Dealing An Ace

Python Puzzles

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In poker, the first person to be dealt an ace gets the role of dealer. Is the probability of being dealt the first ace equal for all players?

Create a simulation to find out.

Running a simulation, we find that the first person being dealt a card has a slightly higher percentage of being dealt the first ace.

After running 100,000 simulations, I get a 28% probability of the first person receiving the first ace.

Probability of Drawing an Ace:

Player 1: 27.89%
Player 2: 26.16%
Player 3: 21.83%
Player 4: 24.12%

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

result = []
loop = 100_000
for _ in range(loop):
         
    #assume cards 1,2,3,4 are Aces
    deck = list(range(1,53))
    random.shuffle(deck)
     
    #i represents the player, assuming there are 4 players
    i = 1
 
    #if the card is an ace, append the player (i) it was dealt to    
    for x in deck:
        if x < 5:
            result.append(i)
            i = 1
            break
        else:
            i +=1
     
        #set i to player 1
        if i > 4: i = 1
 
# equals to list(set(words))
keys = list(Counter(result).keys())

# counts the elements' frequency
values = list(Counter(result).values())
values_pct = []
 
# determine percent
for x in values:
    values_pct.append(x/loop)

# sort the keys based on the values in descending order
keys = [k for _, k in sorted(zip(values, keys), reverse=True)]

# create a bar chart
plt.bar(keys, values_pct)
plt.ylabel("Percentage")
plt.xlabel("Player")
plt.title("Probability of Drawing an Ace\n")
plt.xticks(keys)

# Save the plot
plt.savefig('dealing-an-ace-barchart.png', dpi=300, bbox_inches='tight')
# Show the plot
plt.show()

# print the results in descending order
print("Probability of Drawing an Ace:\n")
for i, k in enumerate(keys):
    print(f"Player {k}: {values_pct[i]:.2%}")