Added capture chance formula.

This commit is contained in:
Eevee 2010-03-21 03:16:24 -07:00
parent a89a616203
commit 597ee5198b

View file

@ -1,5 +1,22 @@
# encoding: utf8 # encoding: utf8
"""Faithful translations of calculations the games make.""" """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): def calculated_stat(base_stat, level, iv, effort):
"""Returns the calculated stat -- i.e. the value actually shown in the game """Returns the calculated stat -- i.e. the value actually shown in the game
@ -26,3 +43,64 @@ def earned_exp(base_exp, level):
""" """
return base_exp * level // 7 return base_exp * level // 7
def capture_chance(current_hp, max_hp, capture_rate,
ball_bonus=1, status_bonus=1, heavy_modifier=0):
"""Calculates the chance that a Pokémon will be caught.
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.
base_chance = ((3 * max_hp - 2 * current_hp) * capture_rate * ball_bonus) \
/ (3 * max_hp) \
* 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.
# The RNG tends to work with integers, so integer math likely kicks in now.
shake_index = int(shake_index)
# 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))
]