X-Git-Url: http://git.veekun.com/zzz-pokedex.git/blobdiff_plain/4c89607b64096bf6662c80da3a0ee420738cd63b..2ec82ef579f8ec72117cacf6e455da8ab8d961d5:/pokedex/formulae.py?ds=sidebyside 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), + ]