LESSON 1 · The Math of Choices
The Lottery Delusion
Powerball asks you to pick 5 numbers from 69, plus 1 from 26. The combinations: C(69,5) × 26 = 292,201,338 possible tickets. At $2 each, buying every combination costs about $584 million — which is why syndicates occasionally consider it when a jackpot climbs past that threshold.
But here is the trap most players miss: across the long run, a typical ticket returns less than you pay for it. The advertised jackpot is split among multiple winners and shrinks after taxes and annuity discounting, so the expected value stays below the ticket price for almost every drawing. Buying a ticket every week for decades reliably costs far more than it ever pays back.