Calculating a break-even lottery price
Simulations allow us to ask more nuanced questions that might not necessarily have an easy analytical solution. Rather than solving a complex mathematical formula, we directly get multiple sample outcomes. We can run experiments by modifying inputs and studying how those changes impact the system. For example, once we have a moderately reasonable model of global weather patterns, we could evaluate the impact of increased greenhouse gas emissions.
In the lottery example, we might want to know how expensive the ticket needs to be for it to not make sense to buy it. To understand this, we need to modify the ticket cost to see when the expected payoff is negative.
grand_prize
, num_tickets
, and chance_of_winning
are loaded in the environment.
This exercise is part of the course
Statistical Simulation in Python
Exercise instructions
- Set
sims
to 3000 and thelottery_ticket_cost
variable to0
. - If the mean value of
outcomes
falls below0
,break
out of thewhile
loop. - Else, increment
lottery_ticket_cost
by 1.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Initialize simulations and cost of ticket
sims, lottery_ticket_cost = ____, ____
# Use a while loop to increment `lottery_ticket_cost` till average value of outcomes falls below zero
while 1:
outcomes = np.random.choice([-lottery_ticket_cost, grand_prize-lottery_ticket_cost],
size=sims, p=[1-chance_of_winning, chance_of_winning], replace=True)
if outcomes.mean() < 0:
____
else:
____ += 1
answer = lottery_ticket_cost - 1
print("The highest price at which it makes sense to buy the ticket is {}".format(answer))