Question

A friend offers you an opportunity to buy a raffle ticket for $50.There were 1,000 tickets sold and the lucky winner will receive $20,000.Your friend promises you that if you don't win, he'll give you a $20 refund.

Should you buy a ticket?
Ignore altruism, as well as incentives to cooperate - such as reciprocity and reputation. Just focus on the numbers.

Answer 1

Based on the calculation of the expected value, you would be expected to lose $10.02 on average per ticket, so it is not a good financial decision to buy the raffle ticket for $50, despite the $20 refund if you don't win.

Step-by-step explanation:

To decide whether you should buy a raffle ticket for $50, with 1,000 tickets sold and a single $20,000 prize, and a $20 refund if you do not win, you need to calculate the expected value. The expected value (EV) is calculated by multiplying the probability of each outcome by the value of that outcome, then summing these products. Here the EV for the win is (1/1000) × $20,000 and the EV for a loss is (999/1000) × $20, as you get a $20 refund if you don't win.

The calculations go as follows:

EV(win) = (1/1000) × $20,000 = $20

EV(loss) = (999/1000) × $20 = $19.98

The combined expected value of buying one ticket is therefore:

EV(total) = EV(win) + EV(loss) = $20 + $19.98 = $39.98

Since you pay $50 for a ticket, and the expected value of your return is $39.98, you would expect to lose, on average, $50 - $39.98 = $10.02 per ticket. Based on the numbers alone, it is not a good financial decision to buy the ticket.