Zobrist Hashing

A hashing scheme for dealing with game decision trees and boards.

Features like board position, chess piece, and color to move, are given random bit strings.

Relevant features are XORed together to create the new hash.

Because XORing is used you can also remove features by just XORing the feature again. This makes it cheaper to update state.

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()
    table.black_to_move = random_bitstring()

function hash(board):
    h := 0
    if is_black_turn(board):
        h := h XOR table.black_to_move
    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