# Does buying 10 lottery tickets increase my odds by a power of ten? **URL:** \ **Category:** Factual Questions\ **Created:** [March 3, 2010, 2:34pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119 "2010-03-03T14:34:11Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Dilton\_Doiley\_Philosopher\_King](https://avatars.discourse-cdn.com/v4/letter/d/f1d935/32.png) [@Dilton\_Doiley\_Philosopher\_King](https://boards.straightdope.com/u/Dilton_Doiley_Philosopher_King)\ **Post date:** [March 3, 2010, 2:34pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/1 "2010-03-03T14:34:11Z")
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”? ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [March 3, 2010, 2:37pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/2 "2010-03-03T14:37:47Z")
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”. ---
**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\ **Post date:** [March 3, 2010, 2:58pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/3 "2010-03-03T14:58:39Z")
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% ---
**Author:** ![Vorpal\_Blade](https://avatars.discourse-cdn.com/v4/letter/v/9de0a6/32.png) [@Vorpal\_Blade](https://boards.straightdope.com/u/Vorpal_Blade)\ **Post date:** [March 3, 2010, 3:01pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/4 "2010-03-03T15:01:55Z")
> [@don\_t\_ask](#): > > …This represents an improvement of > > .00000512203166455910240060177% Whoa! Buzzkill. ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [March 3, 2010, 3:22pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/5 "2010-03-03T15:22:49Z")
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… ---
**Author:** ![footballisplayedwithyourfeet](https://avatars.discourse-cdn.com/v4/letter/f/9f8e36/32.png) [@footballisplayedwithyourfeet](https://boards.straightdope.com/u/footballisplayedwithyourfeet)\ **Post date:** [March 3, 2010, 3:46pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/6 "2010-03-03T15:46:51Z")
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. ---
**Author:** ![UncleFred](https://avatars.discourse-cdn.com/v4/letter/u/f0a364/32.png) [@UncleFred](https://boards.straightdope.com/u/UncleFred)\ **Post date:** [March 3, 2010, 4:42pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/7 "2010-03-03T16:42:53Z")
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. ---
**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\ **Post date:** [March 3, 2010, 4:52pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/8 "2010-03-03T16:52:03Z")
I did the math and decided that my chances of winning the lottery were pretty much the same whether I played or not. ---
**Author:** ![kayaker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kayaker/32/441_2.png) [@kayaker](https://boards.straightdope.com/u/kayaker)\ **Post date:** [March 3, 2010, 4:59pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/9 "2010-03-03T16:59:46Z")
> [@KneadToKnow](#): > > 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. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [March 3, 2010, 5:38pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/10 "2010-03-03T17:38:19Z")
[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. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [March 3, 2010, 5:41pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/11 "2010-03-03T17:41:29Z")
Is that better than getting a 300% raise at your volunteer no-pay job? ---
**Author:** ![CandidGamera](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/candidgamera/32/2878_2.png) [@CandidGamera](https://boards.straightdope.com/u/CandidGamera)\ **Post date:** [March 3, 2010, 6:05pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/12 "2010-03-03T18:05:36Z")
> [@don\_t\_ask](#): > > 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% 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. ---
**Author:** ![UncleFred](https://avatars.discourse-cdn.com/v4/letter/u/f0a364/32.png) [@UncleFred](https://boards.straightdope.com/u/UncleFred)\ **Post date:** [March 3, 2010, 6:09pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/13 "2010-03-03T18:09:18Z")
> [@KneadToKnow](#): > > I did the math and decided that my chances of winning the lottery were pretty much the same whether I played or not. 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. ---
**Author:** ![N9IWP](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/n9iwp/32/3154_2.png) [@N9IWP](https://boards.straightdope.com/u/N9IWP)\ **Post date:** [March 3, 2010, 6:15pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/14 "2010-03-03T18:15:55Z")
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 ---
**Author:** ![The\_Flying\_Dutchman](https://avatars.discourse-cdn.com/v4/letter/t/9fc348/32.png) [@The\_Flying\_Dutchman](https://boards.straightdope.com/u/The_Flying_Dutchman)\ **Post date:** [March 3, 2010, 6:17pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/15 "2010-03-03T18:17:29Z")
> [@UncleFred](#): > > 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. Actually, if you put the dollar in your pocket your return (or expected return) is zero. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [March 3, 2010, 6:49pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/16 "2010-03-03T18:49:00Z")
> [@UncleFred](#): > > 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) Can’t you? You can deduct gambling losses (against gambling wins), and lottery tickets that don’t win sound like gambling losses to me. ---
**Author:** ![Lestrade](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Lestrade](https://boards.straightdope.com/u/Lestrade)\ **Post date:** [March 3, 2010, 7:24pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/17 "2010-03-03T19:24:12Z")
> [@iamthewalrus\_3](#): > > 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. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [March 3, 2010, 7:30pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/18 "2010-03-03T19:30:18Z")
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. ---
**Author:** ![Interconnected\_Series\_of\_Tubes](https://avatars.discourse-cdn.com/v4/letter/i/13edae/32.png) [@Interconnected\_Series\_of\_Tubes](https://boards.straightdope.com/u/Interconnected_Series_of_Tubes)\ **Post date:** [March 3, 2010, 7:31pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/19 "2010-03-03T19:31:51Z")
Oh god, the sigfigs. THEY BURN! ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [March 3, 2010, 7:31pm UTC](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119/20 "2010-03-03T19:31:55Z")
> [@The\_Flying\_Dutchman](#): > > > [@\*\*UncleFred](#): > > > > \*\*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. > > Actually, if you put the dollar in your pocket your return (or expected return) is zero. Yes. And if you buy a $1 ticket the _expected value_ is -$0.50. [Next page](https://boards.straightdope.com/t/does-buying-10-lottery-tickets-increase-my-odds-by-a-power-of-ten/531119.md?page=2)