You want to buy a new guitar. There are three options: Maton, Fender, and Martin; but you are worried about the dreaded 'buyers remorse'.

If you buy a Maton (your dream acoustic guitar!), you think there is an 80% chance that you will feel +100 better (your reward/return); but because it is so expensive, there is a 20% chance of buyer's remorse, which will make you feel -100 (that's a negative reward)

If you buy a Fender, you think there is an 70% chance that you will feel +70 better; and a 30% you feel -100.

If you buy a Martin, you think there is an 60% chance that you will feel +100 better; a 20% you feel -40; and a 20% that you can sell it to your idiot brother whose name is Martin and buys anything that bears his name, which makes you slightly happy (feel +10)

What is the expected return of the Maton?

Question

You want to buy a new guitar. There are three options: Maton, Fender, and Martin; but you are worried about the dreaded 'buyers remorse'.

If you buy a Maton (your dream acoustic guitar!), you think there is an 80% chance that you will feel +100 better (your reward/return); but because it is so expensive, there is a 20% chance of buyer's remorse, which will make you feel -100 (that's a negative reward)

If you buy a Fender, you think there is an 70% chance that you will feel +70 better; and a 30% you feel -100.

If you buy a Martin, you think there is an 60% chance that you will feel +100 better;  a 20% you feel -40; and a 20% that you can sell it to your idiot brother whose name is Martin and buys anything that bears his name, which makes you slightly happy (feel +10)

What is the expected return of the Maton?

BlackTom AI · Accepted Answer

To evaluate the expected return, we consider each outcome, its probability, and its payoff. The Maton option has two possible outcomes:
- With probability 0.80, you gain +100.
- With probability 0.20, you gain -100.
The expected value is the probability-weighted average of these payoffs: EV = (0.80)(+100) + (0.20)(-100).
Compute these terms: (0.80)(100) = 80; (0.20)(-100) = -20.
Add them together: 80 + (-20) = 60.
This EV represents the average payoff you would expect per purchase in the long run, assuming the stated probabilities and payoffs hold.
Note that this metric does not account for other costs, risk preferences, or utility beyond monetary payoff; it is a simple mean of outcomes.
In summary, the calculation yields an expected return of 60 units per purchase under the given scenario.

COMP90054_2025_SM2 Practice Quiz: Markov Decidion Processes (MDPs) (not assessed)

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