Expected value is a helpful idea that helps us make smart choices when playing games that involve luck. By figuring out the average outcome of random events, we can see which options might give us better results.

What is Expected Value?

Expected value (EV) is like a tool to figure out what we can expect to win (or lose) in the long run when we play a game. We find it by multiplying each possible result by how likely that result is, then adding them all together.

An Example

Let’s look at a simple game: tossing a fair coin. If it lands on heads, you win $10. But if it lands on tails, you lose$5.

• The chance of getting heads (winning) is 1 out of 2.
• The chance of getting tails (losing) is also 1 out of 2.

Now, let’s calculate the expected value:

$$EV = (10 \times \frac{1}{2}) + (-5 \times \frac{1}{2}) = 5 - 2.5 = 2.5$$

This means that, on average, you can expect to win $2.50 each time you play this game.

Decision Making

When we know the expected value, we can compare different games or strategies. If another game has a lower EV, we might want to skip it. Expected value helps us understand possible risks and rewards, allowing us to make better choices in games of chance.