The Strategy of an Insurance Company Against Bob at the Casino
How is the insurance company taking advantage of Bob's behavior at the casino?
The insurance company is taking advantage of Bob's behavior by offering him insurance that, in expectation, generates no profit for them. However, by charging a $50 premium, the insurance company can still make money from those rare instances when Bob loses.
Analyzing Bob's Behavior and the Insurance Company's Strategy
- Bob always plays the safe bet at the casino, which means he is unlikely to lose money consistently. Therefore, Bob's chances of winning are relatively high.
- The insurance company is aware of Bob's behavior and understands that as long as Bob continues playing the safe bet, they will not make any profit in expectation. This is because Bob's likelihood of losing is low.
- By offering Bob insurance, the insurance company aims to make a profit by charging him $50 upfront. If Bob loses, the insurance company covers his losses, and they keep the $50. But if Bob wins, he does not have to pay anything extra since he already paid the $50.
- Since Bob's chances of winning are high, the insurance company expects to pay out the insurance only in rare instances. Thus, in expectation, the insurance company makes $0 because the income from the insurance premium ($50) equals the expected payout.