Check the true odds of Powerball and Mega Millions, estimate the lump sum cash value and federal taxes, and find out if buying a lottery ticket is mathematically worth it. Free, instant, and 100% private.
Enter a jackpot to see if a ticket is mathematically worth it
True Expected Value (EV) per Ticket
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What one ticket is actually worth on average, after the cost to buy it
Net Take-Home Cash (If You Win)
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The real prize after the lump sum cut and federal tax, far below the billboard number
Your Odds of Winning
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The chance any single ticket wins the jackpot
🎲 Enter Your Lottery Details
Switching to Mega Millions automatically sets the ticket cost to $5.00.
1 in
Enter the total number of possible combinations for your game.
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The headline annuity jackpot shown on the billboard.
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Powerball is $2.00 per play. Mega Millions is $5.00 per play.
📉 Reality Check: Where the Jackpot Goes
Advertised JackpotThe annuity billboard number--
▼ minus 50% for the lump sum cash option
Gross Lump Sum Cash ValueRoughly half the jackpot, paid now--
▼ minus 37% mandatory federal tax
Federal Tax Withheld (37%)The top federal bracket on big winnings--
▼ equals what you actually keep
Final Net Cash Take-HomeBefore any state or local tax--
🧮 The Math Behind the EV
Win Probability
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Chance per ticket
Prize Value of a Ticket
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Take-home times probability
Cost to Play
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Subtracted to get EV
For educational purposes only. This is not financial, tax, or gambling advice. The lump sum estimate uses a simplified 50% of the advertised jackpot, and the federal tax uses the top 37% bracket. Actual cash values, withholding, and final tax bills vary by drawing, state and local taxes, filing status, and current interest rates. This tool is not affiliated with Powerball, Mega Millions, or any state lottery. If you choose to play, please play responsibly.
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📖 Key Terms Explained
Expected Value (EV)
The average profit or loss per ticket over the very long run. It equals your real take-home prize multiplied by your probability of winning, minus the ticket cost. A negative EV means each ticket loses money on average.
Lump Sum Cash Option
The choice to take a one-time cash payment instead of the annuity. It is roughly half of the advertised jackpot because the lottery only sets aside the cash needed today to fund the future annuity payments.
Annuity
The advertised jackpot paid out as 30 graduated installments over 29 years. The headline number reflects the total of all those future payments, not the cash available right now.
Independent Event
An outcome whose probability is unaffected by previous outcomes. Every lottery draw is independent, so past results have zero influence on which numbers come up next.
Gambler's Fallacy
The false belief that a result is overdue or on a streak based on past draws, such as thinking a number that has not appeared in a while is due. Because draws are independent, this reasoning is always wrong.
Odds vs Probability
Odds are stated as a ratio such as 1 in 292 million, while probability is the same chance written as a fraction or percentage. Both describe how likely a win is, just in different formats.
Advertised Jackpot
The large billboard prize used to market the game. It is the annuity total and is always much larger than the cash you would actually receive and keep after taxes.
Federal Withholding
The mandatory tax taken from large lottery winnings. The top federal income tax bracket of 37% applies to a jackpot, and state taxes may apply on top of that.
Net Take-Home Cash
The amount a winner actually keeps after choosing the lump sum and paying federal tax. This is the real prize figure used to calculate a ticket's expected value.
Negative Expected Value Game
A bet where the expected value is below zero, meaning the player loses money on average over time. Nearly every lottery ticket is a negative expected value game by design.
The Complete Guide to Lottery Expected Value
A billion dollar jackpot makes a lottery ticket feel like a smart bet, but the math tells a colder story. This guide explains how the expected value calculator above works, why the cash you keep is a fraction of the advertised number, and why no system, lucky number, or overdue ball can shift the odds in your favor.
How to Use This Lottery EV Calculator
Start by choosing your game from the dropdown. Powerball loads with its true odds of 1 in 292.2 million and a $2.00 ticket, and selecting Mega Millions automatically switches the odds to 1 in 302.5 million and the ticket cost to $5.00. Choose Custom Odds to model any game by entering the number of possible combinations yourself. Next, set the advertised jackpot to the current billboard amount and adjust the ticket cost if needed. Everything recalculates instantly as you type, with no submit button. The status banner at the top turns red when a ticket has negative expected value and green in the rare case the jackpot is large enough to flip it positive.
