# Does buying 10 lottery tickets increase my odds by a power of ten?

If the odds of winning a lottery jackpot are 1 in 175,711,536, if I buy 10 tickets, do my odds change to 1 in 17,571,153.6? And 100 tickets increases it to 1 in 1,757,115.36?

That is, is “10 in 175,711,536” the same as “1 in 17,571,153.6”?

If you buy multiple tickets each with a different number, your chances increase by a factor of how many tickets you buy.

The “power of 10” phrase is a little misleading. If you buy 5 tickets, your chances increase by a factor of 5. If you buy 127 tickets, your chances increase by a factor of 127. Powers of 10 have nothing to do with it, except that your examples use powers of 10 for the number of tickets.

And yes, “10 in 175,711,536” is the same as “1 in 17,571,153.6”.

Alternatively, if you buy one lottery ticket with 1 chance in 175,711,536 of winning you have 175,711,535 chances of not winning.

If you buy 10 tickets you have 175,711,526 chances of not winning.

So you have improved your chances of not winning from

99.999999430885402993688473590032% to 99.999994308854029936884735900322%

This represents an improvement of

.00000512203166455910240060177%

Whoa! Buzzkill.

There’s the old joke about the poor guy that used to pray every night for God to let him win the lottery. After several years of this, he’s praying one night when there’s a thunderbolt, a cloud appears, a giant hand comes out the cloud, points a finger at him and says “You cheap bastard! The least you could do is help me out by buying a ticket once in a while!”

So - your odds of winning go up tremendously with the first ticket. With the second, you spend \$1 (or whatever) and double your chances. By the fift, an extra dollar only adds 20% to your chjnce of winning. By 10, it’s only 10% for a buck. You have to spend \$10 to double your chances of winning.

So the more tickets you have, the less useful your marginal extra dollar spent is. That’s another way of looking at it. But yes, the theory is every (different) ticket has an equal chance of winning so every dollar is equally well spent.

The only unpredictable factor is whether there are duplicate winners. One group of people where I worked won the lottery - about \$2million - but had to share it 6 ways. That’s a very large split compared to usual, then among the group it was split 11 ways. Each person got \$30,000 or so. Better than nothing, but still…

Also, you forget that once you buy more tickets, the total amount of tickets sold will be larger. It comes down to whether this is a lotery where they draw a number from all possible numbers or a lottery where they guarantee someone is going to win. If you include the possibility of having the same number as somebody else it becomes different alltogether.

poss. 1 As explained above, your chances increase whith the factor of the amount of tickets you buy (buying 10 has a chance of winning of 10 times the probability when buying 1).

poss 2 Almost the same as poss 1, but a tiny bit less because the total amount of tickets sold also grows when you buy more tickets.

poss 3 Depends on how many people have the same number and whether there has to be a winner or not.

But let’s consider the case where you buy one of every available ticket number. Then for sure when they pull the lucky number out of the bowl (or whatever), you’re a winner.

On the other hand, I believe the finances work out that your prize is only 50%, maybe less, of what you spent buying tickets. That’s assuming you don’t have to share the prize. And further that’s before they take out taxes (I doubt you can deduct the cost of the tickets)

So, what may really count is not the odds of winning, but the expected return. Granted for very low numbers of tickets as could realistically happen, that does track the number of tickets bought. And its still depressingly low.

I did the math and decided that my chances of winning the lottery were pretty much the same whether I played or not.

I did the math and played the numbers instead of the state sanctioned version.

[quote=“md2000, post:5, topic:531119”]

So - your odds of winning go up tremendously with the first ticket.QUOTE]

The difference between 0.0000005% and 0.00000000% is only tremendous for certain values of tremendous.

Is that better than getting a 300% raise at your volunteer no-pay job?

Semi-important note : not quite true if you buy them randomly - but correct if you make sure to buy distinct number sets. If bought randomly your chance of winning is :
1 - (175,711,535/175,711,536)[sup]n[/sup]
where n = the number of tickets you buy. There’s a slight diminishment of returns on the second and subsequent tickets with regards to probability, because of the small chance that two (or more) of your tickets will win.

You’re expected return is better if you don’t buy a ticket.

If you buy a \$1 ticket, your expected return is \$0.50 (depending on the game) whereas if you put the \$1 in your pocket the expected return is \$1.

With some progessive jackpots,sometimes it happenes that the payout is over the number of combinations (say, 200,000,000 combinations but the payout is 300,000,000). But even if you buy every combo, you are not guaranteed a profit because someone else may have the same combo. (say only one, the payout diminishes to 150,000,000). (though you might also win some lesser prizes for matching X numbers)

Not to mention the logistics of buying millions of tickets.

Brian

Actually, if you put the dollar in your pocket your return (or expected return) is zero.

Can’t you? You can deduct gambling losses (against gambling wins), and lottery tickets that don’t win sound like gambling losses to me.

Sure, but you’d be hard pressed to legally deduct gambling losses from your taxes.

You can deduct gambling losses, but only against gambling wins. So if you lose \$1000 at the blackjack tables today, win \$8000 tomorrow, and lose \$3000 the next day, you only owe taxes on \$4000.

Oh god, the sigfigs. THEY BURN!

Yes. And if you buy a \$1 ticket the expected value is -\$0.50.