Question

You are a contestant on a game show called “Bargain or No Bargain.” You are presented with three briefcases, which contain rewards of $500,000, $2,000, and $500. The host of the show says you can either open one random case and keep the amount inside, or you can accept a guaranteed award of $160,000. What is the mathematically correct decision, and why?

Answer 1

If you play the game, there's a 1/3 chance each of getting $500,000, $2,000, or $500.
Thus, your expected return (The amount you'd win, on average, for playing) is:
\[\frac{1}{3}$500,000+\frac{1}{3}$2,000+\frac{1}{3}$500 = $167,500\]

Which one is the better deal?