Fair Game Analyzer

Pre-Algebra · Axiom Academy

Carnival games look like fun and easy money. One number — the expected value — tells you who really comes out ahead. The number that decides every bet Walk past any carnival and you'll be invited to pay a dollar, flip or spin, and maybe win a prize. Some of those games are fair, and some quietly take your money every single time. You don't have to guess which is which — there's one number, the expected value , that settles it. It's just the average amount you'd win or lose per play if you played forever. Start with a game that really is fair. Pay 1 to flip a coin: Heads pays you 2 back (you're up 1 ), Tails pays nothing (you're down 1 ). Watch it play out — each flip jolts your balance up or down, but the average per play drifts to exactly 0 . That settling number is the expected value. Single flips swing wildly, but the average per play homes in on 0 — the mark of a fair game. The wheel that looks generous — and isn't Here's a real carnival wheel. Pay 1 to spin; you can win 3 , win 2 , or win nothing. Three ways to win, one way to lose — it feels like a deal. Drag the slider to play it more and more times and watch the average result per play settle. Where does it land — above 0 , or below? The average per play sinks toward − 0.30 — play 100 times and you're down about 30 . The wheel is rigged in the carnival's favor.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.