1. **State the problem:** You draw a single card from a standard 52-card deck. If the card is red, you win 20. Otherwise, you win 0. 2. **Formula for expected value:** The expected value (EV) is calculated as $$EV = \sum (\text{value} \times \text{probability})$$ 3. **Identify probabilities:** There are 26 red cards (hearts and diamonds) out of 52 cards total. - Probability of drawing a red card: $\frac{26}{52} = \frac{1}{2}$ - Probability of drawing a non-red card: $\frac{26}{52} = \frac{1}{2}$ 4. **Calculate expected value:** $$EV = 20 \times \frac{1}{2} + 0 \times \frac{1}{2}$$ $$EV = 10 + 0$$ $$EV = 10$$ 5. **Interpretation:** On average, you expect to win 10 per draw in this game. **Final answer:** The expected value of the game to you is 10.