What is expected value, and how do you use it to judge a game or decision?
Expected value is the probability-weighted average of all outcomes, the long-run average result of repeating a situation many times. A negative expected value means you lose on average, even if you sometimes win.
Explain it simply
If you could play a game thousands of times, what would you win or lose per play on average? That is the expected value (EV). Multiply each outcome by its probability and add.
EV = sum of (outcome x probability)
Example
A fest stall charges Rs 10 to roll a die. You win Rs 50 if a six comes up and nothing otherwise.
- Expected winnings = 50 x 1/6 + 0 x 5/6 = Rs 8.33
- Net EV per play = 8.33 - 10 = Rs -1.67
On average you lose about Rs 1.67 each time. Over 600 plays the stall earns about Rs 1,000 from this game. Some players win big, but the average favours the stall.
p_win = 1 / 6
net = 50 * p_win - 10
print(round(net, 2)) # -1.67The same idea drives business choices: compare the EV of two marketing options, or insurance pricing, where the premium is set above the expected claim.
What to say in the interview
"Expected value is the weighted average of outcomes by their probabilities. It tells me the long-run average, so I use it to compare options. It ignores risk and variance, so for one-off decisions I also look at the spread of outcomes, for instance the chance of a large loss."
Common mistakes
- Forgetting to subtract the cost of playing.
- Treating EV as the most likely outcome. It may never actually occur.