Betting between Tom and Eva
It's time to play a game between Tom and Eva!
Recall that Tom has a regular six-faced die and the results of rolling it follow a discrete uniform distribution in the interval of one and six. Eva has a biased coin that has a probability p of turning heads. The distribution of the number of flips Eva needs to land heads is geometric.
Here are the rules of the game:
- Tom's score: the point of the rolled die
- Eva's score: the number of flips needed to land heads
- The person with the highest score wins
Your task is to simulate this game! For the list of possible p values [0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9] representing the probability of Eva's coin flipping heads, who do you expect to win?
NumPy has been imported as np and SciPy's stats module as st.
This exercise is part of the course
Monte Carlo Simulations in Python
Exercise instructions
- Simulate rolling Tom's die 10,000 times, assigning the results to
die_samples. - Simulate Eva's coin flips to land heads 10,000 times, assigning the results to
coin_samples.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
for p in [0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9]:
low = 1
high = 7
# Simulate rolling Tom's die 10,000 times
die_samples = ____
# Simulate Eva's coin flips to land heads 10,000 times
coin_samples = ____
diff = np.mean(die_samples - coin_samples)
print(diff)