# Matching Cards in Two Decks

Python Puzzles

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If you shuffle two separate decks of cards, what is the probability of the same card appearing in the exact same position in the two separate decks?

Approximately 36% of the time the two decks will have zero matching cards in the same position; 64% of the time it will have at least one matching card. When I run the simulation 1 million times, the most matches I get is 9.

```import random
from collections import Counter
import matplotlib.pyplot as plt

loop = 100_000
result_total = []

# create two decks of cards with 52 cards each
deck_of_cards1 = list(range(1,53))
deck_of_cards2 = list(range(1,53))

for _ in range(loop):
# shuffle both decks
random.shuffle(deck_of_cards1)
random.shuffle(deck_of_cards2)

# compare cards of the same index in both decks
result = []
for d1, d2 in zip(deck_of_cards1, deck_of_cards2):
if d1 == d2:
result.append(1) # if two cards match, add 1 to the result list

# append the count of matches to the result total list
result_total.append(result.count(1))

# sort the result total list and count the number of occurrences of each value
result_total.sort()
keys = list(Counter(result_total).keys())
values = list(Counter(result_total).values())

# determine percentage of each value in the result total list
values_pct = []
for x in values:
values_pct.append(x/loop)

# create a bar chart to show the distribution of results
plt.bar(keys,values_pct)
plt.ylabel("Percentage")
plt.xlabel("# of Card Matches")
plt.title("Probability")
plt.xticks(keys)
plt.savefig('matching-cards-two-decks-barchart.png', dpi=300, bbox_inches='tight')
plt.show()

# print the sorted percentages in descending order
values_pct.sort(reverse=True)
print(values_pct)
```