What a lottery ticket is actually worth
Expected value is the average result of a bet repeated many times: each prize times its odds, added up, minus the ticket price. Summed over every non-jackpot Powerball tier, that average is about $0.32 per $2 play. Add a typical jackpot and the total stays deeply negative; this page shows the arithmetic and explains why even a rare positive result is still not a good bet.
What expected value actually means
Expected value is a way of asking "on average, across a huge number of repeats, what does this bet return?" It is not a prediction of what happens on any single play, and a lottery ticket only gets played once. It is the number you would land on if the exact same ticket were somehow played millions of times and every result were averaged together.
The calculation is simple to state: multiply each possible prize by the probability of winning it, add all of those products together, then subtract what the ticket cost. If that final number is negative, the bet loses money on average. If it is positive, it gains money on average — but, as this page gets to, "on average" is doing a lot of work in that sentence.
Computing it from the tier table
A Powerball play has nine possible outcomes, and every one of them except the jackpot has a fixed prize with a published probability. Multiplying each prize by its odds gives that tier's share of the ticket's expected value:
| Match | Prize | Odds | Contribution to expected value |
|---|---|---|---|
| 5 white, no Powerball | $1,000,000 | 1 in 11,688,054 | $0.0856 |
| 4 white + Powerball | $50,000 | 1 in 913,129 | $0.0548 |
| 4 white, no Powerball | $100 | 1 in 36,525 | $0.0027 |
| 3 white + Powerball | $100 | 1 in 14,494 | $0.0069 |
| 3 white, no Powerball | $7 | 1 in 580 | $0.0121 |
| 2 white + Powerball | $7 | 1 in 701 | $0.0100 |
| 1 white + Powerball | $4 | 1 in 92 | $0.0435 |
| 0 white + Powerball | $4 | 1 in 38 | $0.1053 |
Add those eight contributions together and the non-jackpot tiers are worth about $0.32 of expected value on a $2 play. That is the entire non-jackpot side of the ticket: roughly 16% of the purchase price, on average, before the jackpot tier is even considered. The rest of this page is about what the jackpot tier adds, because that is the part that actually moves.
Why it is negative almost every time
The jackpot tier's contribution to expected value is simply the jackpot amount divided by 292,201,338, the odds of winning it. Because that jackpot amount changes every drawing, so does this number, but most drawings are not the record-setting ones people remember. Powerball's own rules give a useful example of an ordinary-sized jackpot: the 10x Power Play multiplier is only offered when the advertised jackpot is $150 million or less, which puts a real number on what "typical, not enormous" looks like for this game.
| Jackpot size | Contribution to expected value | Total expected value (jackpot + tiers) | Minus the $2 price |
|---|---|---|---|
| $150,000,000 (the Power Play 10x cutoff) | $0.51 | $0.83 | −$1.17 |
At that size, a ticket's total expected value is about $0.83, against a $2 price: a loss of roughly $1.17 on average for every play. That is the ordinary case. The jackpot has to grow enormously, well past where most drawings sit, before the arithmetic changes shape.
What a rollover does to the number
When nobody wins the jackpot, it rolls over and grows for the next drawing, and it can keep growing for many drawings in a row. Kiplinger, 2026 records a real, verified example: a Powerball jackpot advertised at $1.786 billion (the annuity figure) with an estimated cash value of $826.4 million. Both numbers are real dollar amounts that were actually on offer in that drawing, and dividing each by the same 292,201,338 shows what a jackpot that size does to the math:
| Which jackpot figure | Jackpot contribution to EV | Total naive EV (jackpot + tiers) | Minus the $2 price |
|---|---|---|---|
| Cash value: $826,400,000 | $2.83 | $3.15 | +$1.15 |
| Annuity total: $1,786,000,000 | $6.11 | $6.43 | +$4.43 |
At that size, the naive calculation flips positive under either figure. This is the one situation where a lottery ticket's bare expected value, ignoring everything else, is not obviously a bad number. It is also rare: jackpots reach that size only after many consecutive drawings with no jackpot winner, which is itself a low-probability run of events.
Why even a positive number is not a good bet
A positive naive expected value is still not a good bet, for two reasons that both get worse exactly when the jackpot is big enough to look attractive.
Tax. The naive calculation above uses the full jackpot figure. A real winner does not keep it. Twenty-four percent is withheld federally the moment winnings above $5,000 are paid, and that withholding is not the final bill: a jackpot-sized win lands the winner in the top federal bracket, 37% for 2026. Internal Revenue Service, 2026 Run the $826.4 million cash example through even the withholding rate alone and roughly $198 million of it is gone before state tax is considered; the final federal bill, at the top bracket, is higher still. That is not deducted anywhere in the tables above, because the naive expected-value calculation never deducts it — which is exactly the point: the naive number and the number a winner actually receives are not the same number.
