def probability_of_save_fail(dices,
success,
after_crit_wound,
roll: Roll,
context,
rend,
crit_wnd=0) -> float:
if after_crit_wound > success:
raise ValueError(
f'trying to compute {after_crit_wound} success after crit amongst {success} successes'
)
if after_crit_wound > crit_wnd:
raise ValueError(
f'trying to compute {after_crit_wound} success after crit with {crit_wnd} crits'
)
regular_pass_rate = binomial(dices - crit_wnd, success - after_crit_wound)
regular_pass_rate *= pow(roll.fail(context, rend),
success - after_crit_wound)
regular_pass_rate *= pow(roll.success(context, rend),
(dices - crit_wnd) - (success - after_crit_wound))
crit_pass_rate = binomial(crit_wnd, after_crit_wound)
crit_pass_rate *= pow(
roll.fail(context, rend + context.get(CRIT_BONUS_REND, 0)),
after_crit_wound)
crit_pass_rate *= pow(
roll.success(context, rend + context.get(CRIT_BONUS_REND, 0)),
crit_wnd - after_crit_wound)
return regular_pass_rate * crit_pass_rate
def test_4plus_is_fifty_fifty():
# given
roll = Roll(4)
# assert
success, crit = roll.chances({})
assert success + crit == 0.5
assert -0.000001 < success - 2 / 6 < 0.000001
assert -0.000001 < crit - 1 / 6 < 0.000001
def probability_of_hit_and_crit(dices, success, crit, roll: Roll,
context) -> float:
success_rate = binomial(dices, success)
success_rate *= pow(roll.success(context), success) * pow(
roll.fail(context), dices - success)
crit_rate = binomial(success, crit) * pow(
roll.critic_given_success(context), crit) * pow(
roll.no_critic_given_success(context), success - crit)
return success_rate * crit_rate
def __init__(
self,
name: str,
weapons: Union[List[Weapon]],
move: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
save: int,
bravery: int,
wounds: int,
min_size: int,
base: Base,
rules: List[Rule],
keywords: List[str],
cast=0,
unbind=0,
named=False,
max_size=None,
):
self.name = name
self.weapons = weapons
self.move = value(move)
self.save = Roll(save)
self.extra_save = Roll(7)
self.bravery = bravery
self.wounds = wounds
self.min_size = min_size
self.size = min_size
self.max_size = max_size
if self.max_size is None:
self.max_size = min_size if 'MONSTER' in keywords or 'HERO' in keywords else min_size
self.base = base
self.keywords = keywords
keywords.append(self.name.upper())
self.named = named
self.can_fly = False
self.run_distance = value('D6')
self.charge_range = value('2D6')
self.can_run_and_charge = False
self.special_users = []
self.casting_value = value('2D6')
self.unbinding_value = value('2D6')
self.morale_roll = value('D6')
self.notes = []
self.spells_per_turn = value(cast)
self.unbind_per_turn = value(unbind)
self.spells: List[Spell] = [ARCANE_BOLT, MAGIC_SHIELD]
self.command_abilities: List[CommandAbility] = []
self.rules = rules
for r in self.rules:
r.apply(self)
def test_skinks_stats():
# given
context = {
ENEMY_BASE: infantry_base,
ENEMY_NUMBERS: 10,
ENEMY_SAVE: Roll(4),
SELF_NUMBERS: 1,
}
jav = seraphons_by_name['Skinks'].units['Meteoritic Javelin, Star-buckler']
bolt = seraphons_by_name['Skinks'].units['Boltspitter, Star-buckler']
bolt_club = seraphons_by_name['Skinks'].units[
'Boltspitter, Moonstone Club']
club = seraphons_by_name['Skinks'].units['Moonstone Club, Star-buckler']
# assert
assert round(jav.average_damage(context), 2) == 0.03
assert round(bolt.average_damage(context), 2) == 0.03
context[SELF_NUMBERS] = 10
assert round(bolt_club.average_damage(context), 2) == 1.11
assert round(club.average_damage(context), 2) == 0.83
context[SELF_NUMBERS] = 20
context[RANGE] = 5
assert round(jav.average_damage(context), 2) == 2.5
assert round(bolt.average_damage(context), 2) == 1.67
context[SELF_NUMBERS] = 30
context[RANGE] = 5
