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baskuit/main.py

Created November 29, 2023 21:14
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Python script to solve Tauros v. Tauros
Raw
main.py
from fractions import Fraction
value_table = {}
move_table = {}
max_hp = 353
# Body Slam min damage
low_hp = 95
attacks = ["bslam", "blizzard", "hyperbeam"]
crit = {0: Fraction(402, 512), 1: Fraction(110, 512)}
accs = {
"bslam": {0: Fraction(1, 256), 1: Fraction(255, 256)},
"blizzard": {0: Fraction(27, 256), 1: Fraction(229, 256)},
"hyperbeam": {0: Fraction(27, 256), 1: Fraction(229, 256)},
"recharge": {0: Fraction(1, 1), 1: Fraction(0, 1)},
}
procs = {
"bslam": {0: Fraction(1, 1), 1: Fraction(0, 1)},
"blizzard": {0: Fraction(229, 256), 1: Fraction(27, 256)},
"hyperbeam": {0: Fraction(1, 1), 1: Fraction(0, 1)},
"recharge": {0: Fraction(1, 1), 1: Fraction(0, 1)},
}
rolls = [
{
"bslam" : {95: 2, 96: 2, 97: 3, 98: 2, 99: 2, 100: 2, 101: 3, 102: 2, 103: 2, 104: 3, 105: 2, 106: 2, 107: 2, 108: 3, 109: 2, 110: 2, 111: 2, 112: 1},
"blizzard" : {86: 1, 87: 2, 88: 3, 89: 2, 90: 3, 91: 2, 92: 3, 93: 2, 94: 3, 95: 2, 96: 3, 97: 2, 98: 3, 99: 2, 100: 3, 101: 2, 102: 1},
"hyperbeam" : {166: 1, 167: 1, 168: 1, 169: 2, 170: 1, 171: 1, 172: 2, 173: 1, 174: 1, 175: 1, 176: 2, 177: 1, 178: 1, 179: 2, 180: 1, 181: 1, 182: 2, 183: 1, 184: 1, 185: 1, 186: 2, 187: 1, 188: 1, 189: 2, 190: 1, 191: 1, 192: 2, 193: 1, 194: 1, 195: 1, 196: 1},
"recharge": {0: 39},
},
{
"bslam" : {184: 1, 185: 1, 186: 1, 187: 1, 188: 2, 189: 1, 190: 1, 191: 1, 192: 1, 193: 1, 194: 2, 195: 1, 196: 1, 197: 1, 198: 1, 199: 2, 200: 1, 201: 1, 202: 1, 203: 1, 204: 1, 205: 2, 206: 1, 207: 1, 208: 1, 209: 1, 210: 1, 211: 2, 212: 1, 213: 1, 214: 1, 215: 1, 216: 1, 217: 1},
"blizzard" : {168: 1, 169: 1, 170: 2, 171: 1, 172: 1, 173: 2, 174: 1, 175: 1, 176: 1, 177: 2, 178: 1, 179: 1, 180: 2, 181: 1, 182: 1, 183: 1, 184: 2, 185: 1, 186: 1, 187: 2, 188: 1, 189: 1, 190: 1, 191: 2, 192: 1, 193: 1, 194: 2, 195: 1, 196: 1, 197: 1, 198: 1},
"hyperbeam" : {324: 1, 325: 1, 327: 1, 328: 1, 330: 1, 331: 1, 333: 1, 334: 1, 336: 1, 337: 1, 339: 1, 340: 1, 342: 1, 343: 1, 345: 1, 346: 1, 348: 1, 349: 1, 351: 1, 352: 1, 354: 1, 355: 1, 357: 1, 358: 1, 360: 1, 361: 1, 363: 1, 364: 1, 366: 1, 367: 1, 369: 1, 370: 1, 372: 1, 373: 1, 375: 1, 376: 1, 378: 1, 379: 1, 381: 1},
"recharge": {0: 39},
},
{
"bslam" : {0: 39},
"blizzard" : {0: 39},
"hyperbeam" : {0: 39},
"recharge": {0: 39},
},
]
def solve(p1_hp, p2_hp, p1_recharge, p2_recharge):
# flip
if p2_hp > p1_hp:
return Fraction(1, 1) - solve(p2_hp, p1_hp, p2_recharge, p1_recharge)
if p1_hp <= low_hp and p2_hp <= low_hp:
if p1_recharge:
return Fraction(1, 512)
if p2_recharge:
return Fraction(511, 512)
return Fraction(1, 2)
# otherwise just lookup
return value_table[(p1_hp, p2_hp, p1_recharge, p2_recharge)]
def solve_q(p1_hp, p2_hp, p1_move, p2_move):
if p1_hp <= low_hp and p2_hp <= low_hp:
if p1_move == "recharge":
return Fraction(1, 512)
else:
if p2_move == "recharge":
return Fraction(511, 512)
else:
return Fraction(1, 2)
expected_value = Fraction(0, 1)
# count = 0
# total_prob = Fraction(0, 1)
same_prob = Fraction(0, 1)
# p1_win_prob = Fraction(0, 1)
# p2_win_prob = Fraction(0, 1)
p1_accs = accs[p1_move]
p2_accs = accs[p2_move]
p1_procs = procs[p1_move]
p2_procs = procs[p2_move]
for speed_tie in range(2):
for p1_acc in p1_accs:
for p1_proc in p1_procs:
for p1_crit in crit:
p1_roll_idx = 2 if (p1_proc or not p1_acc) else p1_crit
p1_rolls = rolls[p1_roll_idx][p1_move]
for p1_roll in p1_rolls:
for p2_acc in p2_accs:
for p2_proc in p2_procs:
for p2_crit in crit:
p2_roll_idx = 2 if (p2_proc or not p2_acc) else p2_crit
p2_rolls = rolls[p2_roll_idx][p2_move]
