mhapi/mhprob.py

#!/usr/bin/env python

# Calculate probability of getting at least one of a monster part from one
# line in the quest rewards. Also calculates expected value of part
# counts (N), and probabilities of getting a certain number of rewards (C).
#
# usage: mhprob.py reward_percent fixed_rewards gaurenteed_rewards \
#                  [extend_percent]
#
# reward_percent - chance of getting the monster part in %
# fixed_rewards - number of rewards in the reward list with 100% chance and
#                 are not the item you are looking for. Takes away from
#                 the total possible draw attempts for what you want.
#                 Default 1 which is typical for line A in many quests.
# gaurenteed_rewards - minimum number of quest rewards in the line,
#                      including any fixed rewards. In Tri (see link
#                      below) this is 3 for line A and 1 for line B.
#                      Defaults to 3.
# extend_percent - chance of getting one more reward in the line in %,
#                  default 69
#
# You can use http://kiranico.com to get reward percent and fixed rewards
# values.
#
# For extend percent, use the default unless you have the Lucky Cat or
# Ultra Lucky Cat food skills or Good Luck or Great Luck armor skills:
#
# normal extra reward %: 69
# good luck extra reward %: 81
# great luck extra %: 90
#
# Can also be used to calculate chance of getting a part from carving,
# using extend_percent=0, fixed_rewards=0, and gaurenteed_rewards=3 (or
# 4 for monsters with 4 carves).
#
# Source:
# http://www.gamefaqs.com/wii/943655-monster-hunter-tri/faqs/60448
# Not sure if there are differences in 3U or 4U.
#
# Example Plain dangerous in 3U, has 2 fixed rewards in A, one in B, hardhorns
# are 5% both A and B:
# A: ./mhprop.py 5 2 3 69
# B: ./mhprop.py 5 1 1 69
# For great luck, replace 69 with 90

CAP_SKILL_NONE = 0
CAP_SKILL_EXPERT = 1
CAP_SKILL_MASTER = 2
CAP_SKILL_GOD = 3

LUCK_SKILL_NONE = 0
LUCK_SKILL_GOOD = 1
LUCK_SKILL_GREAT = 2

QUEST_A = "A"
QUEST_B = "B"
QUEST_SUB = "Sub"

CARVING_SKILL_NONE = 0
CARVING_SKILL_PRO = 1
CARVING_SKILL_FELYNE_LOW = 2
CARVING_SKILL_FELYNE_HI = 3
CARVING_SKILL_CELEBRITY = 4
CARVING_SKILL_GOD = 5


import sys

def _quest_reward_p(reward_percent, reward_count):
    """
    Propability of getting at least one item from @reward_count draws
    with a @reward_percent chance.
    """
    fail_percent = (100 - reward_percent)
    return 1.0 - (fail_percent / 100.0)**reward_count

def _reward_count_p(reward_count, min_rewards, max_rewards, extend_percent):
    """
    Probability of getting a certain number of rewards for a given chance
    @extend_percent of getting one more drop.
    """
    if reward_count == min_rewards:
        return (100 - extend_percent) / 100.0
    p = 1.0
    extend_p = extend_percent / 100.0
    stop_p = 1.0 - extend_p
    for i in xrange(min_rewards+1, reward_count+1):
        p *= extend_p
    if reward_count < max_rewards:
        p *= stop_p
    return p

def quest_reward_p(reward_percent, min_rewards, max_rewards, extend_percent=69):
    """
    Probability of getting at least one of the item, given the item has
    @reward_percent chance, @min_rewards minimum number of attempts,
    @max_rewards max attempts, and @extend_percent chance of getting each
    extra attempt.
    """
    p = 0.0
    for reward_count in xrange(min_rewards, max_rewards + 1):
        p += (_reward_count_p(reward_count, min_rewards, max_rewards,
                              extend_percent)
              * _quest_reward_p(reward_percent, reward_count))
    return p * 100


def reward_expected_c(min_rewards, max_rewards, extend_percent):
    """
    Expected value for number of rewards, if @min_rewards are gauranteed
    and there is an @extend_percent chance of getting one more each time
    with at most @max_rewards.
    """
    total_p = 0.0
    expected_attempts = 0.0
    for reward_count in xrange(min_rewards, max_rewards + 1):
        p = _reward_count_p(reward_count, min_rewards, max_rewards,
                            extend_percent)
        expected_attempts += p * reward_count
        #print "P(C = %d) = %0.4f" % (reward_count, p)
        total_p += p
    assert abs(total_p - 1.0) < .00001, "total = %f" % total_p
    return expected_attempts


def quest_reward_expected_c(line=QUEST_A, luck_skill=LUCK_SKILL_NONE):
    """
    Expected number of rewards from specified quest line with given skills.

