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Applications and translations

The following examples and translations are intended to showcase dyce’s flexibility. If you have exposure to another tool, they may also help with transition.

Modeling “The Probability of 4d6, Drop the Lowest, Reroll 1s”

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>>> from dyce import H, P
>>> p_4d6 = 4@P(6)
>>> res1 = p_4d6.h(slice(1, None))  # discard the lowest die (index 0)
>>> d6_reroll_first_one = H(6).substitute(lambda h, outcome: H(6) if outcome == 1 else outcome)
>>> p_4d6_reroll_first_one = (4@P(d6_reroll_first_one))
>>> res2 = p_4d6_reroll_first_one.h(slice(1, None))  # discard the lowest
>>> p_4d6_reroll_all_ones = 4@P(H((2, 3, 4, 5, 6)))
>>> res3 = p_4d6_reroll_all_ones.h(slice(1, None))  # discard the lowest

Visualization:

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>>> import matplotlib  # doctest: +SKIP
>>> matplotlib.pyplot.plot(
...   *res1.distribution_xy(),
...   marker=".",
...   label="Discard lowest",
... )  # doctest: +SKIP
>>> matplotlib.pyplot.plot(
...   *res2.distribution_xy(),
...   marker=".",
...   label="Re-roll first 1; discard lowest",
... )  # doctest: +SKIP
>>> matplotlib.pyplot.plot(
...   *res3.distribution_xy(),
...   marker=".",
...   label="Re-roll all 1s; discard lowest",
... )  # doctest: +SKIP
>>> matplotlib.pyplot.legend()  # doctest: +SKIP
>>> matplotlib.pyplot.title(r"Comparing various take-three-of-4d6 methods")  # doctest: +SKIP
>>> matplotlib.pyplot.show()  # doctest: +SKIP

Plot: Comparing various take-three-of-4d6 methods

Translating one example from markbrockettrobson/python_dice

Source:

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# …
program = [
  "VAR save_roll = d20",
  "VAR burning_arch_damage = 10d6 + 10",
  "VAR pass_save = ( save_roll >= 10 ) ",
  "VAR damage_half_on_save = burning_arch_damage // (pass_save + 1)",
  "damage_half_on_save"
]
# …

Translation:

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>>> save_roll = H(20)
>>> burning_arch_damage = 10@H(6) + 10
>>> pass_save = save_roll.ge(10)
>>> damage_half_on_save = burning_arch_damage // (pass_save + 1)

Visualization:

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>>> import matplotlib  # doctest: +SKIP
>>> outcomes, probabilities = damage_half_on_save.distribution_xy()
>>> matplotlib.pyplot.plot(outcomes, probabilities, marker=".")  # doctest: +SKIP
>>> matplotlib.pyplot.title(r"Expected outcomes for attack with saving throw for half damage")  # doctest: +SKIP
>>> matplotlib.pyplot.show()  # doctest: +SKIP

Plot: Expected outcomes for attack with saving throw for half damage

An alternative using the H.substitute method:

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>>> save_roll.substitute(
...   lambda h, outcome:
...     burning_arch_damage // 2 if outcome >= 10
...     else burning_arch_damage
... ) == damage_half_on_save
True

More translations from markbrockettrobson/python_dice

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>>> # VAR name = 1 + 2d3 - 3 * 4d2 // 5
>>> name = 1 + (2@H(3)) - 3 * (4@H(2)) // 5
>>> print(name.format(width=0))
{avg: 1.75, -1:  3.47%, 0: 13.89%, 1: 25.00%, 2: 29.17%, 3: 19.44%, 4:  8.33%, 5:  0.69%}

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>>> # VAR out = 3 * ( 1 + 1d4 )
>>> out = 3 * (1 + 2@H(4))
>>> print(out.format(width=0))
{avg: 18.00, 9:  6.25%, 12: 12.50%, 15: 18.75%, 18: 25.00%, 21: 18.75%, 24: 12.50%, 27:  6.25%}

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>>> # VAR g = (1d4 >= 2) AND !(1d20 == 2)
>>> g = H(4).ge(2) & H(20).ne(2)
>>> print(g.format(width=0))
{..., False: 28.75%, True: 71.25%}

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>>> # VAR h = (1d4 >= 2) OR !(1d20 == 2)
>>> h = H(4).ge(2) | H(20).ne(2)
>>> print(h.format(width=0))
{..., False:  1.25%, True: 98.75%}

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>>> # VAR abs = ABS( 1d6 - 1d6 )
>>> abs_ = abs(H(6) - H(6))
>>> print(abs_.format(width=0))
{avg: 1.94, 0: 16.67%, 1: 27.78%, 2: 22.22%, 3: 16.67%, 4: 11.11%, 5:  5.56%}

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>>> # MAX(4d7, 2d10)
>>> _ = P(4@H(7), 2@H(10)).h(-1)
>>> print(_.format(width=0))
{avg: 16.60, 4:  0.00%, 5:  0.02%, 6:  0.07%, 7:  0.21%, ..., 25:  0.83%, 26:  0.42%, 27:  0.17%, 28:  0.04%}

