dice-calc 0.2.10

Advanced Calculator for Dice

PythonDice

This is a python package that includes a simple to use and powerful dice probability engine.

This package offers features and capabilities to calculate probabilities of arbitrary dice scripts including full capabilities of anydice.com.

Additionaly, this package includes the first* custom built compiler that translates almost any** valid anydice.com code into runnable python code.

This project is still in early development but everything mentioned above is complete. (project started October 2024)

* as far as we know

** very few edge cases mentioned at the end

Installation

pip install dice-calc

This package has no dependencies.

Basic Usage

If you are familiar with the anydice.com language then you should skip to section compiling anydice.com code which automatically converts the provided anydice code to this packages code thus teaching you all the nuances of this package.

The examples below are not comprehensive at all. They just show very basic use cases of our package.

Example #1:

Let's roll a single d20 dice (a d20 is a regular twenty sided-die)

from dice_calc.randvar import roll
X = roll(20)
print(X)

10.5 ± 5.77
 1:  5.00  ████
 2:  5.00  ████
 3:  5.00  ████
 4:  5.00  ████
 5:  5.00  ████
 6:  5.00  ████
 7:  5.00  ████
 8:  5.00  ████
 9:  5.00  ████
10:  5.00  ████
11:  5.00  ████
12:  5.00  ████
13:  5.00  ████
14:  5.00  ████
15:  5.00  ████
16:  5.00  ████
17:  5.00  ████
18:  5.00  ████
19:  5.00  ████
20:  5.00  ████
----------------------------------------------------------------------------------------

The numbers on the first line are the mean and std.

Example #2

Let's roll two d6 dice (a d6 is a regular six sided-die)

from dice_calc.randvar import roll
X = roll(2, 6)  # or roll(6) + roll(6)
print(X)

7.0 ± 2.42
 2:  2.78  ██
 3:  5.56  ████
 4:  8.33  ██████
 5: 11.11  █████████
 6: 13.89  ███████████
 7: 16.67  █████████████
 8: 13.89  ███████████
 9: 11.11  █████████
10:  8.33  ██████
11:  5.56  ████
12:  2.78  ██
----------------------------------------------------------------------------------------

Example #3

What about rolling a D20 plus a D6?

from dice_calc.randvar import roll
X = roll(20) + roll(6)
print(X)

14.0 ± 6.01
 2:  0.83  █
 3:  1.67  █
 4:  2.50  ██
 5:  3.33  ███
 6:  4.17  ███
 7:  5.00  ████
 8:  5.00  ████
 9:  5.00  ████
10:  5.00  ████
11:  5.00  ████
12:  5.00  ████
13:  5.00  ████
14:  5.00  ████
15:  5.00  ████
16:  5.00  ████
17:  5.00  ████
18:  5.00  ████
19:  5.00  ████
20:  5.00  ████
21:  5.00  ████
22:  4.17  ███
23:  3.33  ███
24:  2.50  ██
25:  1.67  █
26:  0.83  █
----------------------------------------------------------------------------------------

Example #4

What about the probability distribution of rolling two D20's with advantage (i.e. rolling two D20's and taking the highest number)

from dice_calc.randvar import roll
X = 1 @ roll(2, 20)
print(X)

13.82 ± 4.71
 1:  0.25  
 2:  0.75  █
 3:  1.25  █
 4:  1.75  █
 5:  2.25  ██
 6:  2.75  ██
 7:  3.25  ███
 8:  3.75  ███
 9:  4.25  ███
10:  4.75  ████
11:  5.25  ████
12:  5.75  ████
13:  6.25  █████
14:  6.75  █████
15:  7.25  ██████
16:  7.75  ██████
17:  8.25  ██████
18:  8.75  ███████
19:  9.25  ███████
20:  9.75  ████████
----------------------------------------------------------------------------------------

Example #5

Let's try a slightly more complex example.