    Note: if the quest has fixed rewards that aren't the desired item, it will
    reduce the expected count for the desired item. Just subtract the number
    of fixed items from the output to get the actual value.
    """
    if luck_skill == LUCK_SKILL_NONE:
        extend_p = 69
    elif luck_skill == LUCK_SKILL_GOOD:
        extend_p = 81
    elif luck_skill == LUCK_SKILL_GREAT:
        extend_p = 90
    else:
        raise ValueError()

    if line == QUEST_A:
        min_c = 3
        max_c = 8
    elif line == QUEST_B:
        min_c = 1
        max_c = 8
    elif line == QUEST_SUB:
        min_c = 1
        max_c = 4
    else:
        raise ValueError()

    return reward_expected_c(min_c, max_c, extend_p)


def capture_reward_expected_c(cap_skill=CAP_SKILL_NONE):
    """
    Expected value for number of capture rewards given the specified
    capture skill (none by default).
    """
    if cap_skill == CAP_SKILL_NONE:
        min_c = 2
        max_c = 3
        extend_p = 69
    elif cap_skill == CAP_SKILL_EXPERT:
        return 3
    elif cap_skill == CAP_SKILL_MASTER:
        min_c = 3
        max_c = 4
        extend_p = 69
    elif cap_skill == CAP_SKILL_GOD:
        return 4
    else:
        raise ValueError()
    return reward_expected_c(min_c, max_c, extend_p)


def carve_delta_expected_c(carve_skill):
    """
    Expected value for the number of extra carves with the given skill.

    Word on the street is that since Tri the felyne skills do not stack with
    the armor skills, i.e. if you have Carving Celebrity plus you get at
    least one extra carves and the felyne skills do nothing.
    """
    if carve_skill == CARVING_SKILL_CELEBRITY:
        # Description: Increases the number of carving chances by one and prevents knockbacks while carving.
        return 1
    elif carve_skill == CARVING_SKILL_GOD:
        # Description: Increases the number of carving chances by one (maybe more) and prevents knockbacks while carving.
        # TODO: max 2 and 50% extend is a guess, find the actual values
        min_c = 1
        max_c = 2
        extend_p = 50
    elif carve_skill == CARVING_SKILL_FELYNE_LOW:
        min_c = 0
        max_c = 1
        extend_p = 25
    elif carve_skill == CARVING_SKILL_FELYNE_HI:
        min_c = 0
        max_c = 1
        extend_p = 50
    elif carve_skill in (CARVING_SKILL_NONE, CARVING_SKILL_PRO):
        # Description: Prevents knockbacks from attacks while carving.
        return 0
    else:
        raise ValueError()
    return reward_expected_c(min_c, max_c, extend_p)


if __name__ == '__main__':
    # in percent
    reward_percent = int(sys.argv[1])
    if len(sys.argv) > 2:
        fixed_rewards = int(sys.argv[2])
    else:
        fixed_rewards = 1
    if len(sys.argv) > 3:
        guarenteed_rewards = int(sys.argv[3])
    else:
        guarenteed_rewards = 3
    if len(sys.argv) > 4:
        extend_percent = int(sys.argv[4])
    else:
        extend_percent = 69

    min_rewards = guarenteed_rewards - fixed_rewards
    max_rewards = 8 - fixed_rewards

    if min_rewards < 0:
        print "Error: fixed_rewards (%d) must be less than or equal to " \
              "guaranteeed_rewards (%d)" % (fixed_rewards, guarenteed_rewards)
        sys.exit(1)

    total_p = 0.0
    expected_attempts = 0.0
    for reward_count in xrange(min_rewards, max_rewards + 1):
        p = _reward_count_p(reward_count, min_rewards, max_rewards,
                            extend_percent)
        expected_attempts += p * reward_count
        # probability of getting @reward_count rewards that could be the
        # desired item
        print "P(C = %d) = %0.4f" % (reward_count, p)
        total_p += p
    # expected value for number of rewards that could be the desired item
    print "E(C)     = %0.2f" % expected_attempts

    # math check, make sure all possibilities add up to 1, allowing for
    # some floating point precision loss.
    assert abs(total_p - 1.0) < .00001, "total = %f" % total_p

    p_at_least_one = quest_reward_p(reward_percent, min_rewards, max_rewards,
                                    extend_percent)
    expected = expected_attempts * reward_percent / 100.0

    print "P(N > 0) = %0.2f%%" % p_at_least_one
    print "E(N)     = %0.4f" % expected