pokedex/formulae.py

   1 # encoding: utf8
   2 """Faithful translations of calculations the games make."""
   3 from __future__ import division
   4
   5 from itertools import izip
   6
   7 def nCr(n, r):
   8     """n-choose-r.
   9
  10     Thanks for the "compact" solution go to:
  11     http://stackoverflow.com/questions/2096573/counting-combinations-and-permutations-efficiently
  12     """
  13
  14     return reduce(
  15         lambda x, y: x * y[0] / y[1],
  16         izip(xrange(n - r + 1, n + 1),
  17              xrange(1, r + 1)),
  18         1)
  19
  20
  21 def calculated_stat(base_stat, level, iv, effort):
  22     """Returns the calculated stat -- i.e. the value actually shown in the game
  23     on a Pokémon's status tab.
  24     """
  25
  26     # Remember: this is from C; use floor division!
  27     return (base_stat * 2 + iv + effort // 4) * level // 100 + 5
  28
  29 def calculated_hp(base_hp, level, iv, effort):
  30     """Similar to `calculated_stat`, except with a slightly different formula
  31     used specifically for HP.
  32     """
  33
  34     # Shedinja's base stat of 1 is special; its HP is always 1
  35     if base_hp == 1:
  36         return 1
  37
  38     return (base_hp * 2 + iv + effort // 4) * level // 100 + 10 + level
  39
  40 def earned_exp(base_exp, level):
  41     """Returns the amount of EXP earned when defeating a Pokémon at the given
  42     level.
  43     """
  44
  45     return base_exp * level // 7
  46
  47 def capture_chance(percent_hp, capture_rate,
  48                    ball_bonus=1, status_bonus=1, heavy_modifier=0):
  49     """Calculates the chance that a Pokémon will be caught, given its capture
  50     rate and the percentage of HP it has remaining.
  51
  52     Returns five values: the chance of a capture, then the chance of the ball
  53     shaking three, two, one, or zero times.  Each of these is a float such that
  54     0.0 <= n <= 1.0.  Feel free to ignore all but the first.
  55     """
  56
  57     if heavy_modifier:
  58         # Only used by Heavy Ball.  Changes the target's capture rate outright
  59         capture_rate += heavy_modifier
  60         if capture_rate <= 1:
  61             capture_rate = 1
  62
  63     # This should really be integer math, right?  But the formula uses FOURTH
  64     # ROOTS in a moment, so it can't possibly be.  It probably doesn't matter
  65     # either way, so whatever; use regular ol' division.  ball_bonus and
  66     # status_bonus can be 1.5, anyway.
  67
  68     # A slight math note:
  69     # The formula is originally: (3 max - 2 curr) rate bonus / (3 max)
  70     # I have reduced this to: (1 - 2/3 * pct) rate bonus
  71     # My rationale is that this cannot possibly be integer math, so rounding is
  72     # not a problem and commutation won't make a difference.  It also
  73     # simplifies the input considerably.
  74     base_chance = (1 - 2/3 * percent_hp) * capture_rate \
  75                 * ball_bonus * status_bonus
  76
  77     shake_index = (base_chance / 255) ** 0.25 * (2**16 - 1)
  78
  79     # Iff base_chance < 255, then shake_index < 65535.
  80     # The game now picks four random uwords.  However many of them are <=
  81     # shake_index is the number of times the ball will shake.  If all four are
  82     # <= shake_index, the Pokémon is caught.
  83
  84     # If shake_index >= 65535, all four randoms must be <= it, and the Pokémon
  85     # will be caught.  Skip hard math
  86     if shake_index >= 65535:
  87         return (1.0, 0.0, 0.0, 0.0, 0.0)
  88
  89     # This brings up an interesting invariant: sum(return_value) == 1.0.
  90     # Something is guaranteed to happen.
  91
  92     # Alrighty.  Here's some probability.
  93     # The chance that a single random number will be <= shake_index is:
  94     p = (shake_index + 1) / 65536
  95     # Now, the chance that two random numbers will be <= shake_index is p**2.
  96     # And the chance that neither will be is (1 - p)**2.
  97     # With me so far?
  98     # The chance that one will be and one will NOT be is p * (1 - p) * 2.
  99     # The 2 is because they can go in any order: the first could be less, or
 100     # the second could be less.  That 2 is actually nCr(2, 1); the number of
 101     # ways of picking one item in any order from a group of two.
 102     # Try it yourself add up those three values and you'll get 1.
 103
 104     # Right.  Hopefully, the following now makes sense.
 105     # There are five cases: four randoms are <= shake_index (which means
 106     # capture), or three are, etc.
 107     return [
 108         p**i * (1 - p)**(4 - i) * nCr(4, i)
 109         for i in reversed(range(5))
 110     ]