Sharing. A bigger jackpot sells far more tickets, because more people notice it. More tickets in play means a higher chance that more than one of them matches the winning combination, and a jackpot split between two or three winners divides that $826.4 million or $1.786 billion by the number of winners before any tax is even applied. The naive calculation above assumes one winner keeps the whole prize; the bigger the jackpot, the less safe that assumption gets, for reasons that have nothing to do with the odds of any individual ticket changing.
Put together, a positive naive expected value at a record jackpot is real, and also not a reason to treat a lottery ticket as a good use of money at any jackpot size. The gap between the naive number and what a winner actually keeps is largest exactly when the naive number looks best.
What this page is not
Two more limits on this whole exercise. First, every non-jackpot prize used above is the fixed national amount; California pays these tiers pari-mutuel instead, so a real California ticket's expected value differs from the figures on this page by whatever that drawing's actual pari-mutuel prizes turn out to be. Second, none of this is tax or financial advice — the withholding and bracket figures above describe published rules, not a specific person's situation, and a real win is a reason to talk to an accountant before anything else.
None of it is advice to play, either, at a small jackpot or a record one. Lottery play is gambling with a negative expected return in the overwhelming majority of drawings, and even the rare exception above is not a recommendation, just an honest description of what the arithmetic does at that size. More on playing safely, including where to get help, is on responsible play.
Expected value of a ticket: FAQ
What is expected value on a lottery ticket?
The average result if the exact same ticket were played many times: each prize times its odds, added up, minus the ticket price. It describes an average across repeats, not any single play.
What is the expected value of a Powerball ticket?
The eight non-jackpot tiers together are worth about $0.32 of expected value on a $2 play. Adding a typical, not record-sized jackpot still leaves the total well below the $2 price.
Can a lottery ticket ever have a positive expected value?
In the naive calculation, yes, at a large enough rolled-over jackpot — a real $1.786 billion example put the total above $2. This ignores tax and the chance of sharing the jackpot with other winners, both of which get worse at exactly that size.
Why does a jackpot rollover change the expected value?
The jackpot tier's contribution to expected value is the jackpot amount divided by 292,201,338. A bigger jackpot, after many drawings with no winner, makes that one division much larger, even though the odds of winning stay exactly the same.
Does tax change whether a ticket is a good bet?
Yes. The naive expected-value figure uses the full jackpot amount, but a real winner keeps far less after 24% federal withholding and, at the top 37% bracket a jackpot creates, an even larger final tax bill.
Does a bigger jackpot also mean a higher chance of splitting it?
Yes. Larger jackpots sell more tickets, which raises the chance that more than one ticket matches the winning numbers, dividing the prize before tax is even applied — something a naive expected-value calculation does not account for.
Expected value of a ticket: common questions
What is expected value on a lottery ticket?
The average result if the exact same ticket were played many times: each prize times its odds, added up, minus the ticket price. It describes an average across repeats, not any single play.
What is the expected value of a Powerball ticket?
The eight non-jackpot tiers together are worth about $0.32 of expected value on a $2 play. Adding a typical, not record-sized jackpot still leaves the total well below the $2 price.
Can a lottery ticket ever have a positive expected value?
In the naive calculation, yes, at a large enough rolled-over jackpot — a real $1.786 billion example put the total above $2. This ignores tax and the chance of sharing the jackpot with other winners, both of which get worse at exactly that size.
Why does a jackpot rollover change the expected value?
The jackpot tier's contribution to expected value is the jackpot amount divided by 292,201,338. A bigger jackpot, after many drawings with no winner, makes that one division much larger, even though the odds of winning stay exactly the same.
Does tax change whether a ticket is a good bet?
Yes. The naive expected-value figure uses the full jackpot amount, but a real winner keeps far less after 24% federal withholding and, at the top 37% bracket a jackpot creates, an even larger final tax bill.
Does a bigger jackpot also mean a higher chance of splitting it?
Yes. Larger jackpots sell more tickets, which raises the chance that more than one ticket matches the winning numbers, dividing the prize before tax is even applied — something a naive expected-value calculation does not account for.
Keep reading
Powerball odds
The full tier-by-tier table this page's expected-value calculation is built from.
Read →How lottery odds are calculated
Where the 1 in 292,201,338 figure behind these odds actually comes from.
Read →Odds in perspective
The same jackpot number turned into things arithmetic can picture.
Read →The odds do not move, so check them yourself
Powerball is 1 in 292,201,338 and Mega Millions is 1 in 290,472,336 for one play. Every figure on this site is dated, sourced and shown with its arithmetic, and we sell nothing that could change any of it.