strategy X

box_game.py

"""python proof for: https://www.youtube.com/watch?v=eivGlBKlK6M

100 boxes randomly containing numbers 1-100.

50 choices per player.

100 players numbered 1-100.

all players must find their number in a box to win.

random selection strategy vs strategy X (use -x on the cmd line to enable)
"""


import sys
import random


class Game(object):
    """A complete playthrough of 100 players playing the game."""

    def __init__(self, strat_x=False, players=100):
        numbers = list(range(1, players + 1))
        random.shuffle(numbers)
        self.boxes = {
            box: num for box, num in zip(range(1, players + 1), numbers)
        }
        self.strategy = self.strat_x if strat_x else self.random_strat
        self.players = players
        self.selections = None
        self.wins = 0

    def strat_x(self, player, previous):
        """Perform strategy X for a player.

        Args::

            player: the player's number
            previous: the previous result selected by this player, or None
        """

        return self.select(player if previous is None else previous)

    def random_strat(self, player, previous):
        """Use random selection for all players."""

        return self.select(random.choice(list(
            set(range(1, self.players + 1)) - set(self.selections)
        )))

    def select(self, box):
        """Returns the number inside of the box and tracks the selection."""

        self.selections.append(box)
        return self.boxes[box]

    def play(self):
        """Plays the game for self.players using self.strategy."""

        for player in range(1, self.players + 1):
            self.selections = []  # reset this players choices
            choice = None
            while len(self.selections) <= 50:
                choice = self.strategy(player, choice)
                if choice == player:
                    self.wins += 1
                    break

        if self.wins == self.players:
            # print("all players have won the game")
            return 1
        else:
            # print("some players lost the game :/ {} wins/{} players".format(
            #     self.wins, self.players
            # ))
            return 0


if __name__ == "__main__":
    WINS = 0
    GAMES = 1000
    STRAT_X = "-x" in sys.argv
    for _ in range(GAMES):
        WINS += Game(STRAT_X).play()
    print("TOTAL WINS: {}/{} = {:.2f}%".format(
        WINS, GAMES, (WINS / GAMES) * 100
    ))