Rolling a D20 with advantage + two D6's + 5

from dice_calc.randvar import roll
D20_adv = 1 @ roll(2, 20)
two_D6 = roll(2, 6)
result = D20_adv + two_D6 + 5
print(result)

25.82 ± 5.29
 8:  0.01  
 9:  0.03  
10:  0.10  
11:  0.21  
12:  0.38  
13:  0.63  
14:  0.96  █
15:  1.35  █
16:  1.78  █
17:  2.26  ██
18:  2.75  ██
19:  3.25  ███
20:  3.75  ███
21:  4.25  ███
22:  4.75  ████
23:  5.25  ████
24:  5.75  ████
25:  6.25  █████
26:  6.75  █████
27:  7.25  ██████
28:  7.47  ██████
29:  7.38  ██████
30:  6.99  █████
31:  6.26  █████
32:  5.20  ████
33:  3.78  ███
34:  2.57  ██
35:  1.57  █
36:  0.80  █
37:  0.27  
----------------------------------------------------------------------------------------

Complex Example:

Let's try calculating the total damage of the following attack on a boss in an RPG:

• TO HIT: 1d20 + 7 against 22 AC (less than 22 is a miss. rolling a 20 is a CRITICAL so double the damage die)
• DAMAGE: 2d8 + 4 blunt damange
• + 1d4 thunder damage
• + 1d10 + 3 radiant damange (half damage if the target succeeds a 16 DC wisdom saving throw, boss has +5 wis saving throw)

from dice_calc.randvar import roll, anydice_casting

@anydice_casting()
def calculate(to_hit_roll: int, save_roll: int):  # type hinting as int REQUIRED!!!
    if to_hit_roll + 7 < 22:  # miss
        return 0
    is_crit = (to_hit_roll == 20)
    dmg_die_mult = 2 if is_crit else 1
    blung_dmg = roll(2 * dmg_die_mult, 8) + 4
    thund_dmg = roll(1 * dmg_die_mult, 4)
    radiant_dmg = roll(1 * dmg_die_mult, 10) + 3
    if save_roll + 5 >= 16:  # save success
        radiant_dmg = radiant_dmg // 2
    return blung_dmg + thund_dmg + radiant_dmg


X = calculate(roll(20), roll(20))

# plotting code
from matplotlib import pyplot as plt
vals, probs = zip(*X.get_vals_probs())
plt.bar(vals, probs); plt.xlabel('Damage'); plt.ylabel('Probability');

Notice how we used the decorator @anydice_casting to use if conditions on dice inside of a custom function. Typehinting the input to int is required, the engine knows that you want to calculate the function many times based on all possible combinations of the input random variable.

Getting probabilities as dict

from dice_calc.randvar import roll
X = 1 @ roll(2, 20)  # D20 with advantage
pdf = dict(X.get_vals_probs())
print(pdf)

{1: 0.0025, 2: 0.0075, 3: 0.0125, 4: 0.0175, 5: 0.0225, 6: 0.0275, 7: 0.0325, 8: 0.0375, 9: 0.0425, 10: 0.0475, 11: 0.0525, 12: 0.0575, 13: 0.0625, 14: 0.0675, 15: 0.0725, 16: 0.0775, 17: 0.0825, 18: 0.0875, 19: 0.0925, 20: 0.0975}

plotting using matploblib

from dice_calc.randvar import roll
X = 1 @ roll(2, 20) + 8  # D20 with advantage + 8

# plotting code
from matplotlib import pyplot as plt
vals, probs = zip(*X.get_vals_probs())
percent = [p * 100 for p in probs]
plt.bar(vals, percent); plt.xlabel('Roll'); plt.ylabel('Probability %');

compiling anydice.com code

anydice is a powerful and popular online dice calculater which inspired the creation of this package. Any* valid code from anydice can be converted to valid python code using this package in a single function call.

Below we take an example piece of code from the anydice articles legend of the five rings.

