Expected Value Explained - Should You Play This Game?

You’re playing a game where you roll a dice and get money based on what you roll, should you play it? Let’s find out.

Imagine you have a dice with six sides, numbered 1 to 6. When you roll it:

• If you roll a 1, you get $1
• If you roll a 2, you get $2
• … and so on up to 6, where you get $6

Now, let’s say the game costs $3 to play. Should you play it?

When you roll the dice, each number has an equal chance of coming up, like flipping a coin, but with six sides instead of two.

So on average, you can expect to win:

• $ (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 = $3.50

That’s your expected value, what you can reasonably expect to get from the game each time you play.

The game costs $3, and on average, you win $3.50. That means, over many games, you’ll make a little money every time.

So yes, if you like making small wins, it’s worth playing!