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>>> # MIN(50, d%)
>>> _ = P(H((50,)), P(100)).h(0)
>>> print(_.format(width=0))
{avg: 37.75, 1:  1.00%, 2:  1.00%, 3:  1.00%, ..., 47:  1.00%, 48:  1.00%, 49:  1.00%, 50: 51.00%}

Translations from LordSembor/DnDice

Example 1 source:

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from DnDice import d, gwf
single_attack = 2*d(6) + 5
# …
great_weapon_fighting = gwf(2*d(6)) + 5
# …
# comparison of the probability
print(single_attack.expectancies())
print(great_weapon_fighting.expectancies())
# [ 0.03,  0.06, 0.08, 0.11, 0.14, 0.17, 0.14, ...] (single attack)
# [0.003, 0.006, 0.03, 0.05, 0.10, 0.15, 0.17, ...] (gwf attack)
# …

Example 1 translation:

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>>> single_attack = 2@H(6) + 5

>>> def gwf(h: H, outcome):
...   return h if outcome in (1, 2) else outcome

>>> great_weapon_fighting = 2@(H(6).substitute(gwf)) + 5  # reroll either die if it is a one or two
>>> print(single_attack.format(width=0))
{..., 7:  2.78%, 8:  5.56%, 9:  8.33%, 10: 11.11%, 11: 13.89%, 12: 16.67%, 13: 13.89%, ...}
>>> print(great_weapon_fighting.format(width=0))
{..., 7:  0.31%, 8:  0.62%, 9:  2.78%, 10:  4.94%, 11:  9.88%, 12: 14.81%, 13: 17.28%, ...}

Example 1 visualization:

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>>> import matplotlib  # doctest: +SKIP
>>> from dyce.viz import display_burst
>>> plot_ax = matplotlib.pyplot.subplot2grid((1, 2), (0, 0))  # doctest: +SKIP
>>> burst_ax = matplotlib.pyplot.subplot2grid((1, 2), (0, 1))  # doctest: +SKIP
>>> sa_label = "Normal attack"
>>> plot_ax.plot(
...     *single_attack.distribution_xy(),
...     color="tab:green",
...     label=sa_label,
...     marker=".",
... )  # doctest: +SKIP
>>> gwf_label = "“Great Weapon Fighting”"
>>> plot_ax.plot(
...     *great_weapon_fighting.distribution_xy(),
...     color="tab:blue",
...     label=gwf_label,
...     marker=".",
... )  # doctest: +SKIP
>>> plot_ax.legend()  # doctest: +SKIP
>>> plot_ax.set_title(r"Comparing a normal attack to an enhanced one")  # doctest: +SKIP
>>> display_burst(
...     burst_ax,
...     h_inner=great_weapon_fighting,
...     outer=single_attack,
...     desc=f"{sa_label} vs. {gwf_label}",
...     inner_color="RdYlBu_r",
...     outer_color="RdYlGn_r",
...     alpha=0.9,
... )  # doctest: +SKIP
>>> matplotlib.pyplot.tight_layout()  # doctest: +SKIP
>>> matplotlib.pyplot.show()  # doctest: +SKIP

Plot: Comparing a normal attack to an enhanced one

Example 2 source:

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from DnDice import d, advantage, plot

normal_hit = 1*d(12) + 5
critical_hit = 3*d(12) + 5

result = d()
for value, probability in advantage():
  if value == 20:
    result.layer(critical_hit, weight=probability)
  elif value + 5 >= 14:
    result.layer(normal_hit, weight=probability)
  else:
    result.layer(d(0), weight=probability)
result.normalizeExpectancies()
# …

Example 2 translation:

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>>> normal_hit = H(12) + 5
>>> critical_hit = 3@H(12) + 5
>>> advantage = (2@P(20)).h(-1)

>>> def crit(_: H, outcome):
...   if outcome == 20: return critical_hit
...   elif outcome + 5 >= 14: return normal_hit
...   else: return 0

>>> advantage_weighted = advantage.substitute(crit)

Example 2 visualization:

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>>> import matplotlib  # doctest: +SKIP
>>> matplotlib.pyplot.plot(
...   *normal_hit.distribution_xy(),
...   marker=".",
...   label="Normal hit",
... )  # doctest: +SKIP
>>> matplotlib.pyplot.plot(
...   *critical_hit.distribution_xy(),
...   marker=".",
...   label="Critical hit",
... )  # doctest: +SKIP
>>> matplotlib.pyplot.plot(
...   *advantage_weighted.distribution_xy(),
...   marker=".",
...   label="Advantage-weighted",
... )  # doctest: +SKIP
>>> matplotlib.pyplot.legend()  # doctest: +SKIP
>>> matplotlib.pyplot.title(r"Modeling an advantage-weighted attack with critical hits")  # doctest: +SKIP
>>> matplotlib.pyplot.show()  # doctest: +SKIP

Plot: Modeling an advantage-weighted attack with critical hits

Translation of the accepted answer to “Roll and Keep in Anydice?”

