Maps for Math

What are the odds of winning the lottery, and is a ticket worth it?

Powerball's jackpot odds are 1 in 292,201,338: ways to choose 5 of 69 numbers, times 26 bonus balls. A ticket's expected value is that chance times what you'd actually keep, after the lump sum, taxes, and splitting with other winners. It's almost always far less than the $2 ticket.

1 in 13,983,816about as likely as flipping 23.7 heads in a rowthat many $1 bills stacked: 1530 m tallticket price $1.00$2 million: worth 8.7¢
Odds of the jackpot (1 in …)
14,000,000
Jackpot value of one ticket
$0.09
Return on the ticket price
8.7%
Jackpot needed to be worth the price
$22,999,642.48

This counts the jackpot only. Smaller prizes add a little value, and your actual tax depends on your state and the rest of your income.

Challenge: Find a Powerball drawing where the jackpot alone is worth the ticket price.

$
Big jackpots draw big crowds, and every other ticket is a chance you’ll have to share.
More settings
%
The advertised jackpot is paid over about 30 years. Taking cash now is usually about 45 to 50% of it.
%
The top US federal rate is 37%. Many states add more.

Play

Load the $500 million drawing, then raise the jackpot. Watch what the crowd of other tickets does to it.

Challenge: Find a Powerball drawing where the jackpot alone is worth the ticket price. The box under the picture turns green when you get it.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

EV=1N×J×c×(1−t)×s\text{EV} = \frac{1}{N}\times J \times c \times (1 - t) \times s

The odds come from counting. Choosing 5 of 69 numbers, when order doesn't matter, is a combination: (695)=11,238,513\binom{69}{5} = 11{,}238{,}513 ways. Times 26 bonus balls gives 292,201,338 possible tickets.

A ticket's expected value is the chance times what you'd keep: the lump sum, after taxes, and after splitting with anyone else who picked the same numbers. The line shows that value against the advertised jackpot, next to the ticket price.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. Ways to choose 6 numbers from 49 (order doesn’t matter)\binom{49}{6} = 13{,}980{,}000
  2. No bonus ballN = \binom{49}{6} = 13{,}980{,}000
  3. Expected number of other winning tickets\lambda = \frac{1{,}000{,}000}{13{,}980{,}000} = 0.0715
  4. Share you’d keep on average if you win (splitting)s = \frac{1 - e^{-\lambda}}{\lambda} = 0.965
  5. Expected value: chance × what you’d actually take home\text{EV} = \frac{1}{13{,}980{,}000} \times 2{,}000{,}000 \times 1 \times 0.63 \times 0.965 = \$0.087

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Pick a game and a jackpot. "More settings" changes the lump-sum share and taxes.

  • The jackpot odds are exact for these game rules. The lump-sum share and tax rates are typical, not specific to your state.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

N=(695)×26=292,201,338N = \binom{69}{5} \times 26 = 292{,}201{,}338
EV=1N×J×c×(1−t)×s\text{EV} = \frac{1}{N}\times J \times c \times (1 - t) \times s
s=1−e−λλ,λ=other ticketsNs = \frac{1 - e^{-\lambda}}{\lambda},\quad \lambda = \frac{\text{other tickets}}{N}
SymbolMeaningUnit
NNnumber of possible tickets (1 in N odds)
JJadvertised jackpot$
cclump-sum share
tttax rate
ssshare kept after splitting
  • Order doesn't matter for the main numbers, so use combinations, not permutations.
  • Bigger jackpots draw more tickets, so the chance of splitting grows too.
  • Expected value says what a ticket is worth on average, not what will happen to you.

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Where it’s used

Questions people ask

How are lottery odds calculated?

Count every possible ticket. For Powerball that's C(69, 5) = 11,238,513 ways to pick five numbers, times 26 bonus balls, which is 292,201,338.

Is buying a lottery ticket ever worth it?

Mathematically, almost never. Even huge jackpots shrink a lot after the lump sum, taxes, and the chance of sharing with other winners.

Does buying more tickets help?

Each extra ticket adds the same tiny chance. Ten tickets make you ten times as likely to win, which is still about 1 in 29 million for Powerball.

Sample PRB-0003 · rev 1 · model PRB-M03 · Level 3 · algebra · updated 2026-09-30