X-Git-Url: http://git.veekun.com/zzz-pokedex.git/blobdiff_plain/10177b445c97cc328e1fa4cf7849594a2a4541b5..2ec82ef579f8ec72117cacf6e455da8ab8d961d5:/pokedex/formulae.py diff --git a/pokedex/formulae.py b/pokedex/formulae.py index 29ab514..19ed568 100644 --- a/pokedex/formulae.py +++ b/pokedex/formulae.py @@ -45,43 +45,54 @@ def earned_exp(base_exp, level): return base_exp * level // 7 def capture_chance(percent_hp, capture_rate, - ball_bonus=1, status_bonus=1, heavy_modifier=0): + 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. """ - 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. + # 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 formula is originally: (3 max - 2 curr) rate bonus / (3 max) - # I have reduced this to: (1 - 2/3 * pct) rate bonus - # My rationale is that this cannot possibly be integer math, so rounding is - # not a problem and commutation won't make a difference. It also - # simplifies the input considerably. - base_chance = (1 - 2/3 * percent_hp) * capture_rate \ - * ball_bonus * status_bonus - - shake_index = (base_chance / 255) ** 0.25 * (2**16 - 1) + # 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 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 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 + # 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) @@ -90,21 +101,20 @@ def capture_chance(percent_hp, capture_rate, # 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. + # 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**i * (1 - p)**(4 - i) * nCr(4, i) - for i in reversed(range(5)) + p**4, # capture + p**3 * (1 - p), + p**2 * (1 - p), + p**1 * (1 - p), + (1 - p), ]