Lottery Expected Value Calculator
Calculate the expected value of a lottery ticket and the true odds of winning.
See how jackpot size, taxes, and lump-sum discounts affect the rational value.
Expected Value of a Lottery Ticket Expected value (EV) = Sum of (prize value x probability of winning that prize) - ticket cost. For most lotteries, EV is deeply negative. Powerball with a $100M jackpot has an EV of roughly -$0.75 per $2 ticket after taxes.
Why the EV Is Almost Always Negative The lottery is designed to return only 50-60% of ticket revenue as prizes. The rest funds government programs or operator profit. Even at very large jackpots, taxes reduce the real value dramatically.
Lump Sum vs Annuity Most jackpots can be taken as a 30-year annuity (full amount) or a lump sum (typically 60% of the advertised amount). After federal taxes (~37%) and state taxes (~5%), a $100M jackpot annuity might yield only $55M total, or a lump sum of ~$35M net.
The Mega Jackpot Fallacy At extreme jackpot sizes (e.g. $1 billion), ticket sales surge and the EV can briefly turn positive in theory — but shared prizes from many winners typically reduce it back below zero. The rational value also ignores diminishing marginal utility of money.