# encoding: utf8
"""Faithful translations of calculations the games make."""
+from __future__ import division
-def calculated_stat(base_stat, level, iv, effort):
+from itertools import izip
+
+def nCr(n, r):
+ """n-choose-r.
+
+ Thanks for the "compact" solution go to:
+ http://stackoverflow.com/questions/2096573/counting-combinations-and-permutations-efficiently
+ """
+
+ return reduce(
+ lambda x, y: x * y[0] / y[1],
+ izip(xrange(n - r + 1, n + 1),
+ xrange(1, r + 1)),
+ 1)
+
+
+def calculated_stat(base_stat, level, iv, effort, nature=None):
"""Returns the calculated stat -- i.e. the value actually shown in the game
on a Pokémon's status tab.
"""
# Remember: this is from C; use floor division!
- return (base_stat * 2 + iv + effort // 4) * level // 100 + 5
+ stat = (base_stat * 2 + iv + effort // 4) * level // 100 + 5
-def calculated_hp(base_hp, level, iv, effort):
+ if nature:
+ stat = int(stat * nature)
+
+ return stat
+
+def calculated_hp(base_stat, level, iv, effort, nature=None):
"""Similar to `calculated_stat`, except with a slightly different formula
used specifically for HP.
"""
# Shedinja's base stat of 1 is special; its HP is always 1
- if base_hp == 1:
+ if base_stat == 1:
return 1
- return (base_hp * 2 + iv + effort // 4) * level // 100 + 10 + level
+ return (base_stat * 2 + iv + effort // 4) * level // 100 + 10 + level
def earned_exp(base_exp, level):
"""Returns the amount of EXP earned when defeating a Pokémon at the given
"""
return base_exp * level // 7
+
+def capture_chance(percent_hp, capture_rate,
+ ball_bonus=10, status_bonus=1,
+ capture_bonus=10, capture_modifier=0):
+ """Calculates the chance that a Pokémon will be caught, given its capture
+ rate and the percentage of HP it has remaining.
+
+ Bonuses are such that 10 means "unchanged".
+
+ Returns five values: the chance of a capture, then the chance of the ball
+ shaking three, two, one, or zero times. Each of these is a float such that
+ 0.0 <= n <= 1.0. Feel free to ignore all but the first.
+ """
+
+ # HG/SS Pokéballs modify capture rate rather than the ball bonus
+ capture_rate = capture_rate * capture_bonus // 10 + capture_modifier
+ if capture_rate < 1:
+ capture_rate = 1
+ elif capture_rate > 255:
+ capture_rate = 255
+
+ # A slight math note:
+ # The actual formula uses (3 * max_hp - 2 * curr_hp) / (3 * max_hp)
+ # This uses (1 - 2/3 * curr_hp/max_hp)
+ # Integer division is taken into account by flooring immediately
+ # afterwards, so there should be no appreciable rounding error.
+ base_chance = int(
+ capture_rate * ball_bonus // 10 * (1 - 2/3 * percent_hp)
+ )
+ base_chance = base_chance * status_bonus // 10
+
+ # Shake index involves integer sqrt. Lovely.
+ isqrt = lambda x: int(x ** 0.5)
+ if not base_chance:
+ # This is very silly. Due to what must be an oversight, it's possible
+ # for the above formula to end with a zero chance to catch, which is
+ # then thrown blindly into the below denominator. Luckily, the games'
+ # division function is a no-op with a denominator of zero.. which
+ # means a base_chance of 0 is effectively a base chance of 1.
+ base_chance = 1
+ shake_index = 1048560 // isqrt(isqrt(16711680 // base_chance))
+
+ # Iff base_chance < 255, then shake_index < 65535.
+ # The Pokémon now has four chances to escape. The game starts picking
+ # random uint16s. If such a random number is < shake_index, the Pokémon
+ # stays in the ball, and it wobbles. If the number is >= shake_index, the
+ # ball breaks open then and there, and the capture fails.
+ # If all four are < shake_index, the Pokémon is caught.
+
+ # If shake_index >= 65535, all four randoms must be < it, and the Pokémon
+ # will be caught. Skip hard math
+ if shake_index >= 65535:
+ return (1.0, 0.0, 0.0, 0.0, 0.0)
+
+ # This brings up an interesting invariant: sum(return_value) == 1.0.
+ # Something is guaranteed to happen.
+
+ # Alrighty. Here's some probability.
+ # The chance that a single random uint16 will be < shake_index, thus
+ # keeping the Pokémon in the ball, is:
+ p = shake_index / 65536
+
+ # Now, the chance for n wobbles is the chance that the Pokémon will stay in
+ # the ball for (n-1) attempts, then break out on the nth.
+ # The chance of capture is just the chance that the Pokémon stays in the
+ # ball for all four tries.
+
+ # There are five cases: captured, wobbled three times, etc.
+ return [
+ p**4, # capture
+ p**3 * (1 - p),
+ p**2 * (1 - p),
+ p**1 * (1 - p),
+ (1 - p),
+ ]
projects / zzz-pokedex.git / blobdiff