assert round(jav.average_damage(context), 2) == 5
assert round(bolt.average_damage(context), 2) == 3.33
def probability_of_wound_and_crit(dices,
success,
crit,
roll: Roll,
context,
crit_hit=0) -> float:
succ_crit_hit = min(crit_hit, success)
failed_crit_hit = crit_hit - succ_crit_hit
if context.get(AUTO_WOUND_ON_CRIT,
False) and (failed_crit_hit
or crit > success - succ_crit_hit):
# cannot fail, nor get a critical wound roll an automatic success
return 0
success_rate = binomial(dices, success)
# successful after a critical_hit
if not context.get(AUTO_WOUND_ON_CRIT, False):
success_rate *= pow(
roll.success(context, context.get(TOWOUND_MOD_ON_CRIT_HIT, 0)),
succ_crit_hit)
# successful without a critical_hit
success_rate *= pow(roll.success(context), success - succ_crit_hit)
# failed despite a critical_hit
success_rate *= pow(
roll.fail(context, context.get(TOWOUND_MOD_ON_CRIT_HIT, 0)),
failed_crit_hit)
# failed without a critical_hit
success_rate *= pow(roll.fail(context), dices - success - failed_crit_hit)
# crit rate may be flawed in case of crit_hit bonuses TODO: fix
crit_rate = binomial(success, crit)
# critical wound after a critical_hit
crit_rate *= pow(roll.critic_given_success(context), crit)
if not (context.get(AUTO_WOUND_ON_CRIT, False) and crit_hit):
crit_rate *= pow(roll.no_critic_given_success(context), success - crit)
return success_rate * crit_rate
def test_liberators_stats():
# given
context = {
CHARGING: False,
ENEMY_BASE: infantry_base,
ENEMY_NUMBERS: 10,
ENEMY_SAVE: Roll(4),
SELF_NUMBERS: 1,
}
context2 = {
CHARGING: False,
ENEMY_BASE: infantry_base,
ENEMY_NUMBERS: 10,
ENEMY_WOUNDS: 5,
ENEMY_SAVE: Roll(4),
SELF_NUMBERS: 1,
}
shield_libs = stormcasts_by_name['Liberators'].units[
'Warhammer, Sigmarite shields']
# assert
assert round(shield_libs.average_damage(context), 2) == 0.33
assert round(shield_libs.average_damage(context2), 2) == 0.44
def test_kroxigor_stats():
# given
context = {
ENEMY_BASE: infantry_base,
ENEMY_NUMBERS: 10,
ENEMY_SAVE: Roll(4),
SELF_NUMBERS: 1,
RANGE: 0.1
}
krok = seraphons_by_name['Kroxigors'].units['']
# assert
assert round(krok.average_damage(context), 2) == 1.58
context[RANGE] = 1.5
assert round(krok.average_damage(context), 2) == 1.33
def __init__(
self,
name: str,
range_: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
attacks: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
tohit,
towound,
rend,
damage: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
rules: List[Rule],
) -> None:
self.name = name
self.range = value(range_)
self.attacks = value(attacks)
self.tohit = Roll(tohit)
self.towound = Roll(towound)
self.rend = value(rend)
self.damage = value(damage)
self.attack_rules: List[Callable] = []
self.rules = rules
for r in rules:
r.apply(self)
def test_dryad_stats():
# given
context = {
CHARGING: False,
ENEMY_BASE: infantry_base,
ENEMY_NUMBERS: 10,
ENEMY_SAVE: Roll(4),
SELF_NUMBERS: 1,
}
dryads = sylvaneth_by_name['Dryads'].units['']
# assert
assert round(dryads.average_damage(context), 2) == 0.25
assert round(dryads.average_health(context), 2) == 1.5
context[SELF_NUMBERS] = 12
assert round(dryads.average_health(context), 2) == 24
def test_saurus_stats():
# given
context = {
ENEMY_BASE: infantry_base,
ENEMY_NUMBERS: 10,
ENEMY_SAVE: Roll(4),
SELF_NUMBERS: 1,
}
clubs = seraphons_by_name['Saurus Warriors'].units['Celestite Club']
spears = seraphons_by_name['Saurus Warriors'].units['Celestite Spear']
# assert
assert round(clubs.average_damage(context), 2) == 0.25
assert round(spears.average_damage(context), 2) == 0.21
context[SELF_NUMBERS] = 10
assert round(clubs.average_damage(context), 2) == 2.5
assert round(spears.average_damage(context), 2) == 2.08
