Zobrist Hashing, a technique to transform a board position of arbitrary size into a number of a set length, with an equal distribution over all possible numbers. - chessprogramming.org

wikipedia: Zobrist hashing starts by randomly generating bitstrings for each possible element of a board game, i.e. for each combination of a piece and a position… Now any board configuration can be broken up into independent piece/position components, which are mapped to the random bitstrings generated earlier. The final Zobrist hash is computed by combining those bitstrings using bitwise XOR.

Updating hash

Because of XOR properties, the hash can be delta updated:

• by xoring (out) the bitstring of removed events,
• by xoring (in) the bitstring of new events. Xoring in/out being the same XOR operation, it onlys express the intent.

Pseudo code

Example pseudocode for the game of chess

constant indices
    white_pawn := 1
    white_rook := 2
    # etc.
    black_king := 12

function init_zobrist():
    # fill a table of random numbers/bitstrings
    table := a 2-d array of size 64×12
    for i from 1 to 64:  # loop over the board, represented as a linear array
        for j from 1 to 12:      # loop over the pieces
            table[i][j] := random_bitstring()

function hash(board):
    h := 0
    for i from 1 to 64:      # loop over the board positions
        if board[i] ≠ empty:
            j := the piece at board[i], as listed in the constant indices, above
            h := h XOR table[i][j]
    return h

References

• Zobrist Hashing - You won’t be encountering this algorithm until and unless you are facing a really large board. Some thing like 8x8 (chess) or 16x16 (ultimate tic-tac-toe)
• An Efficient Work Distribution Method for ParallelBest-First Search
• Transposition Table and Zobrist Hashing
• Zobrist Hashing
• Correctly Implementing Zobrist Hashing
• Zobrist Hashing