tries.py

import random

def generate_choices():
    yield 4
    yield 5
    yield 6
    yield 7
    while True:
        yield 8

def get_tries():
    # 26 cards from A to Z
    cards = list(range(26))

    # one card is removed at random
    removed_card = random.choice(cards)
    del cards[removed_card]

    # remaining cards shuffled (not actually necessary)
    random.shuffle(cards)

    # list of all letters from A to Z
    letter_list = list(range(26))

    # initially N is 4
    tries = 1

    for N in generate_choices():
        # choose N letters from list
        N_letters = random.sample(letter_list, min(N, len(letter_list)))
        for letter in N_letters:
            if letter == removed_card:
                return tries
            # cross out
            del letter_list[letter_list.index(letter)]

        # draw two letters from shuffled deck
        two_letters = random.sample(cards, min(2, len(cards)))
        for letter in two_letters:
            if letter == removed_card:
                return tries
            if letter in letter_list:
                # cross out
                del letter_list[letter_list.index(letter)]
            # discard
            del cards[cards.index(letter)]
            
        tries += 1

def generate_expected_value():
    total_count = 0
    tries_count = 0.0
    while True:
        total_count += 1
        tries_count += get_tries()
        if total_count % 1000 == 0:
            expected_tries = tries_count / total_count
            yield expected_tries

def generate_probabilities():
    values = {}
    trials = 0
    while True:
        tries = get_tries()
        trials += 1
        
        if tries not in values:
            values[tries] = 0
        values[tries] += 1

        if trials % 1000 == 0:
            yield sorted([(i[0], 100*round(i[1]/float(trials),2)) for i in values.items()])


if __name__ == "__main__":
    for p in generate_probabilities():
        print(p)