Questions / Quant trading, Expected value & odds
A profitable-looking coin game
A game pays +12 points with probability 0.4 and −3 points otherwise. What is its expected net payoff?
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Show the answer and worked solution
Answer: 3 points
- List mutually exclusive outcomes: +12 with probability 0.4, and −3 with probability 0.6.
- Weight each signed payoff: 0.4 × 12 = 4.8; 0.6 × (−3) = −1.8.
- Add the contributions: 4.8 − 1.8 = 3 points per play on average. This is an expectation, not the payoff of one play.
Interview shortcut. Shift the payoffs: you always get −3, plus an extra 15 with probability 0.4. That is −3 + 6 = 3.
Takeaway. Use signed payoffs before weighting by probabilities.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.