# encoding: utf8
"""Faithful translations of calculations the games make."""
+from __future__ import division
+
+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):
"""Returns the calculated stat -- i.e. the value actually shown in the game
return 1
return (base_hp * 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
+ level.
+ """
+
+ return base_exp * level // 7
+
+def capture_chance(percent_hp, capture_rate,
+ ball_bonus=1, status_bonus=1, heavy_modifier=0):
+ """Calculates the chance that a Pokémon will be caught, given its capture
+ rate and the percentage of HP it has remaining.
+
+ 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.
+ """
+
+ if heavy_modifier:
+ # Only used by Heavy Ball. Changes the target's capture rate outright
+ capture_rate += heavy_modifier
+ if capture_rate <= 1:
+ capture_rate = 1
+
+ # This should really be integer math, right? But the formula uses FOURTH
+ # ROOTS in a moment, so it can't possibly be. It probably doesn't matter
+ # either way, so whatever; use regular ol' division. ball_bonus and
+ # status_bonus can be 1.5, anyway.
+
+ # A slight math note:
+ # The formula is originally: (3 max - 2 curr) rate bonus / (3 max)
+ # I have reduced this to: (1 - 2/3 * pct) rate bonus
+ # My rationale is that this cannot possibly be integer math, so rounding is
+ # not a problem and commutation won't make a difference. It also
+ # simplifies the input considerably.
+ base_chance = (1 - 2/3 * percent_hp) * capture_rate \
+ * ball_bonus * status_bonus
+
+ shake_index = (base_chance / 255) ** 0.25 * (2**16 - 1)
+
+ # Iff base_chance < 255, then shake_index < 65535.
+ # The game now picks four random uwords. However many of them are <=
+ # shake_index is the number of times the ball will shake. 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 number will be <= shake_index is:
+ p = (shake_index + 1) / 65536
+ # Now, the chance that two random numbers will be <= shake_index is p**2.
+ # And the chance that neither will be is (1 - p)**2.
+ # With me so far?
+ # The chance that one will be and one will NOT be is p * (1 - p) * 2.
+ # The 2 is because they can go in any order: the first could be less, or
+ # the second could be less. That 2 is actually nCr(2, 1); the number of
+ # ways of picking one item in any order from a group of two.
+ # Try it yourself add up those three values and you'll get 1.
+
+ # Right. Hopefully, the following now makes sense.
+ # There are five cases: four randoms are <= shake_index (which means
+ # capture), or three are, etc.
+ return [
+ p**i * (1 - p)**(4 - i) * nCr(4, i)
+ for i in reversed(range(5))
+ ]
projects / zzz-pokedex.git / blobdiff