Lottery Odds and Expected Value Calculator

What a lottery odds number measures

Every lottery odds figure is a count of equally likely outcomes. Powerball draws five white balls from a drum of 69 and one red ball from a drum of 26. A single ticket names one set of five white numbers and one red number. The number of possible tickets is the number of ways to choose those balls, and the jackpot odds are one divided by that count.

That is the whole idea, and it explains why the number is so large. You are not competing against other players. You are picking one combination out of 292,201,338, and every combination has the same chance. Buying a ticket with the numbers 1, 2, 3, 4, 5 does not make that combination less likely than any other, even though it feels wrong.

Mega Millions works the same way with different drums. Since the drawing on April 8, 2025 it uses five balls from 70 and one gold ball from 24, which the game's own how to play page documents along with the prize at each tier. That change from 25 gold balls to 24 is what moved the jackpot odds from 1 in 302,575,350 to 1 in 290,472,336.

The combination formula, worked out

The count of ways to choose 5 numbers from 69 is written C(69,5) and read as 69 choose 5. The arithmetic is a product divided by a product: multiply the top five numbers counting down from 69, then divide by 5 factorial, which is 5 times 4 times 3 times 2 times 1.

Step by step, 69 times 68 is 4,692. Times 67 is 314,364. Times 66 is 20,748,024. Times 65 is 1,348,621,560. Divide by 120 and you have 11,238,513. The division is what makes order irrelevant: the same five numbers can be drawn in 120 different sequences, and all of them count as one ticket.

Then the red ball. There are 26 of them and the ticket names one, so 11,238,513 times 26 is 292,201,338. That is the denominator for the jackpot, and it is also the number the official Powerball prize chart prints next to the grand prize.

Mega Millions runs the same steps with its own numbers. C(70,5) is 12,103,014, and 12,103,014 times 24 is 290,472,336. The two games land within 0.6 percent of each other, which is why their jackpots feel interchangeable even though the drums differ.

Powerball prizes and the odds at each tier

Nine tiers pay a prize in Powerball, and the odds below come from the same combination count applied to each match pattern. The prize amounts are the standard ones, before the optional Power Play multiplier.

Add the winning combinations up and you get 11,750,538 of the 292,201,338 possible tickets. Divide and the overall chance of some prize is 1 in 24.87, the number printed at the bottom of the chart. Most of that total comes from the two $4 tiers: matching only the Powerball is 1 in 38.32 on its own, and that single tier accounts for 7,624,512 of the winning tickets.

The gap between the top and the bottom of that table is the part people underestimate. You are about 11.75 million times more likely to win some prize than to win the jackpot, and the prize you are most likely to win is $4 on a $2 ticket.

Mega Millions prizes and the new matrix

Mega Millions pays nine tiers as well, and the April 2025 change raised the lower prizes at the same time it removed a gold ball. The table shows the base prize for each tier, which is the 2X column of the game's multiplier grid.

The multiplier is built into the $5 price rather than sold as an add on. Each ticket gets a 2X, 3X, 4X, 5X or 10X multiplier at random, and the odds of each are 1 in 2.13, 1 in 3.2, 1 in 8, 1 in 16 and 1 in 32. Weighted by those odds, the average multiplier works out to about 3.0, which is the factor to use when you compare this game with one that sells its multiplier separately.

The overall chance of a prize is 1 in 23.07, slightly better than Powerball's 1 in 24.87. The ticket also costs more than twice as much, which matters more than the odds difference once you look at expected value.

Why the expected value is always negative

Expected value is the average result if you could play the same ticket millions of times. Multiply each prize by the chance of winning it, add the results, and subtract what the ticket costs. For Powerball with a $298 million advertised jackpot and a $126.6 million cash value, the sum looks like this.

The cash jackpot is divided by 292,201,338 to give 43.3 cents. The fixed prizes add 32 cents, most of it from the two $4 tiers. Together that is 75.3 cents against a $2 price, so the ticket returns about 38 cents on the dollar in expected terms. The other $1.25 does not vanish into a fee: it funds the prizes that other players win, plus retailer commissions and the state share.

Mega Millions looks better per dollar of return, at 2.6844 divided by 5, which is 53.7 percent, and worse in absolute dollars, because you lose $2.32 per ticket instead of $1.25. Neither game ever crosses into positive territory at a normal jackpot. The structure guarantees it, since every dollar paid out comes from dollars collected.

What ten tickets per drawing buys you

Buying more tickets does raise your chance, just not by much. Ten Powerball tickets per drawing cover 10 of the 292,201,338 jackpot combinations, so the jackpot chance moves from 1 in 292,201,338 to 10 in 292,201,338. In percentage terms that is 0.0000034 percent, which rounds to zero on any screen.

The any-prize number moves more, because the base chance is bigger. One ticket wins something 4.0 percent of the time. Ten tickets, treated as independent draws, give a 33.7 percent chance of at least one prize, which is 1 minus 0.9598 raised to the tenth power. That sounds encouraging until you notice that most of those prizes are $4, and ten tickets cost $20.

The wait for a jackpot is the number that puts the odds in perspective. At 10 tickets per drawing and three Powerball drawings a week, the expected wait for one jackpot is 292,201,338 divided by 10, divided by 3, divided by 52, which is 187,309 years. Spending $20 a week for that long is about $194.8 million, which is more than the jackpot you are chasing.

None of this argues that playing is irrational. A ticket buys a few days of a specific daydream, and that is a real thing people pay for. It argues that the purchase should be sized as entertainment rather than as an investment, and that the size should not change after a near miss.

When the jackpot gets big enough to matter

Rollovers are the one time the arithmetic moves toward the player. A $1.5 billion Powerball jackpot with a $640 million cash value puts 640 million divided by 292,201,338, or $2.19, into the jackpot share alone, and the fixed prizes add 32 cents. That is $2.51 of expected return on a $2 ticket, which is the rare case where the raw expected value turns positive.

Three things eat that edge. The first is tax. The IRS treats lottery winnings as gambling income, and its Topic 419 guidance on gambling income covers how that is reported. Federal withholding takes 24 percent off a large prize at the payout window, while the top bracket is 37 percent, so a big win settles up at filing time and most states add their own tax on top.

The second is sharing. A jackpot large enough to make the math work is also large enough to attract millions of extra tickets, and the chance of splitting rises with them. A prize split three ways is a third of the value you calculated.

The third is that the advertised figure is an annuity, paid over 30 graduated yearly payments, not a lump sum. The cash value is what the lottery has on hand today, and it runs at roughly 42 cents per advertised dollar in the example above, 126.6 divided by 298.

Put together, the positive expected value at a record jackpot is thin, fragile, and available only to someone who ignores taxes, splitting and the time value of the annuity. It is not a reason to buy more tickets than you would have bought anyway.

Playing with clear eyes

A few habits keep the math in its place. Set a monthly amount you would spend on any other entertainment, and treat it as spent. Buy the tickets in one trip rather than adding one more after each drawing. Skip the multiplier add on unless you have run the numbers for that specific game, because it raises the price faster than it raises the expected return.

Check the ticket before you leave the store, sign the back if you win, and know the claim deadline in your state, since it is often 180 days from the drawing. Those are the practical details that turn a winning ticket into money.

The numbers on this page are the published prize tables from both games, converted into expected value. They describe an average over millions of plays, not a prediction about any single ticket, and no calculator can change the odds of one drawing.

Prize amounts, matrices and odds change when the games change their rules. Confirm the current table with the official game site or your state lottery before relying on a figure. This page is an educational estimate, not financial advice.