The Expected Value Math, Step by Step
The engine first turns the advertised jackpot into the cash a winner would actually keep. It takes the lump sum cash value as 50% of the advertised jackpot, then removes a 37% mandatory federal tax to find the net take-home cash. It converts the game odds into a probability by dividing 1 by the number of combinations. Multiplying the net take-home cash by that probability gives the prize value of a single ticket, which is almost always a tiny fraction of a cent. Finally it subtracts the ticket cost. The result is the expected value: the average amount you win or lose every time you buy one ticket.
Why the Lump Sum Is So Much Smaller
The advertised jackpot is an annuity spread across three decades, and the lottery only needs enough cash today to fund those future payments. That is why taking the money now hands you roughly half the headline figure. Then federal tax claims another large share at the top 37% bracket, and many states add their own tax on top. By the time the dust settles, a one billion dollar billboard can become a take-home figure closer to three hundred million dollars. This calculator makes that shrinkage visible in the Reality Check funnel so the gap between the marketing number and the real prize is impossible to miss.
Why a Ticket Almost Always Has Negative Expected Value
For the expected value of a ticket to turn positive, the prize value, which is the net take-home cash multiplied by the minuscule probability of winning, must exceed the ticket cost. Because the odds are hundreds of millions to one, the jackpot has to grow to extraordinary levels before the math even approaches break-even. Even then, the simple model ignores the very real chance that multiple winners split the prize, which slices the take-home cash and pushes the expected value back below zero. In practice this means buying a ticket is an entertainment expense, not an investment.
The Gambler's Fallacy and Why No Number Is Due
Every drawing is an independent event. The machines have no memory, so a combination that has not appeared in years is exactly as likely as one drawn last week. The belief that a cold number is due to hit, or that a hot number is riding a streak, is the classic Gambler's Fallacy. Quick picks, birthdays, and elaborate number systems all share the identical probability on every single draw. The only thing that changes your real odds is buying more tickets, and even then the per ticket expected value stays the same.
Frequently Asked Questions
Expected Value, or EV, is the average amount you would win or lose per ticket if you could play the same draw an enormous number of times. For the lottery it is calculated by multiplying the real take-home prize (the lump sum cash value after federal tax) by your probability of winning, then subtracting the ticket cost. A negative EV means that, on average, every ticket you buy loses you money. Almost every lottery ticket ever sold has a negative expected value, which is precisely how the games fund their prizes and their operators.
The advertised jackpot is an annuity, paid out in 30 graduated annual installments over 29 years. To advertise that headline number the lottery only needs enough cash today to buy an investment that will fund those future payments, so the immediate cash value is roughly half of the billboard figure. If you take the cash option you receive that smaller lump sum at once. On top of that, a mandatory federal tax applies to the winnings, which shrinks the take-home amount even further before any state tax is considered.
Expected value subtracts the ticket cost from the value of your tiny chance at the prize. Because a Mega Millions ticket costs $5 while a Powerball ticket costs $2, the Mega Millions ticket has to overcome a larger upfront cost to reach break-even. Combined with slightly longer odds, a higher ticket price drags the expected value further into negative territory. In short, paying more per ticket makes the math worse, not better, unless the jackpot rises high enough to offset the extra cost.
No. Each lottery draw is an independent event, meaning the balls have no memory of previous draws. A number that has not appeared in months is exactly as likely to be drawn as one that came up last week. Believing that a cold number is due, or that a hot number is on a streak, is the Gambler's Fallacy. The mechanical odds for every combination are identical on every single draw, so no pattern, system, or overdue number can improve your chances.
No. Every calculation runs entirely inside your own browser using client-side JavaScript. The jackpot amount, ticket cost, and odds you enter are never transmitted, saved, or sent to any server. Nothing you type leaves your device, so your inputs stay completely private.