ToC_prob.py

EMPIRICAL_PROBS = \
    [0,
     0.558510638,
     0.260638298,
     0.079787234,
     0.015957447,
     0.053191489,
     0.015957447,
     0.005319149,
     0,
     0,
     0,
     0.010638298]

SMOOTHED_PROBS = [0, .54, .26, .08, .05, .03, .015, .005, .005, .005, .01]


CHAMP_WINS = 3
PROBABILITY_CHAMP_WON_LESS_MONEY_WITH_SAME_VICTORIES = 0.1
GAMES_LEFT = 41
MAX_STRONGER_CHAMPS_TO_REMAIN_ELIGIBLE = 1

TOTAL_SITUATIONS = MAX_STRONGER_CHAMPS_TO_REMAIN_ELIGIBLE + 2


import numpy as np

for CHAMP_WIN_PROBS in (EMPIRICAL_PROBS, SMOOTHED_PROBS):
    assert sum(CHAMP_WIN_PROBS) == 1
    if CHAMP_WIN_PROBS == EMPIRICAL_PROBS:
        print 'Empirical Estimates\n'
    else:
        print 'Smoothed (pessimistic) estimates\n'
    output_array = np.zeros((GAMES_LEFT, TOTAL_SITUATIONS))
    output_array[0][0] = 1
    # print output_array

    for i in range(GAMES_LEFT - 1):
        for j in range(len(CHAMP_WIN_PROBS)):
            win_prob = CHAMP_WIN_PROBS[j]
            for k in range(TOTAL_SITUATIONS):
                if i + j >= GAMES_LEFT:
                    if j > CHAMP_WINS and i + CHAMP_WINS < GAMES_LEFT:
                        output_array[-1][min(k + 1, TOTAL_SITUATIONS - 1)] += \
                            output_array[i][k] * win_prob
                    else:
                        output_array[-1][k] += \
                            output_array[i][k] * win_prob
                elif j <= CHAMP_WINS - 1:
                    output_array[i + j][k] += \
                        output_array[i][k] * win_prob
                elif j == CHAMP_WINS:
                    output_array[i + j][k] += \
                        output_array[i][k] * win_prob * (1.0 - PROBABILITY_CHAMP_WON_LESS_MONEY_WITH_SAME_VICTORIES)
                    output_array[i + j][min(k + 1, TOTAL_SITUATIONS - 1)] += \
                        output_array[i][k] * win_prob * PROBABILITY_CHAMP_WON_LESS_MONEY_WITH_SAME_VICTORIES
                else:
                    output_array[i + j][min(k + 1, TOTAL_SITUATIONS - 1)] += \
                        output_array[i][k] * win_prob
                    # print i
                    # print output_array

    # print output_array
    output_probs = output_array[-1]
    assert abs(output_probs.sum() - 1) < .001

    output_range = range(TOTAL_SITUATIONS)

    format_str = 'Probability of {}{} additional winners in the next {} games: {:.2%}'

    output_range_names = [format_str.format(i, '', GAMES_LEFT, output_probs[i]) for i in output_range[:-1]]
    output_range_names += [format_str.format(output_range[-1], ' or more', GAMES_LEFT, output_array[-1][-1])]

    print '\n'.join(output_range_names)
    print '\n=============\n'
    print 'ToC Probability: {:.2%}'.format(output_probs[:-1].sum())
    print '\n'