perudo-script

"""
A tool to calculate probabilities in Perudo.
David Fernig, 2018
"""

from __future__ import division
import scipy.special


class Round(object):

    def __init__(self, *args):
        self.my_dice = args[1:]
        self.num_unknown_dice = args[0] - len(args[1:])

    def a(self, n):
        num_needed = n - self.__i_have(1)
        return self.__at_least(num_needed, self.num_unknown_dice)

    def p(self, m, n):
        num_needed = m - self.__i_have(n)
        return self.__perudo(num_needed, self.num_unknown_dice)

    def __i_have(self, n):
        if n == 1:
            return len([i for i in self.my_dice if i==1])
        return len([i for i in self.my_dice if i==1 or i == n])

    def __perudo(self, n, t):
        """Probability of getting at least n of [a particular value | 1] in t rolls."""
        num_possibilities=6**t
        num_accepted = 0
        for i in range(n, t+1):
            tmp=0
            # Compute number of ways that of t dice, exactly i are either 1 or 4
            for j in range(0,i+1):
                # Compute number of ways that of t dice, exactly j are a 1 and i-j are a 4
                tmp = scipy.special.binom(t, j) * scipy.special.binom(t-j, i-j) * (4**(t - i))
                num_accepted+=tmp
        return num_accepted/num_possibilities
    
    def __at_least(self, n, t):
        """Probability of getting at least n of a particular value in t rolls."""
        num_possibilities=6**t
        num_accepted=0
        for i in range(n, t+1):
            tmp=(5**(t - i))*scipy.special.binom(t, i)
            num_accepted+=tmp
        return num_accepted/num_possibilities