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Basics
Expected value
Expected value is the average outcome per ticket if you could play the same game forever. For lotteries it is almost always negative — the house keeps a share of every pool.
The formula
EV = Σ (probability of each outcome × its value). For a jackpot-only view: EV ≈ P(jackpot) × jackpot − ticket price. Add every smaller prize tier and the number only gets closer to the true (still negative) value.
Rollovers change the picture, not the principle
A huge rolled-over jackpot can push the jackpot-only EV positive — the famous 'positive EV' moments. They are rare, short-lived, and still lose money on average across all prize tiers and taxes. And the draw remains fair: a positive EV ticket is still a losing ticket most of the time.