context[SELF_NUMBERS] = 20
assert round(clubs.average_damage(context), 2) == 6.94
assert round(spears.average_damage(context), 2) == 5.83
context[SELF_NUMBERS] = 30
assert round(clubs.average_damage(context), 2) == 17.08
assert round(spears.average_damage(context), 2) == 13.75
Rule('Mastery of Magic', mastery_of_magic),
Rule('Oracle of Eternity', can_reroll_x_dice_during_game(1)),
Spell('Gift of Change', 8, None),
], keywords=[CHAOS, DAEMON, TZEENTCH, WIZARD, HERO, MONSTER, 'LORD OF CHANGE'], cast=2, unbind=2, named=True))
def arcane_tome(u: Unit):
u.casting_value = u.casting_value + OncePerGame('D6')
sky_sharks = Rule('Sky-sharks', extra_damage_on_keyword(value('D3') - 1, MONSTER))
TZEENTCH_WS.append(Warscroll(
'Herald of Tzeentch on Burning Chariot', [
[Weapon('Staff of Change', 2, 1, 4, 3, -1, 'D3', []),
Weapon('Wake of Fire', 'move across', 1, 7, 7, 0, 0, [Rule('', deal_x_mortal_wound_on_roll('D3', Roll(4)))]),
Weapon('Screamer`s Lamprey Bites', 1, 6, 4, 3, 0, 1, [sky_sharks])],
[Weapon('Ritual Dagger', 1, 2, 4, 4, 0, 1, []),
Weapon('Wake of Fire', 'move across', 1, 7, 7, 0, 0, [Rule('', deal_x_mortal_wound_on_roll('D3', Roll(4)))]),
Weapon('Screamer`s Lamprey Bites', 1, 6, 4, 3, 0, 1, [sky_sharks])],
], 14, 5, 10, 8, 1, monster_base, rules=[
FLIGHT,
Rule('Arcane Tome', arcane_tome),
Spell('Tzeentch`s Firestorm', 9, None),
], keywords=[CHAOS, DAEMON, HORROR, TZEENTCH, WIZARD, HERO, 'HERALD ON CHARIOT'], cast=1, unbind=1))
TZEENTCH_WS.append(Warscroll(
'Herald of Tzeentch on Disc', [
[Weapon('Magical Flames', 18, 2, 4, 4, 0, 1, []),
Weapon('Staff of Change', 2, 1, 4, 3, -1, 'D3', []),
class Weapon:
def __init__(
self,
name: str,
range_: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
attacks: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
tohit,
towound,
rend,
damage: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
rules: List[Rule],
) -> None:
self.name = name
self.range = value(range_)
self.attacks = value(attacks)
self.tohit = Roll(tohit)
self.towound = Roll(towound)
self.rend = value(rend)
self.damage = value(damage)
self.attack_rules: List[Callable] = []
self.rules = rules
for r in rules:
r.apply(self)
def average_hits(self,
dices,
extra_data: dict,
mod=0) -> Tuple[float, float]:
return self.tohit.average(dices, extra_data, mod)
def average_wounds(self,
dices,
extra_data: dict,
mod=0) -> Tuple[float, float]:
return self.towound.average(dices, extra_data, mod)
def unsaved_chances(self, extra_data: dict, extra_rend=0) -> float:
chances, crit = extra_data[ENEMY_SAVE].chances({},
mod=self.rend.average(
extra_data,
extra_rend))
return 1 - chances - crit
def average_damage(self, context: dict, users=1):
if context.get(RANGE, 0) > self.range.average(context) or \
self.range.average(context) > 3 >= context.get(RANGE, 0):
return 0
context[WEAPON_RANGE] = self.range.average(context)
dmg = self.attack_round(copy(context), users)
return sum([e['damage'] * e['proba'] for e in dmg])
def attack_round(self, context, users=1):
my_context = copy(context)
for r in self.attack_rules:
r(my_context)
potential_attacks = {}
potential_hits = {}
potential_wounds = {}
potential_unsaved = {}
potential_damage = {}
cleaned_damage = []
try:
potential_attacks = [{
'attacks':
nb * users,
'proba':
proba,
'mortal_wounds':
my_context.get(MORTAL_WOUNDS, value(0)) +
my_context.get(MORTAL_WOUNDS_PER_ATTACK, 0) * nb * users,
} for (nb, proba) in self.attacks.potential_values(my_context)]
assert abs(sum([att['proba']
for att in potential_attacks]) - 1) <= pow(0.1, 5)
potential_attacks = cleaned_dict_list(potential_attacks,
['attacks', 'mortal_wounds'])
potential_hits = compute_potential_hits(my_context,
