Little math problem(s) February 2019

[Albert Chan]

Hi, pier4r

After the few best-of-n's, computations by calculator a bit too much.
This is the Python code that I used to build the winning percentages:

PHP Code:

from gmpy2 import comb as nCr

def win_percent(coefs, x, r=0):
    for coef in coefs: r = r * x + coef     # Horner's rule
    return (100 * r * (1-x)**len(coefs),)   # scaled to percent

for n in range(1,25):                       # best-of-n
    coefs = [ nCr(n-1+i, i) for i in range(n-1,-1,-1) ]
    print n, '\t',
    for p in [0.60, 0.65, 0.7]: print '%5.1f' % win_percent(coefs, 1-p),
    print 


If I extend the range to best-of-41, winning precentages = 96.6, 99.7, 100.0