We convert it using the function compile_anydice and then execute it using our package (p.s. don't forget to import all the library functions as we do below).

from dice_calc.parser.parse_and_exec import compile_anydice

EXAMPLE_CODE = """
function: convert SUM:n {
 if SUM >= 1000 {
  TENSROLLED: SUM / 1000
  result: SUM - TENSROLLED * 990 + TENSROLLED d [explode d10]
 }
 result: SUM
}

output [convert [highest 3 of 6d{1..9, 1000}]] named "6k3 exploded after keeping"
"""

code = compile_anydice(EXAMPLE_CODE)
print(f'compile retured type:{type(code)}\n')
print(code)

compile retured type:<class 'str'>

@anydice_casting()
def convert_X(SUM: int):
  if SUM >= 1000:
    TENSROLLED = SUM // 1000
    return SUM - TENSROLLED * 990 + roll(TENSROLLED, explode_X(roll(10)))
  
  return SUM

output(convert_X(highest_X_of_X(3, roll(6, Seq([myrange(1, 9), 1000])))), named=f"6k3 exploded after keeping")

# IMPORT EVERYTHING
from dice_calc.randvar import RV, Seq, anydice_casting, output, roll, settings_set
from dice_calc.utils import myrange
from dice_calc.funclib import absolute as absolute_X, contains as X_contains_X, count_in as count_X_in_X, explode as explode_X, highest_N_of_D as highest_X_of_X, lowest_N_of_D as lowest_X_of_X, middle_N_of_D as middle_X_of_X, highest_of_N_and_N as highest_of_X_and_X, lowest_of_N_and_N as lowest_of_X_and_X, maximum_of as maximum_of_X, reverse as reverse_X, sort as sort_X

# EXECUTE CODE FROM COMPILE_ANYDICE
@anydice_casting()
def convert_X(SUM: int):
  if SUM >= 1000:
    TENSROLLED = SUM // 1000
    return SUM - TENSROLLED * 990 + roll(TENSROLLED, explode_X(roll(10)))
  
  return SUM

output(convert_X(highest_X_of_X(3, roll(6, Seq([myrange(1, 9), 1000])))), named=f"6k3 exploded after keeping")

6k3 exploded after keeping 26.53 ± 8.32
  3:  0.00  
  4:  0.00  
  5:  0.00  
  6:  0.01  
  7:  0.02  
  8:  0.04  
  9:  0.09  
 10:  0.17  
 11:  0.29  █
 12:  0.48  █
 13:  0.76  █
 14:  1.12  ██
 15:  1.62  ███
 16:  2.22  ████
 17:  2.92  █████
 18:  3.71  ███████
 19:  4.55  ████████
 20:  5.31  █████████
 21:  6.00  ███████████
 22:  6.40  ███████████
 23:  6.51  ████████████
 24:  6.20  ███████████
 25:  5.61  ██████████
 26:  4.65  ████████
 27:  3.78  ███████
 28:  3.14  ██████
 29:  3.45  ██████
 30:  3.40  ██████
 31:  3.32  ██████
 32:  3.16  ██████
 33:  2.93  █████
 34:  2.60  █████
 35:  2.21  ████
 36:  1.78  ███
... output cropped ...

Or you can do it all in one line

from dice_calc.parser.parse_and_exec import compile_anydice, _get_lib

EXAMPLE_CODE = """
function: convert SUM:n {
 if SUM >= 1000 {
  TENSROLLED: SUM / 1000
  result: SUM - TENSROLLED * 990 + TENSROLLED d [explode d10]
 }
 result: SUM
}

output [convert [highest 3 of 6d{1..9, 1000}]] named "6k3 exploded after keeping"
"""

exec(compile_anydice(EXAMPLE_CODE), _get_lib())

