Face to Face rolls using Neutronicus's formulas

infinity.py

def binomial_coefficient(n, k):
    """Returns the binomial coefficient, "n choose k"."""
    if k > n-k: # if k is greater than n/2, swap it for n-k which will be
        k = n-k

    result = 1;
    for i in range(k): # loop from 0 to k-1
        result *= (n-i) / (i+1) # multiply in one term of the result

    return result

def neutronicus_coef(B1, b1, B2, b2, c, k):
    choose = binomial_coefficient # shorthand
    if B1 <= B2:
        l = 1
    else:
        l = 0

    if k == 0:
        return choose(b1,c)*(20-B1)**(b1-c)*(20-l)**b2
    
    result = 0
    for m in range(1, B1):
        for M in range(1, m-l+1):
            result += choose(b1, c)*(b1-c)*b2*\
                      choose(b1-c-1,k-1)*(B1-m)**(k-1)*\
                      ((20-B1)+M-l)**(b1-c-k)*\
                      ((20-B2)+M)**(b2-1)

    return result

def neutronicus_MvsN(defender_dice, defender_target,
                     attacker_dice, attacker_target):
    denom = 20**(defender_dice+attacker_dice)
    defender_results = [[neutronicus_coef(defender_target, defender_dice,
                                          attacker_target, attacker_dice,
                                          crits, hits-crits) / denom
                         for crits in range(0, hits+1)]
                        for hits in range(1, defender_dice+1)]
    return defender_results