Powerball Odds Calculator

This Powerball odds calculator is wired to the United States Multi-State Lottery Association matrix that has been in force since 7 October 2015: five white balls drawn from 1 through 69 plus one red Powerball drawn from 1 through 26. A standard play is $2. Drawings are Monday, Wednesday and Saturday. Begin with the Tickets field. Enter how many distinct $2 boards you will buy for one drawing—not how many weeks you intend to subscribe, and not whether those boards are Quick Picks or hand-picked. Ten unique combinations means Tickets = 10. Every combination is equally likely, so the engine does not care how you chose the numbers.

Ticket Price defaults to 2. Leave it there unless you are modelling a rare retail surcharge or you want to treat a multi-draw strip as a blended cost per line. Do not add the extra $1 for Power Play if the question you care about is the jackpot. Power Play can multiply some of the fixed lower prizes (and, in participating states, the Match-5 prize), but it never multiplies the jackpot. Raising Ticket Price to $3 to “include Power Play” only makes Jackpot EV look worse; Jackpot Odds stay 1 in 292,201,338 either way.

Jackpot is the advertised prize you want to value. MUSL publishes an annuity headline. The record remains about $2.04 billion, hit on 7 November 2022 by a single California ticket. If you want cash-option economics, paste the published cash value instead of the annuity figure—the engine treats whatever you type as a lump prize and does not convert a 30-year graduated annuity. It also ignores sharing, so a $2 billion headline is valued as if one ticket takes the entire amount.

Main Matches is how many of the five white balls you want probability for, an integer from 0 through 5. Leave it at 5 when you are asking about jackpot-tier prize odds. Drop it to 4, 3 or 2 when you want to see how much likelier the mid board is. Bonus Matches is the Powerball itself: 0 or 1, drawn from a 26-number pool. The jackpot pattern is Main Matches = 5 and Bonus Matches = 1. Match 5 with Bonus Matches = 0 is the second prize (the million-dollar class that Power Play can touch). Matching the Powerball alone is Main Matches = 0 and Bonus Matches = 1.

Press calculate. Jackpot Odds reports 1 in C(69,5)×C(26,1), which is 1 in 292,201,338 for a single board. This Prize Odds uses the hypergeometric count for the Main Matches and Bonus Matches you chose. Jackpot Chance and This Prize Chance convert those single-ticket probabilities into at-least-once figures for your Tickets count via 1−(1−p)^n. Jackpot EV equals tickets×(jackpot×jackpotP − price)—jackpot only, no lower prizes, no split, no tax. Expected Jackpot Return is the gross expected jackpot dollars before subtracting stake. Use both numbers to see whether a headline prize even covers the $2 outlay in expectation before you start arguing about sharing, withholding, or Power Play.

Powerball is the flagship jackpot game of the Multi-State Lottery Association, sold across most U.S. states, the District of Columbia, Puerto Rico and the U.S. Virgin Islands. It is not Mega Millions: different consortium, different matrix, different draw nights. Since 7 October 2015 the white-ball pool has been 69 and the Powerball pool 26, a change that stretched jackpot odds to 1 in 292,201,338 and allowed advertised annuities to climb into ten figures. A line costs $2. Optional Power Play is typically another $1 and does not apply to the jackpot.

Drawings are Monday, Wednesday and Saturday. Monday was added in 2021; the original twice-weekly cadence is now three nights. Jackpots start in the tens of millions and roll until someone matches 5+1. The annuity is paid over 30 graduated years; winners may elect a cash option worth roughly half the advertised figure, with the exact cash percentage moving with interest rates. Federal withholding applies; state tax depends on where you played and where you claim. California, which sold the $2.04 billion winner, does not tax lottery prizes at the state level.

That November 2022 California ticket remains the largest lottery prize in U.S. history and the number people quote when they ask whether Powerball can ever be “positive EV.” Headline annuity EV can look positive at $1.5–$2 billion if you ignore sharing, tax, and the cash discount. In practice, sales explode at those levels, so the expected number of winners is well above one, and the cash option plus tax pulls the real expected value back below the $2 price. This calculator is honest about what it omits: lower tiers, Power Play, splits, and tax.

Prize structure besides the jackpot is a mix of fixed amounts and, in some jurisdictions, a pari-mutuel Match-5 pool. Official second prize for matching five white balls and missing the Powerball is $1 million (Power Play can make it $2 million in most states). Matching the Powerball with zero white balls still pays $4. Those fixed rungs are why people buy Power Play; they are also why this tool’s Jackpot EV understates total return. If you need a full parimutuel model, this is the wrong page—use it to price the top prize under the published matrix.

Compared with Mega Millions (5/70 + 1/25, Tuesday/Friday, same $2), Powerball is slightly easier on jackpot odds (292 million versus 303 million) and runs three nights instead of two. Compared with Lotto America, also a MUSL game, Powerball is an order of magnitude harder and an order of magnitude richer. Compared with Cash4Life or Lucky for Life, Powerball is a rolling mega-jackpot product, not a marketed lifetime stipend. Use this page when the question is specifically MUSL Powerball, not “U.S. lottery” in the abstract.

American Powerball since October 2015 is a two-urn combinatorial object: five unordered whites from sixty-nine and one red from twenty-six. The Multi-State Lottery Association froze that matrix after an earlier five-from-fifty-nine white pool; expanding the white drum is why the jackpot sits at one in 292,201,338 rather than the friendlier pre-2015 product. A line costs two dollars. The working advertised prize in this lecture is two hundred million dollars, an annuity headline, not a cash cheque, and not a shared pool.

Begin the jackpot count with the white urn. The number of ways to choose five numbers from sixty-nine is C(69,5) = 69×68×67×66×65 / 120 = 11,238,513. Exactly one of those five-subsets is the drawn set, so the white-ball jackpot factor is one over 11,238,513. The red Powerball is an independent one-subset of a twenty-six set, hence one over C(26,1), which is one twenty-sixth. Because the machines are separate, the joint probability is the product: one over 11,238,513 times 26, which equals one in 292,201,338. Order of draw does not enter; tickets are combinations, not permutations.

Lower prizes use the hypergeometric law on each urn. For exactly k white hits among five drawn from sixty-nine, the count is C(5,k)×C(64,5−k) / C(69,5), provided the leftovers fit among the sixty-four non-winners. The red factor is one twenty-sixth if the Powerball hits and twenty-five twenty-sixths if it misses. Matching five whites and missing the red is therefore (1/11,238,513)×(25/26) = 25/292,201,338, about one in 11,688,054, the million-dollar class. Matching four whites and the red is C(5,4)×C(64,1)/11,238,513 times 1/26 = 320/292,201,338, about one in 913,129.

Independence of boards is the usual Bernoulli story. Ten distinct slips give chance 1−(1−1/292,201,338)^10 of at least one jackpot, which for such a tiny probability is about ten over 292,201,338, not a tenfold ticket that can overflow one. Expected jackpot dollars on a two-hundred-million headline are 200,000,000/292,201,338 ≈ 0.68 against a two-dollar stake, so jackpot-only expectation is about minus 1.32 dollars a line before sharing, tax, cash-option haircut, and Power Play. Those omissions are modelling assumptions, not rounding error.

Historical five-from-fifty-nine Powerball, often paired with a thirty-five red pool, is a different polynomial and must not be mixed with a 2015-or-later headline. Power Play never multiplies the jackpot. Correlated wheels change prize-tier dependence but not the six-number jackpot event so long as the tickets differ. The lecture is the MUSL 5/69 plus 1/26 matrix and nothing else.