I am getting an incorrect average, and not sure why? What's wrong with my code?

[deanhystad]

I think the averages in your last post look fine. 1000 hands is a pretty small sample size for this game as the number of hands required to win or lose varies greatly. I modified my program slightly to collect the counts and do a little statistical analysis and plotting.

import random
import statistics
import collections
import matplotlib.pyplot as plt
 
deck = 'A234567890JQK'*4
hand = 6
 
def play(start):
    count = 0
    bank = start
    while 0 < bank < start*2:
        if 'A' in random.sample(deck, hand):
            bank += 1
        else:
            bank -= 1
        count += 1
    return count

while True:
    start = int(input('Enter inital amount: '))
    counts = [play(start) for _ in range(1000)]
    unique_counts = collections.Counter(counts)
    print('Mean =', statistics.mean(counts))
    print('Median =', statistics.median(counts))
    print('Number of different counts =', len(unique_counts))
    print('Count range =', min(counts), 'to', max(counts))
    mode = statistics.mode(counts)
    print('Mode =', mode, 'Count =', unique_counts[mode])
    print('Standard Deviation =', statistics.stdev(counts))
    plt.bar(unique_counts.keys(), unique_counts.values())
    plt.show()

Output:
Enter inital amount: 100
Mean = 484.818
Median = 474.0
Number of different counts = 222
Count range = 238 to 952
Mode = 454 Count = 15
Standard Deviation = 103.47417929987066
Enter inital amount: 100
Enter inital amount: 100
Mean = 492.046
Median = 480.0
Number of different counts = 227
Count range = 250 to 934
Mode = 466 Count = 15
Standard Deviation = 102.92227591186895

Running two tests the average count changed from 484 to 492. Such variation is not surprising when you see the number of hands required to win or lose a game ranges from the low 200's to over 1000 upon occasion. When I increased the sample size from 1000 to 10,000 I also noticed some interesting clumping in the plots. The kind of non-uniform distribution that raises hell with statistical analysis.

What I found really interesting is how bad this game is. You never win. I modified the code to count wins and losses and I never win. I guess this makes sense considering you only have a 38% chance of winning any given hand and you need to win a lot of hands to double your money. The odds are not in your favor.