6k3 exploded after keeping 26.53 ± 8.32
  3:  0.00  
  4:  0.00  
  5:  0.00  
  6:  0.01  
  7:  0.02  
  8:  0.04  
  9:  0.09  
 10:  0.17  
 11:  0.29  █
 12:  0.48  █
 13:  0.76  █
 14:  1.12  ██
 15:  1.62  ███
 16:  2.22  ████
 17:  2.92  █████
 18:  3.71  ███████
 19:  4.55  ████████
 20:  5.31  █████████
 21:  6.00  ███████████
 22:  6.40  ███████████
 23:  6.51  ████████████
 24:  6.20  ███████████
 25:  5.61  ██████████
 26:  4.65  ████████
 27:  3.78  ███████
 28:  3.14  ██████
 29:  3.45  ██████
 30:  3.40  ██████
 31:  3.32  ██████
 32:  3.16  ██████
 33:  2.93  █████
 34:  2.60  █████
 35:  2.21  ████
 36:  1.78  ███
... output cropped ...

Note that calls to the built-in python function exec executes arbitrary code and could be dangerous if malicious code is run. Only run exec on code you trust.

compile_anydice was developed to only generate safe code, but no garuntees are made.

compile_anydice edge cases

The compile_anydice function was a large part of this project. Under the hood it is a custom compiler built using Python's implementation of lex and yacc provided by PLY (Python Lex-Yacc).

As far as we tested, almost all valid anydice code worked perfectly using our compiler, except for very few intentionally ignored subsets of anydice code mentioned below:

1. Code that includes the expression #int: in anydice, if you perform this operation it returns the number of digits in the integer (i.e. #X is equivalent to the Python code int(math.log10(X))+1 (except #0 which is 1)). This is awkward syntax and is intentionally ignored as you really should avoid using #int. In the rare cases that you do use it, replace that part with int(math.log10(X))+1 in the compiled code manually.

   • The global fix for this is simple, instead of resolving the # character to the built-in len, we would resolve it to a custom function mylen. The function would return len unless the input is a number in which case it returns int(math.log10(X))+1. This is ignored to avoid having the generated code having more ambiguous functions as mylen (myrange was enough)

2. Code that includes the expression int @ int: in anydice, if you you perform the N @ M operation where both are ints, it returns the N-th digit of M which is a weird syntax and has very few legitimate use cases. The @ symbol in Python calls the __matmul__ function (which is obviously implemented for both custom objects, RV and Seq). However, calling __matmul__ on an int and int would raise a TypeError

   • The global fix for this is simple but very annoying. The solution would be to implement our own function mymatmul(p1, p2) which returns p1 @ p2 unless both are ints in which case it would return int(str(p2)[p1-1]). This is annoying because it would resolve all instances of P1 @ P2 in anydice code (frequently occurring) to the ugly syntax mymatmul(p1, p2) instead of literally the same P1 @ P2. And the only reason to use this nasty syntax is to properly handle a very rare case of int @ int.

3. Limit on global function depth: As mentioned in the Anydice Documentation, functions can only support a limited number of nested function calls until results are truncated. By default, this value is 10. You can try this by running the code function: r {result: 1 + [r]} output [r] which will yield 10 despite theoretically running indefinitely. Additionally, running the following function: hello {result: [r]} output [hello] yields 9 yet it's logically equivelant to the previous function. Thus, in anydice, a function's result depends on where it was called which is strange behavior and is bad programming. If this is really what you want then pass a depth variable and decrement it until it reaches zero and stop the recursion with a 0.

   • Note: the explode function provided in this pacakges funclib is correctly implemented including a limit on its depth. Additionally, set "maximum function depth" to X is correctly implemented. The limit on explode is trivially implemented using a decrementing depth counter as suggested above. If you need a similar behavior in your custom functions you should do the same.

   • The solution to this for a single function is trivial, track a depth variable. The solution for all arbitrary functions is not complex; Simply having a decorator track the current stack level using a global CUR_DEPTH variable and refuse to call the function if CUR_DEPTH reaches MAX_DEPTH. This is yet to be implemented but could be depending on if it's needed

If you discover any code that behaves differently when run on anydice.com and when run here using compile_anydice then please report it to us as an issue so we can keep improving this package.