X-Git-Url: http://git.veekun.com/zzz-pokedex.git/blobdiff_plain/4c89607b64096bf6662c80da3a0ee420738cd63b..2ec82ef579f8ec72117cacf6e455da8ab8d961d5:/pokedex/formulae.py

diff --git a/pokedex/formulae.py b/pokedex/formulae.py
index 805812d..19ed568 100644
--- a/pokedex/formulae.py
+++ b/pokedex/formulae.py
@@ -1,5 +1,22 @@
 # 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
@@ -26,3 +43,78 @@ def earned_exp(base_exp, level):
     """
 
     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),
+    ]