python-dice-top-k-game-probabilities/pydiceprob.py

import sys
import json
import pprint
from fastapi import FastAPI, Header

pp = pp.Printer = pprint.PrettyPrinter(indent=2, compact=True)

def usagequit():
    print("""Usage: python pydiceprob.py [k] [mode]
    k between 6 and 99 (higher numbers are supported, up to however much your memory can handle; given that win probabilities approach 50%, this isn't very useful past about 100.)
    modes: single, single-table, multi, multi-table
    single prints out the probability of a single throw with a k-sided dice yielding k.
    single-table prints out a table between 6 and k with the probabilities of a single throw yielding k.
    multi prints out the probability of winning (assuming we're going first) in a game where two players take turns and the person who throws k first wins.
    multi-table prints out the probability of winning for a range between 6 and k if you have the first throw.""")
    quit()

app = FastAPI()

@app.get("/")
async def api_get(k: int =  Header(default=None)):
    if not isinstance(k, int) and k is not None:
        return {"message": "Header k must be an integer between 6 and 100 inclusive or not present."}
    if k is None:
        result = one_turn_table(100)
        return {"Probabilities of throwing the highest number on dice of size": result}
    elif k >= 6 and k <= 100:
        result = one_turn_single(k)
        return {f"Probability of throwing the highest number of dice of size {k}": result}
    else:
        return {"message": "Usage: no request body, use header k to specify what probability you want, if no k, then a table is given between dice sizes 6 and 100 inclusive."}

def main():
    global k
    try:
        if int(sys.argv[1]) >= 6:
            k = int(sys.argv[1])
        else:
            usagequit()
    except IndexError:
        usagequit()
    global mode
    try:
        mode = sys.argv[2]
    except IndexError:
        usagequit()
    dispatch(mode, k)

def dispatch(mode, k):
    modes = ["single", "multi", "single-table", "multi-table"]
    if mode not in modes:
        usagequit()
    if mode == "single":
        print(one_turn_single(k))
    elif mode == "multi" :
        print(multi_turn_single(k))
    elif mode == "single-table":
        print(one_turn_table(k))
    elif mode == "multi-table":
        print(multi_turn_table(k))

def one_turn_table(k):
    result = {}
    for k in range(6, int(k)+1):
        result[k] = 1/k
    return result

def one_turn_single(k):
    return one_turn_table(k)[k]

def multi_turn_single(k):
    p_win = 1 / k  # Winning probability on any given throw
    p_lose = (k-1) / k   # Losing probability on any given throw
    bob_wins_prob_sum = 0
    r = p_lose**2
    probability_win = p_win / (1 - r)
    return probability_win

def multi_turn_table(k):
    result = {}
    for i in range(6, int(k+1)):
        result[i] = multi_turn_single(i)
    return result

def print(stuff):
    pp.pprint(stuff)

if __name__ == "__main__":
    main()