If you buy ten or 100 tickets do your odds of winning the Powerball lottery get better? Sure they do, but let’s look at by how much.
Your odds of winning with a single $2 entry are 1 in 292 million (I am rounding here since it’s actually 292.2). As is regularly pointed out those are terrible odds. But surely buying more than one entry makes them not so terrible right? Yes, but still terrible.
In probability this is an addition of probabilities. When you’re asking if one thing OR another will happen then you add the two probabilities together. Assuming you let the computer pick two tickets then the odds of the first one winning (1/292M) are added as a fraction to the odds of the second ticket winning (1/292M). I don’t know how they teach that to kids these days but when the denominator is the same you add the two numerators. Your odds are now 2/292M. Similarly if you bought ten tickets your odds would be 10/292M.
That seems pretty good until you look at it as a percentage (by dividing the two numbers and multiplying by 100).
| Tickets | Probability of Winning |
| 1 | 0.0000003425% |
| 2 | 0.0000006849% |
| 3 | 0.0000010274% |
| 4 | 0.0000013699% |
| 5 | 0.0000017123% |
| 6 | 0.0000020548% |
| 7 | 0.0000023973% |
| 8 | 0.0000027397% |
| 9 | 0.0000030822% |
| 10 | 0.0000034247% |
When your probability of winning has that many zeros after the decimal it’s really low no matter what.
But if you really stepped up your game and bought 1000 tickets (a $2000 gamble), your probability of winning is now 0.0006849315%.
Following this logic you’d have to buy 146 million tickets to get a 50% chance of winning.
If you bought all 292 million tickets at a cost of $584M then you’d be guaranteed to win. If you took the cash payout of the current estimate $806M you’d make money before taxes and only if nobody else won. If you deduct the cost of the losing tickets, which is allowed, then your taxable amount would be $222M. If you paid the highest income tax rate of 39.6% then you’d be paying $87.9M in taxes which would net out like this:
$806M winning – $584M ticket cost – $87.9M taxes = $134.1M take home.
That’s not bad but if you had to split the winnings with one other person it would look like this, note there are no taxes as the entire amount of losing tickets offset the winnings.
$403M winning – $584M ticket cost – $0 taxes = -$181M (a loss)
Don’t spend $584 million on lottery tickets.
