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)