Implementation of the game described in https://projecteuler.net/problem=503; Paired on with Louis Hyde

alice_compromise.py

import random

class Deck():
    def __init__(self, n=3):
        self.cards = list(range(1,n+1))
        random.shuffle(self.cards)
        self.position = 0
    def __len__(self):
        return len(self.cards)
    def _number_of_cards_left(self):
        return len(self) - self.position
    def draw(self):
        assert(self._number_of_cards_left() > 0)
        card = self.cards[self.position]
        self.position += 1
        return card
    def alice_draw(self):
        previousCards = self.cards[:self.position]
        card = self.draw()
        previousGreaterCards = len(list(filter(lambda c : card < c, previousCards)))
        return (card,previousGreaterCards)


def game(n=3):
    deck = Deck(n)
    final_score = 0
    for turn in range(n):
        (card, previousGreaterCards) = deck.alice_draw()
        if previousGreaterCards == 1:
            verb = "is "
        else:
            verb = "are "
        print("Bob says, \"There " + verb + str(previousGreaterCards) + " previous card that are greater than your card.\"")
        if deck._number_of_cards_left() == 0:
            print("No cards left! Your score is " + str(card) + "!")
            print("The deck was " + str(deck.cards))
            final_score = card
            break
        response = input("Do you want to stop? [y/N] ")
        if response.lower() == "y":
            print("Your score is " + str(card) + "!")
            print("The deck was " + str(deck.cards))
            final_score = card
            break
        else:
            print("Drawing another card...")
    return final_score


"""
>>> game(6)
Bob says, "There are 0 previous card that are greater than your card."
Do you want to stop? [y/N] n
Drawing another card...
Bob says, "There is 1 previous card that are greater than your card."
Do you want to stop? [y/N] n
Drawing another card...
Bob says, "There are 2 previous card that are greater than your card."
Do you want to stop? [y/N] y
Your score is 1!
The deck was [6, 5, 1, 2, 4, 3]
1

>>> game(6)
Bob says, "There are 0 previous card that are greater than your card."
Do you want to stop? [y/N] n
Drawing another card...
Bob says, "There are 0 previous card that are greater than your card."
Do you want to stop? [y/N] n
Drawing another card...
Bob says, "There is 1 previous card that are greater than your card."
Do you want to stop? [y/N] n
Drawing another card...
Bob says, "There are 2 previous card that are greater than your card."
Do you want to stop? [y/N] y
Your score is 3!
The deck was [2, 6, 4, 3, 1, 5]
3
"""