In this lesson:
By the end of this lesson, you should be able to:
A lottery ticket costs 2 dollars and advertises a 1,000,000-dollar jackpot.
Should you buy it?
The signed-table method is unchanged. What's new at lottery scale:
Almost all the probability sits on winning nothing.
2-dollar ticket. Jackpot prize 1,000,000 with probability ; small prize 10 with probability ; else nothing.
The probabilities must total 1:
You expect to lose about 1.42 dollars per ticket — the state's edge.
"You could win a million, so it's a good bet."
Pick A or B before advancing.
The jackpot is real, but its tiny probability makes its contribution small.
A $5 raffle gives a $500 prize with probability , else nothing.
Find the expected payoff per ticket.
Include the lose row. Commit before advancing.
Lotteries are one kind of game. Promotional games — collect-and-win — are another.
Same method, often with by-design or data-based probabilities.
Prize $5 meal, won with probability per purchase; incremental cost $1.
A value-maximizer's rule says don't play. Yet people do — and not irrationally:
A scratch game costs 2 dollars and wins 5 dollars with probability one-fifth, else nothing.
Compute the expected payoff and decide whether a value-maximizer plays.
Commit before advancing.
Include the lose row — it carries almost all the probability and makes the payoff negative
A big prize is not favorable — weight it by its tiny probability first
✓ A lottery's expected payoff includes the dominant lose row — here about −1.42 dollars
✓ A big prize times a tiny chance is a small contribution
✓ Expected value informs the decision but isn't the whole story
So far we've scored one option at a time.
Next standard: when you have two options, compare their expected values to choose.
Click to begin the narrated lesson
Find the expected payoff for a game of chance