannot hold an entry for every possible position key, so several keys may map to one slot. A stored signature helps detect when a slot contains a different key than the one being probed.
Can Zobrist hashes collide?
Yes. It helps to distinguish two different cases:
- Index collision: different full keys reduce to the same table slot. This is expected in a bounded table; replacement rules determine which entry remains. Comparing the stored signature catches many such mismatches.
- Full-key collision: two distinct positions produce the same finite-width key. No comparison of that same full key can distinguish them. Wider keys reduce the probability, but do not make the hash mathematically unique.
The Chess Programming Wiki describes 64-bit keys as usual in modern chess programs. That size makes a full-key collision a low-probability risk, not an impossibility. A bounded, replacement-based table also does not retain every position ever examined, so collision exposure cannot be inferred simply by treating all searched positions as simultaneously stored.
Origin of the method
Albert L. Zobrist’s A New Hashing Method With Application for Game Playing is University of Wisconsin Technical Report #88, dated April 1970. The university record describes a general hash-coding method for game-playing programs, including chess, checkers, and Go, and notes an auxiliary method for detecting retrieval errors. The university report record preserves its bibliographic details.
The method was later reprinted in the 1990 ICGA Journal; its notes say it was refined in 1971 for subsets of the chessboard in the Zobrist–Carlson–Kalme chess program. The implementation patterns described here reflect modern chess-programming practice, rather than a claim that every engine uses identical tables or update code.
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