potential_attacks,
self.tohit)
assert abs(sum([hit['proba']
for hit in potential_hits]) - 1) <= pow(0.1, 5)
potential_hits = cleaned_dict_list(
potential_hits, ['hits', 'crit_hits', 'mortal_wounds'])
potential_wounds = compute_potential_wounds(
my_context, potential_hits, self.towound)
assert abs(sum([wnd['proba']
for wnd in potential_wounds]) - 1) <= pow(0.1, 5)
potential_wounds = cleaned_dict_list(
potential_wounds, ['wounds', 'crit_wounds', 'mortal_wounds'])
potential_unsaved = [
{
**wnd, 'unsaved':
nb,
'unsaved_crit_wound':
nb_crit,
'proba':
wnd['proba'] * probability_of_save_fail(
wnd['wounds'],
nb,
nb_crit,
my_context[ENEMY_SAVE],
my_context,
rend=self.rend.average(my_context),
crit_wnd=wnd['crit_wounds'])
} for wnd in potential_wounds
for nb in range(wnd['wounds'] + 1) for nb_crit in range(
max(0, wnd['crit_wounds'] - (wnd['wounds'] - nb)),
min(wnd['crit_wounds'], nb) + 1)
]
assert abs(
sum([unsvd['proba']
for unsvd in potential_unsaved]) - 1) <= pow(0.1, 5)
potential_unsaved = cleaned_dict_list(
potential_unsaved,
['unsaved', 'unsaved_crit_wound', 'mortal_wounds'])
potential_damage = compute_potential_damage(
self.damage, my_context, potential_unsaved)
assert abs(sum([dmg['proba']
for dmg in potential_damage]) - 1) <= pow(0.1, 5)
potential_full_damage = [{
**dmg,
'damage': dmg['damage'] + nb,
'mortal_wounds': nb,
'proba': dmg['proba'] * proba,
} for dmg in potential_damage for (
nb, proba) in dmg['mortal_wounds'].potential_values(my_context)
]
potential_full_damage = cleaned_dict_list(potential_full_damage,
['damage'])
cleaned_damage = [{
'damage':
pick * (1 + context.get(MW_ON_DAMAGE, 0)),
'proba':
sum([
dmg['proba'] for dmg in potential_full_damage
if dmg['damage'] == pick
])
} for pick in set(dmg['damage'] for dmg in potential_full_damage)]
# raise AssertionError # testing
except AssertionError:
info = {
'potential_attacks': potential_attacks,
'potential_hits': potential_hits,
'potential_wounds': potential_wounds,
'potential_unsaved': potential_unsaved,
'potential_damage': potential_damage,
'cleaned_damage': cleaned_damage,
}
print(self.name)
for k, potent in info.items():
print(f'- {k}:')
for e in potent:
print(
str({k: str(v)
for k, v in e.items()
}).replace("'", "").replace("\"", ""))
sum_proba = sum(e['proba'] for e in potent)
print(f' total={sum_proba}')
average = sum(
d.get('damage') * d.get('proba') for d in cleaned_damage)
print(f'AVERAGE: {average}')
return cleaned_damage
def test_average_of_3_5plus_is_one():
# given
roll = Roll(5)
# assert
success, crit = roll.average(3, {})
assert success + crit == 1
def cloak_of_feathers(u: Unit):
fly(u)
u.move = value(14)
u.save = Roll(4)
def rule_func(u: Unit):
u.extra_save = Roll(roll)
class Unit:
def __init__(
self,
name: str,
weapons: Union[List[Weapon]],
move: Union[int, str, Value, Dict[int, Union[int, str, Value]]],
save: int,
bravery: int,
wounds: int,
min_size: int,
base: Base,
rules: List[Rule],
keywords: List[str],
cast=0,
unbind=0,
named=False,
max_size=None,
):
self.name = name
self.weapons = weapons
self.move = value(move)
self.save = Roll(save)
self.extra_save = Roll(7)
self.bravery = bravery
self.wounds = wounds
self.min_size = min_size
self.size = min_size
self.max_size = max_size
if self.max_size is None:
self.max_size = min_size if 'MONSTER' in keywords or 'HERO' in keywords else min_size
self.base = base
self.keywords = keywords
keywords.append(self.name.upper())
self.named = named
self.can_fly = False
self.run_distance = value('D6')
self.charge_range = value('2D6')
self.can_run_and_charge = False
self.special_users = []
self.casting_value = value('2D6')
self.unbinding_value = value('2D6')
