How Does Expected Value Work?

Expected value is like knowing what you can expect to get on average if you play a game many times.

Imagine you have a magic coin that lands heads 60% of the time and tails 40% of the time. If it lands heads, you win 2 candies. If it lands tails, you lose 1 candy. To find out how many candies you can expect to get on average each time you flip the coin, you use expected value.

To figure this out, you multiply the chance of each outcome by what happens in that outcome and then add them together:

• Heads: 60% (or 0.6) × 2 candies = 1.2 candies
• Tails: 40% (or 0.4) × -1 candy = -0.4 candies

Then you add those two numbers:

1.2 candies + (-0.4 candies) = 0.8 candies

That means, on average, you can expect to get 0.8 candies every time you flip the coin. It’s like knowing that if you play this game many times, you’ll end up with about 0.8 candies per round, not exactly magical, but pretty predictable!

So expected value helps us know what we can probably expect in the long run, like how much candy you'll get from your magic coin after flipping it a hundred times!