for p2_roll in p2_rolls:
prob = (
crit[p1_crit]
* p1_rolls[p1_roll]
* p1_accs[p1_acc]
* p1_procs[p1_proc]
* crit[p2_crit]
* p2_rolls[p2_roll]
* p2_accs[p2_acc]
* p2_procs[p2_proc]
* Fraction(1, 2 * 39**2) #accounting for damage rolls and speed tie
)
# total_prob += prob
p1_win = (p1_roll >= p2_hp) or (p1_proc and p1_acc)
p2_win = (p2_roll >= p1_hp) or (p2_proc and p2_acc)
# count += 1
if p1_win:
if p2_win:
if speed_tie:
expected_value += prob # p1 won
# p1_win_prob += prob
else:
# p2_win_prob += prob
pass
else:
expected_value += prob
# p1_win_prob += prob
elif p2_win:
# p2_win_prob += prob
pass # done, since we add 0 * prob
else:
# Not terminal
p1_dmg = p1_acc * p1_roll
p2_dmg = p2_acc * p2_roll
p1_will_recharge = (
p1_move == "hyperbeam" and p1_acc
)
p2_will_recharge = (
p2_move == "hyperbeam" and p2_acc
)
if not p1_dmg and not p2_dmg:
if p1_move == "recharge" or p2_move == "recharge":
value = solve(
p1_hp,
p2_hp,
False,
False,
)
expected_value += value * prob
else:
# both miss
same_prob += prob
else:
# no result, lookup
value = solve(
p1_hp - p2_dmg,
p2_hp - p1_dmg,
p1_will_recharge,
p2_will_recharge,
)
expected_value += value * prob
# to account for "no change"
expected_value = expected_value / (Fraction(1, 1) - same_prob)
return expected_value
if __name__ == "__main__":
for p1_hp in range(low_hp + 1, max_hp + 1):
for p2_hp in range(1, p1_hp + 1):
print("P1 HP:", p1_hp, "P2 HP:", p2_hp)
matrix = {}
for p1_attack in attacks:
for p2_attack in attacks:
value = solve_q(p1_hp, p2_hp, p1_attack, p2_attack)
matrix[(p1_attack, p2_attack)] = value
# get optimal moves and value
worst = []
for p1_attack in attacks:
worst_case = Fraction(1, 1)
for p2_attack in attacks:
value = matrix[(p1_attack, p2_attack)]
if value < worst_case:
worst_case = value
worst.append(worst_case)
best = []
for p2_attack in attacks:
best_case = Fraction(0, 1)
for p1_attack in attacks:
value = matrix[(p1_attack, p2_attack)]
if value > best_case:
best_case = value
best.append(best_case)
assert(max(worst) == min(best))
value = max(worst)
p1_best_moves = []
for i, p1_attack in enumerate(attacks):
if worst[i] == value:
p1_best_moves.append(p1_attack)
p2_best_moves = []
for i, p2_attack in enumerate(attacks):
if best[i] == value:
p2_best_moves.append(p2_attack)
# must be stored here for vs recharge below
value_table[(p1_hp, p2_hp, False, False)] = value
move_table[(p1_hp, p2_hp, False, False)] = (p1_best_moves, p2_best_moves)
p1_vs_charge_values = []
for p1_attack in attacks:
value = solve_q(p1_hp, p2_hp, p1_attack, "recharge")
p1_vs_charge_values.append(value)
p2_vs_charge_values = []
for p2_attack in attacks:
value = solve_q(p1_hp, p2_hp, "recharge", p2_attack)
p2_vs_charge_values.append(value)
p1_vs_charge_value = max(p1_vs_charge_values)
p2_vs_charge_value = min(p2_vs_charge_values)
p1_vs_charge_best_moves, p2_vs_charge_best_moves = [], []
for i, p1_attack in enumerate(attacks):
if p1_vs_charge_values[i] == p1_vs_charge_value:
p1_vs_charge_best_moves.append(p1_attack)
for i, p2_attack in enumerate(attacks):
if p2_vs_charge_values[i] == p2_vs_charge_value:
p2_vs_charge_best_moves.append(p2_attack)
value_table[(p1_hp, p2_hp, False, True)] = p1_vs_charge_value
value_table[(p1_hp, p2_hp, True, False)] = p2_vs_charge_value
move_table[(p1_hp, p2_hp, False, True)] = (p1_vs_charge_best_moves, ["recharge"])
move_table[(p1_hp, p2_hp, True, False)] = (["recharge"], p2_vs_charge_best_moves)
# print(p1_vs_charge_values, p2_vs_charge_values)
print("RESULT:", value, p1_best_moves, p2_best_moves)
print("RESULT (p1 vs charge):", p1_vs_charge_value, p1_vs_charge_best_moves)
print("RESULT (p2 vs charge):", p2_vs_charge_value, p2_vs_charge_best_moves)
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