self.morale_roll = value('D6')
self.notes = []
self.spells_per_turn = value(cast)
self.unbind_per_turn = value(unbind)
self.spells: List[Spell] = [ARCANE_BOLT, MAGIC_SHIELD]
self.command_abilities: List[CommandAbility] = []
self.rules = rules
for r in self.rules:
r.apply(self)
def formation(self, data: dict, front_size) -> List[int]:
nb = data.get(SELF_NUMBERS, self.size)
data[SELF_NUMBERS] = nb
rows = []
while nb > 0:
row = max(min(front_size // self.base.width, nb), 1)
rows.append(row)
nb -= row
return rows
def describe_formation(self, data: dict, front_size) -> str:
rows = self.formation(data, front_size)
if len(rows) == 1 and rows[0] <= 1:
return ''
attacking = 0
_range = data.get(RANGE, 0)
for row in rows:
if sum([1 if w.range.average(data) > _range else 0 for w in self.weapons if isinstance(w, Weapon)]):
attacking += row
else:
break
_range += self.base.depth / INCH
if len(rows) > 1:
return f'({rows[0]}x{len(rows)}, {attacking} attacking)'
return f'({attacking} attacking)'
def average_damage(self, data: dict, front_size=1000):
total = 0
unit_data = copy(data)
unit_data[SELF_BASE] = self.base
unit_data[SELF_MOVE] = self.move.average(data)
_range = data.get(RANGE, 0)
data[RANGE] = _range
for row in self.formation(unit_data, front_size):
# specials
specials = 0
if total == 0:
for sp_usr in self.special_users:
total += sp_usr.size * sum([w.average_damage(copy(unit_data)) for w in sp_usr.weapons])
specials += sp_usr.size
users = row - specials
if users <= 5:
total += sum([w.average_damage(copy(unit_data), users=users) for w in self.weapons])
else: # let's avoid taking years to compute
total += users * sum([w.average_damage(copy(unit_data)) for w in self.weapons])
data[RANGE] += self.base.depth / INCH
data[RANGE] = _range
return total
def average_health(self, context: dict):
nb = context.get(SELF_NUMBERS, self.size)
rend = context.get(REND, 0)
save, crit = self.save.chances(context, mod=rend)
save += crit
wounds = min(self.wounds, context.get(SELF_WOUNDS, self.wounds))
life = nb * wounds / (1 - save)
life /= self.extra_save.fail(context)
return life
def average_speed(self, context: dict):
average_move = self.move.average(context)
average_sprint = self.run_distance.average(context) + average_move
average_charge = self.charge_range.average(context) + average_move
if self.can_run_and_charge:
average_charge += self.run_distance.average(context)
return average_move, average_sprint, average_charge
def speed_grade(self, context: dict):
m, s, c = self.average_speed(context)
return round((m + s + c) / 3) - 3
def speed_description(self, context: dict):
flight = 'F' if self.can_fly else ''
m, s, c = self.average_speed(context)
return f'{int(round(m))}-{int(round(s))}-{int(round(c))}{flight}'
def magic_power(self, context: dict):
if self.spells_per_turn == 0:
return 0
potential_cast = self.casting_value.potential_values(context)
spells = []
for sp in self.spells:
chances = sum(proba for val, proba in potential_cast if val >= sp.power)
spells.append(chances * sp.power)
return self.spells_per_turn.average(context) * sum(spells) / len(spells)
def unbind_power(self, context: dict):
if self.unbind_per_turn == 0:
return 0
potential_unbind = self.unbinding_value.potential_values(context)
spells = []
for sp_power in [5, 6, 7, 8, 9]:
chances = sum(proba for val, proba in potential_unbind if val >= sp_power)
spells.append(chances * sp_power)
return self.unbind_per_turn.average(context) * sum(spells) / len(spells)
def morale_grade(self, context: dict):
if HERO in self.keywords or MONSTER in self.keywords:
return self.bravery
mod = value('D6').average(context) - self.morale_roll.average(context)
return self.bravery + mod