The Carnival Spinner
Expected Value is the average outcome if you played many times.
Drag the probabilities to match their prizes in the formula.
Build the Equation:
${{ prize }}
×
+
{{ s1.targets[index].label }}
Probabilities:
{{ item.label }}
Balancing the Game
A game is fair if its Expected Net Gain is $0.
That means: Expected Winnings = Cost to Play
Game Pays
${{ s2.winPrize }}
{{ s2.winProb * 100 }}% chance to win
→
Expected Winnings
${{ s2.expectedWinnings }}
Set Cost to Play:
${{ s2.cost }}
✨ It's a Fair Game! ✨
Adjust slider to make Expected Net Gain $0
The Local Lottery
Calculate the Expected Net Gain for one ticket.
- {{ s3.tickets }} tickets sold total
- 1 grand prize of ${{ s3.prize }}
- Tickets cost ${{ s3.cost }} each
Step 1: Gross EV
${{ s3.prize }} × (1/{{ s3.tickets }}) = ${{ s3.grossEV }}
Step 2: Net EV
Gross EV - Ticket Cost
Set the Expected Net Gain:
-+ ${{ Math.abs(s3.userVal) }}
Correct! It's a losing game on average.
The Insurance Dilemma
Compare the Expected Financial Loss.
Tap the option that makes the most pure mathematical sense.
You buy a ${{ s4.itemValue }} e-bike. There is a {{ s4.probLoss * 100 }}% chance it gets stolen this year.
Theft insurance costs ${{ s4.insCost }} per year.
Theft insurance costs ${{ s4.insCost }} per year.
Correct! Mathematically, insurance is usually a negative expected value.
Look closely at which expected cost is lower!
🏆
Master of Probability!
You now know how to calculate Expected Value to evaluate games, lotteries, and real-world financial decisions.