Thue-Morse (Fair Sharing) Sequence: A possible alternative to komi?

Go Variants
113

This is my move tracker:

def thueMorse(n: int) -> int:
    return bin(n).count('1')%2
thueMorse_move = 0
move_number_to_thueMorse_move = ""
thueMorse_sequence = ""
for i in range(10000):
    if (i%2 == thueMorse(thueMorse_move)):
        if i%2:
            thueMorse_sequence += 'W'
            move_number_to_thueMorse_move += "W"
        else:
            thueMorse_sequence += "B"
            move_number_to_thueMorse_move += "B"
        thueMorse_move += 1
    else:
        move_number_to_thueMorse_move += "_"


def on_move(msg):
    game_id = msg["game_id"]
    move_number = msg["move_number"]
    game = active_games.get(game_id, None)
    move_numbers[game_id] = move_number
    if game is None:
        return
    # Thue-Morse
    if "Thue-Morse" in game["name"] and game["handicap"] == 0:
        is_black = (game["black"] == player_id)
        is_white = (game["white"] == player_id)
        if (is_black and (move_number % 2 == 0)) or (is_white and (move_number % 2 == 1)):
            if move_number_to_thueMorse_move[move_number] == "_":
                game_pass(game_id)
        if move_number % 10 == 0:
            game_chat(game_id, "next 30 moves: " + move_number_to_thueMorse_move[move_number:move_number + 30],
                      move_number)
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