Source:

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output [highest 3 of 10d [explode d10]] named "10k3"

Translation:

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>>> res = (10@P(H(10).explode(max_depth=3))).h(slice(-3, None))

Visualization:

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>>> import matplotlib  # doctest: +SKIP
>>> matplotlib.pyplot.plot(*res.distribution_xy(), marker=".")  # doctest: +SKIP
>>> matplotlib.pyplot.title(r"Modeling taking the three highest of ten exploding d10s")  # doctest: +SKIP
>>> matplotlib.pyplot.show()  # doctest: +SKIP

Plot: Modeling taking the three highest of ten exploding d10s

Translation of the accepted answer to “How do I count the number of duplicates in anydice?”

Source:

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function: dupes in DICE:s {
  D: 0
  loop X over {2..#DICE} {
    if ((X-1)@DICE = X@DICE) { D: D + 1}
  }
  result: D
}

Translation:

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>>> def dupes(p: P):
...   for roll, count in p.rolls_with_counts():
...     dupes = 0
...     for i in range(1, len(roll)):
...       # Outcomes are ordered, so we only have to look at one neighbor
...       if roll[i] == roll[i - 1]:
...         dupes += 1
...     yield dupes, count

>>> res = H(dupes(8@P(10)))

Visualization:

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>>> from dyce.viz import plot_burst
>>> plot_burst(
...   res,
...   desc=r"Chances of rolling $n$ duplicates in 8d10",
... )  # doctest: +SKIP
>>> matplotlib.pyplot.tight_layout()  # doctest: +SKIP
>>> matplotlib.pyplot.show()  # doctest: +SKIP

Plot: Chances of rolling <i>n</i> duplicates in 8d10

Translation of the accepted answer to “Modelling [sic] opposed dice pools with a swap”

Source of basic brawl:

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function: brawl A:s vs B:s {
  SA: A >= 1@B
  SB: B >= 1@A
  if SA-SB=0 {
    result:(A > B) - (A < B)
  }
  result:SA-SB
}
output [brawl 3d6 vs 3d6] named "A vs B Damage"

Translation:

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>>> from itertools import product

>>> def brawl(a: P, b: P):
...   for (roll_a, count_a), (roll_b, count_b) in product(
...       a.rolls_with_counts(),
...       b.rolls_with_counts(),
...   ):
...     a_successes = sum(1 for v in roll_a if v >= roll_b[-1])
...     b_successes = sum(1 for v in roll_b if v >= roll_a[-1])
...     yield a_successes - b_successes, count_a * count_b

Rudimentary visualization using built-in methods:

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>>> res = H(brawl(3@P(6), 3@P(6))).lowest_terms()
>>> print(res.format(width=65))
avg |    0.00
std |    1.73
var |    2.99
 -3 |   7.86% |###
 -2 |  15.52% |#######
 -1 |  16.64% |########
  0 |  19.96% |#########
  1 |  16.64% |########
  2 |  15.52% |#######
  3 |   7.86% |###

Source of brawl with an optional dice swap:

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function: set element I:n in SEQ:s to N:n {
  NEW: {}
  loop J over {1 .. #SEQ} {
    if I = J { NEW: {NEW, N} }
    else { NEW: {NEW, J@SEQ} }
  }
  result: NEW
}
function: brawl A:s vs B:s with optional swap {
  if #A@A >= 1@B {
    result: [brawl A vs B]
  }
  AX: [sort [set element #A in A to 1@B]]
  BX: [sort [set element 1 in B to #A@A]]
  result: [brawl AX vs BX]
}
output [brawl 3d6 vs 3d6 with optional swap] named "A vs B Damage"

Translation:

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>>> def brawl_w_optional_swap(a: P, b: P):
...   for (roll_a, count_a), (roll_b, count_b) in product(
...       a.rolls_with_counts(),
...       b.rolls_with_counts(),
...   ):
...     if roll_a[0] < roll_b[-1]:
...       roll_a, roll_b = roll_a[1:] + roll_b[-1:], roll_a[:1] + roll_b[:-1]
...     roll_a = tuple(sorted(roll_a, reverse=True))
...     roll_b = tuple(sorted(roll_b, reverse=True))
...     a_successes = sum(1 for v in roll_a if v >= roll_b[0])
...     b_successes = sum(1 for v in roll_b if v >= roll_a[0])
...     result = a_successes - b_successes or (roll_a > roll_b) - (roll_a < roll_b)
...     yield result, count_a * count_b

Rudimentary visualization using built-in methods:

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>>> res = H(brawl_w_optional_swap(3@P(6), 3@P(6))).lowest_terms()
>>> print(res.format(width=65))
avg |    2.36
std |    0.88
var |    0.77
 -1 |   1.42% |
  0 |   0.59% |
  1 |  16.65% |########
  2 |  23.19% |###########
  3 |  58.15% |#############################

>>> res = H(brawl_w_optional_swap(4@P(6), 4@P(6))).lowest_terms()
>>> print(res.format(width=65))
avg |    2.64
std |    1.28
var |    1.64
 -2 |   0.06% |
 -1 |   2.94% |#
  0 |   0.31% |
  1 |  18.16% |#########
  2 |  19.97% |#########
  3 |  25.19% |############
  4 |  33.37% |################