Best Tic-tac-toe starting position

solution.py

from functools import lru_cache


def straight(board, i):
    return (
        board[i][0] == board[i][1] == board[i][2] is not None
        or board[0][i] == board[1][i] == board[2][i] is not None
    )


def across(board):
    return (
        board[0][0] == board[1][1] == board[2][2] is not None
        or board[0][2] == board[1][1] == board[2][0] is not None
    )


def update(board, y, x, value):
    return board[:y] + (board[y][:x] + (value,) + board[y][x + 1 :],) + board[y + 1 :]


@lru_cache(maxsize=None)
def outcome(board, turn=False, *, win):
    if any(straight(board, i) for i in range(3)) or across(board):
        return win != turn
    return sum(
        outcome(update(board, y, x, turn), not turn, win=win)
        for y in range(3)
        for x in range(3)
        if board[y][x] is None
    )


def find_ratio(pos):
    board = update(empty_board, *pos, True)
    return outcome(board, win=True) / outcome(board, win=False)


cache = {}
empty_board = ((None, None, None),) * 3
print(max([(0, 0), (0, 1), (1, 1)], key=find_ratio))