PSY 333 — Assignment 7

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Expected Value Theory

1. Compute the expected values for these two options. What choice would Expected Value Theory make? (2 points) Which do you prefer:

   • Option A: 100% chance of $240
   • Option B: 25% chance of $1000 and 75% chance of $0

2. Compute the expected values for these two options. What choice would Expected Value Theory make? (2 points) Which do you prefer:

   • Option A: 100% chance to lose $750
   • Option B: 75% chance to lose $1000 and 25% chance to lose $0

3. Compute the expected value for the two options in each of these three questions (3 points):

   • Q1
     • Option A: 100% chance of $3000
     • Option B: 80% chance of $4000
   • Q2
     • Option A: 25% chance of $3000 and 75% chance of nothing
     • Option B: 20% chance of $4000 and 80% chance of nothing
   • Q3
     • Option A: 1% chance of $3000 and 99% chance of nothing
     • Option B: 0.8% chance of $4000 and 99.2% chance of nothing

4. For the 3 questions in question 3, which of the two options does Expected Value Theory prefer (1 points)?

5. What is the expected value of these options? (2 points) Which do you prefer:

   • Option A: 95% chance to win $2.50 and a 5% chance to lose $0.75
   • Option B: 40% chance to win $8.50 and 60% chance to lose $1.50

Extra credit (bonus 2 points total)

The house edge on slot machines varies depending on the type of machine. For $1 slots (where you pay one dollar to play once), the house edge is about 10%. For $100 slots (where you pay $100 to play once), they house edge is about 5%.

1. If you play a $100 slot machine once, how much can you expect to get back on average?

2. If you play a $1 slot machine once, how much can you expect to get back on average?

3. If you play a $1 slot machine 100 times, how much would you expect to get back?

4. By considering your answers to part a) and c), if you are committed to spending a fixed amount of money (say $1,000) on gambling, which machine ($1 slots or $100 slots) is the best (i.e. least worst) choice?

5. By considering your answers to part a) and b), if you are committed to playing for a fixed number of plays (say 100 pulls of the lever), which machine ($1 slots or $100 slots) is the best (i.e. least worst)?

6. Based on your answers to part d) and e), why do you think the house edge gets smaller for $100 slots?