veekun_pokedex/pokedex/formulae.py

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# encoding: utf8
"""Faithful translations of calculations the games make."""
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from __future__ import division
from six.moves import reduce, xrange, zip
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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],
zip(xrange(n - r + 1, n + 1),
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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!
stat = (base_stat * 2 + iv + effort // 4) * level // 100 + 5
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_stat == 1:
return 1
return (base_stat * 2 + iv + effort // 4) * level // 100 + 10 + level
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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
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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.
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Bonuses are such that 10 means "unchanged".
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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))
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# 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.
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# If shake_index >= 65535, all four randoms must be < it, and the Pokémon
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# 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.
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return [
p**4, # capture
p**3 * (1 - p),
p**2 * (1 - p),
p**1 * (1 - p),
(1 - p),
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]