How can this lottery play be expressed mathematically?

Re this story can his play be expressed as a statistical equation?

Skill trumps luck for Pick 3 player, friends

*This story was via Fark, and no, I don’t mean that it was by way of an incontinent bum named “Fark” who tipped me off about this story while he was dancing a wobbly little jig in front of the bodega. Oh no, not at all, Fark is website that collects the amusing news tidbits that come floating up from the cloudy tidal pool of a restless and agitated humanity that’s off its feed, a gill net of the zeitgeist slicing through the depths of human folly searching for the plumpest morsels of infotainment. Fark members are mostly a collection of eager young, rosy cheeked teenage lads that like to “game”, read science fiction, and have “Photoshop” (a product of Adobe) contests where they put amusing words to pictures. *

I’m not sure just what you’re looking for here. But for each $1000 they spent on tickets (one $1 ticket for each of the possible numbers 000 through 999), they could expect a return of $1200 ($600 for each of the two winning numbers drawn), which is a profit of $200 over their original investment. Since they spent $23,000 on tickets, their profit was 20% of this ($200 for each of those 23 thousands), or $4,600.

What the article doesn’t say is whether they had to pay taxes on their winnings, which could eat into their profits significantly.

I’m not sure how detailed you want this to be.

p(winning the first drawing) = 1
p(winning the 2nd drawing) = 1-(1/10^6)

From here, you can analyze it two ways:

expected winnings:

x = amount invested
winnings = .6xp[sub]1[/sub] + .6xp[sub]2[/sub]

This is the amount you expect to win over the long run.

Or, you can look at it this way:

since your p[sub]1[/sub] is 1, you will always win at least $600.
for the second drawing, there’s only a one in a million chance you won’t win $600.
999,999 times out of 1,000,000 you will win 1.2 times your initial investment

Thanks! Exactly what I was looking for!

It’s a one in a thousand chance, not a million, that the second draw matches the first, which is how you don’t win the second draw, so 999 times out of a thousand you’ll win 1.2 times your wager.

The expectation is 1.2 - ( 0.6 * 1/1000 ) = 1.2 - 0.0006 = 1.1994 times your wager

Of course, you’re right. I thought something looked a bit off.

My guess is that these guys will be in for a shock when they do their taxes. They will have to itemize their deductions to claim the losses they took on their losing tickets against their winnings. This means they will lose the standard deduction they would have had. This can be as much as $9700 for married couples. If their marginal tax rate is 25% this means they will have to pay $2425 more on their current income before the gambling winnings than they would otherwise have had to pay. Add this to the 25% they will have to pay on their net gambling winnings (25% of $4600 = $1150) and you get $3575 of their winnings going to the government for a net gain of $1025. This figure may be worse if they are in a state with an income tax or in a higher tax bracket. If they are in the 33% bracket they will actually lose money.

If they claim the standard deduction they would also take a loss since they couldn’t offset the gains on their winning tickets with the losses on the losing ones. They would owe 25% of $27,600… or $6,900 for a net loss of $2300!

It’s bad enough that most of the state lottery games are rigged so that you have a better chance of being struck by lightning than you do of winning, but when they screw up and actually give you decent odds you still can’t come away with much to show for the effort.

BTW I am not an accountant (just an insomniac :wink: ) so take all of this with a huge grain of salt.

I mentioned my story to a coworker then googled the story.
Never saw this back in 2004. No taxes had to be paid. Each win was treated separately. Only wins over $$$$ in the state of Missouri require tax forms. Missouri Lottery changed the format of the promotions after that. Big Fun!!

Sure, but wouldn’t the winnings still be taxed? Tax forms may not have been automatically issued, but surely one would still be responsible for taxes on the winnings, whether you win $1 each a million times or $1,000,000 once, no? Or is that not how it works?

Perhaps state income tax?

Because the IRS definitely considers lottery winnings taxable income.

Either that, or they mean that because each win was below a certain amount, it wasn’t automatically reported. But that would imply tax evasion, which is a big no-no.

And stupid tax evasion, when your winnings are making the media.