Lottery Jackpot EV Calculator

The Lottery Jackpot EV Calculator prices only the top prize. Defaults recreate a textbook US Powerball-shaped ticket: jackpot $100,000,000, odds 1 in 292,201,338 (that is C(69,5)×26 for 5/69 plus 1/26), tickets 1, price $2, expected winners 1. You do not have to play Powerball; paste any advertised headline prize and any published 1-in-N jackpot figure.

Fill Jackpot with the cash-equivalent headline you are evaluating, not the 30-year annuity billboard, unless you really intend to treat the annuity face as cash — that would overstate EV. Fill Odds (1 in N) from the official matrix, not from a blogger’s rounded “one in 300 million.” Tickets is how many distinct lines you buy for this draw. Price is the stake per line. Expected Winners is the pari-mutuel split factor: 1 means you keep the whole jackpot if you hit; 2 means you model an even split with one other winner.

Calculate. Expected Value is tickets × ((jackpot / winners) × p − price) with p = 1/odds. With defaults: p = 1/292,201,338 ≈ 3.4223×10^−9, share = $100,000,000, so share×p ≈ $0.3422, minus $2, EV ≈ −$1.66 per ticket. Jackpot Chance is the at-least-once probability 1−(1−p)^tickets, which for one ticket is just p (about 0.000000342 percent). Prize Share is jackpot/winners = $100,000,000 here.

Raise Jackpot to the break-even cash value: price × odds × winners = 2 × 292,201,338 × 1 = $584,402,676. At that headline, share×p = $2 and EV = $0 before lower-tier prizes and tax. Real advertised Powerball annuities often print above that while the cash option sits below; always convert to cash before you call a ticket “positive EV.” Set Expected Winners to 2 and the same $100 million jackpot yields share $50 million, share×p ≈ $0.171, EV ≈ −$1.83.

The tool ignores 5+0, 4+1, and every other fixed-odd or pari-mutuel rung. Those rungs add a few tens of cents of EV on a typical $2 ticket — not enough to flip a $100 million cash jackpot positive, enough to matter when the cash jackpot is near break-even. Tax, annuity discounting, and the chance of a roll-down are also out of scope; use the tax and annuity calculators for those layers. Treat a negative EV as the price of the dream, not as a rounding error you can martingale away.

Expected value is the law of large numbers applied to a single draw: if you could buy the same ticket under the same jackpot forever, your average profit per ticket would converge to EV. Charles Clotfelter and Philip Cook’s Selling Hope (1989) and subsequent public-finance papers documented that lotteries are designed as negative-EV products with a few occasionally positive-EV jackpot spikes, sold to people who overweight tiny probabilities (Kahneman and Tversky prospect theory, not a conspiracy). The Jackpot EV Calculator is the back-of-envelope that those papers assume every buyer skipped.

Rollover economics: each unsold jackpot night transfers residual prize-fund money into the next headline. Demand is convex in the headline — Cook and Clotfelter, and later papers on Powerball “lottomania,” show ticket sales surge when the billboard crosses round hundreds of millions. That surge raises expected co-winners, which is why the Expected Winners field exists. A $1.5 billion annuity headline with three likely winners is not three times as attractive as a $500 million unique-winner night; the cash share may be similar after splits, while you paid extra in crowding.

Syndicates and office pools sometimes chase theoretically +EV cash jackpots. Even then, coverage is incomplete, liquidity is terrible (you cannot sell the ticket), and a win is a taxable lump that the simple EV ignores. Most weeks the cash jackpot sits well under price×odds. For the default 1-in-292,201,338 matrix at $2, cash must clear about $584 million (one winner, pre-tax, jackpot-only) before EV turns non-negative. Lower-tier prizes knock maybe $0.30–$0.50 off that hurdle depending on the game; federal-plus-state tax pushes it back up.

SorteCalc isolates jackpot EV on purpose. Mixing in estimated lower-tier EV, multiplier add-ons, and insurance products turns the page into a full parimutuel simulator, which is a different tool. Journalists quoting “the ticket is worth $0.34” are quoting share×p, not EV; subtract the $2. Players quoting “but someone has to win” are confusing the existence of a winner in the population with the expected return to a specific ticket. Those are not the same number.

Use this calculator before you scale a pool, not after you have already bought 10,000 lines. If EV is −$1.66, buying 10,000 tickets has EV ≈ −$16,580 and a 10,000/292,201,338 ≈ 0.0034 percent chance of the jackpot. That is entertainment with a known sticker, not an investment. Pair with the multi-ticket tool for the probability layer and the prize-split tool for the co-winner layer.

Expected value is the law of large numbers applied to a single drawing: average profit per ticket converges to the probability-weighted payoff minus the price. Charles Clotfelter and Philip Cook, in Selling Hope, documented that state lotteries are designed as negative-expectation products with occasional jackpot spikes that can look less ugly on paper. This page isolates the top prize only. Lower rungs, tax, and annuity packaging are out of scope here; they belong on the neighbouring worksheets.

The default illustration is Powerball-scale. Jackpot one hundred million dollars, published odds one in 292,201,338, one ticket, price two dollars, one expected winner. Probability p is one over 292,201,338, about 3.422 times ten to the minus nine. Prize share is the jackpot divided by the winner count, hence the full one hundred million when that count is one. Linearity then gives expected value equal to tickets times (share times p minus price).

Work the default arithmetic in order. Share times p equals 100,000,000 / 292,201,338, which is about 0.3422 dollars. Subtract the two-dollar stake and the ticket is worth about minus 1.66 dollars. That is negative, as advertised. Ten tickets scale the same loss to about minus 16.58 dollars; they do not improve the price. Two expected winners cut the share in half, so share times p falls to about 0.171 and expected value is about minus 1.83 dollars on one ticket.

Break-even, jackpot only and pre-tax, sets expected value to zero and solves for the headline: jackpot star equals price times odds times winners. Defaults yield 2 times 292,201,338 times 1, which is 584,402,676 dollars of cash-equivalent jackpot before the ticket stops being a pure loss on the top prize. Real advertised annuities often print above that line while the cash option sits below it. Convert to cash before you call a ticket positive. Tax at a combined rate tau replaces the jackpot by jackpot times (1 minus tau) and pushes the hurdle up.

Jackpot chance on a bundle of tickets is one minus (1 minus p) to the power of the ticket count, the complement of total miss. For one ticket that is simply p. The formula treats the winner count as an exogenous split factor, not as a random occupancy variable. A Poisson model of co-winners is a different lecture. Lower-tier prizes add a nearly constant intercept of a few tens of cents on a typical two-dollar ticket; they shift break-even but they do not rewrite the slope against the jackpot.

Assumptions: cash prize, not a thirty-year face; no sharing beyond the winner field; no multiplier; no roll-down. Prospect theory, not combinatorics, explains why people buy a minus 1.66 dollar claim. Recalculate when the headline, the 1-in-N matrix, or the expected split changes. Expected value is not a promise that you will lose 1.66 dollars tonight; it is the mean of a distribution that is almost always minus two dollars and very rarely plus a fortune.