add quest reward script, readme

README.adoc

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+= Monster Hunter scripts
+
+This repository contains scripts for calculating probalities and expected
+values for rewards and carves in Monster Hunter games.

mhprob.py

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+#!/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
+
+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
+
+
+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_v = 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_v += 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_v
+
+    # 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_v * reward_percent / 100.0
+
+    print "P(N > 0) =", p_at_least_one
+    print "E(N)     =", expected