raza_shadowform.py

    from scipy.stats import hypergeom

    deck_size = 30
    hand_size = 4

    def mul_for_card(copies_in_deck=2, hand_size=3):
        deck_size = 30
        prb = hypergeom(deck_size, copies_in_deck, hand_size)
        # P(initial_miss)
        p_none_in_first3 = prb.cdf(0)

        # GIVEN that we mul our first 3 what is prob we still are unlucky
        # P(miss_turn0 | initial_miss)
        prb = hypergeom(deck_size - hand_size, copies_in_deck, hand_size)
        p_none_in_mul = prb.cdf(0)
        # TODO: add constraints about 2 drops
        #  P(miss_turn0) = P(miss_turn0 | initial_miss) *  P(initial_miss)
        p_none_at_start = p_none_in_mul * p_none_in_first3
        return p_none_at_start

    num_shadowform = 2

    p_no_shadowform_on_turn0 = mul_for_card(copies_in_deck=num_shadowform,
                                            hand_size=hand_size)
    turn = 5
    # P(miss_turn5 | miss_mul)
    no_shadowform_turn5_given_mulmis = hypergeom(deck_size - hand_size, num_shadowform, turn).cdf(0)
    # P(miss_turn5) = P(miss_turn5 | miss_mul) P(miss_mul)
    no_shadowform_turn5 = no_shadowform_turn5_given_mulmis * p_no_shadowform_on_turn0

    def prob_nohave_card_thats_always_mulled(copies=2, hand_size=3):
        # probability of getting the card initially
        p_nohad_premul = hypergeom(deck_size, copies, hand_size).cdf(0)
        # probability of getting the card if everything is thrown away
        # (TODO: factor in the probability that you need to keep something)
        # for now its fine because if we keep shadowform the end calculation is fine
        p_nohave_postmul_given_nohave = hypergeom(deck_size - hand_size, copies, hand_size).cdf(0)
        # not necessary, but it shows the theory
        p_nohave_postmul_given_had = 1
        p_nohave_turn0 = p_nohave_postmul_given_nohave * p_nohad_premul + (1 - p_nohad_premul) * p_nohave_postmul_given_had
        return p_nohave_turn0

    # Assume you always mul raza
    turn = 5
    p_noraza_initial = prob_nohave_card_thats_always_mulled(copies=1, hand_size=hand_size)
    p_noraza_turn5_given_noinitial = hypergeom(deck_size - hand_size, 1, turn).cdf(0)
    p_noraza_turn5 = p_noraza_initial * p_noraza_turn5_given_noinitial
    p_raza_turn5 = 1 - p_noraza_turn5

    # probability that you have raza and no shadowform by turn 5
    p_raza_and_noshadowform_turn5 = p_raza_turn5 * no_shadowform_turn5
    print('p_raza_and_noshadowform_turn5 = %r' % (p_raza_and_noshadowform_turn5,))