# 50 dollars or 50 $1 lottery tickets? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [February 16, 2012, 7:52pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058 "2012-02-16T19:52:50Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Laggard](https://avatars.discourse-cdn.com/v4/letter/l/9de053/32.png) [@Laggard](https://boards.straightdope.com/u/Laggard)\ **Post date:** [February 16, 2012, 7:52pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/1 "2012-02-16T19:52:50Z")
By looking at the odds, is there a way to determine which of these will more likely end up putting the most money in your pocket when all is said and done. And these are scratch off tickets. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 16, 2012, 7:55pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/2 "2012-02-16T19:55:39Z")
The $50 cash. You don’t even need any math; just realize that the state will happily give you the tickets in exchange for the cash, and they make a tidy profit on it. ---
**Author:** ![Leaffan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leaffan/32/299_2.png) [@Leaffan](https://boards.straightdope.com/u/Leaffan)\ **Post date:** [February 16, 2012, 7:58pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/3 "2012-02-16T19:58:07Z")
If it was the tickets, then everyone would gladly trade $50 for tickets. Of course it’s not the tickets. ---
**Author:** ![Laggard](https://avatars.discourse-cdn.com/v4/letter/l/9de053/32.png) [@Laggard](https://boards.straightdope.com/u/Laggard)\ **Post date:** [February 16, 2012, 7:58pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/4 "2012-02-16T19:58:18Z")
> [@Chronos](#): > > The $50 cash. You don’t even need any math; just realize that the state will happily give you the tickets in exchange for the cash, and they make a tidy profit on it. So the chances of winning $51 + dollars after scratching off all the tickets is pretty slim? Even if you have a 2:1 chance for each ticked of winning $50? ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [February 16, 2012, 8:01pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/5 "2012-02-16T20:01:50Z")
> [@Laggard](#): > > So the chances of winning $51 + dollars after scratching off all the tickets is pretty slim? Of course. Otherwise, why not buy up as many tickets as you could afford? ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 16, 2012, 8:02pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/6 "2012-02-16T20:02:11Z")
The UK National Lottery pays 50% of all income as prizes. So your expected result on buying $50 of lottery tickets here is $25. Think of it as a tax on poor, hopeful people. :eek: ---
**Author:** ![Rigamarole](https://avatars.discourse-cdn.com/v4/letter/r/77aa72/32.png) [@Rigamarole](https://boards.straightdope.com/u/Rigamarole)\ **Post date:** [February 16, 2012, 8:03pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/7 "2012-02-16T20:03:04Z")
> [@Laggard](#): > > So the chances of winning $51 + dollars after scratching off all the tickets is pretty slim? You’d have to calculate the [expected value](http://en.wikipedia.org/wiki/Expected_value) of a ticket to determine the exact odds. Usually lotteries tell you exactly what the odds are somewhere in the fine print. I remember reading somewhere that the lotteries with the most favorable odds can give an EV of about 0.5, meaning on average you’ll win about half as much money as you put in. Some lotteries can have a considerably lower EV. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [February 16, 2012, 8:04pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/8 "2012-02-16T20:04:30Z")
> [@Laggard](#): > > So the chances of winning $51 + dollars after scratching off all the tickets is pretty slim? Even if you have a 2:1 chance for each ticked of winning $50? Why would you have a 2:1 chance of winning $50? I assure you, you don’t. If you want to know the odds, look on the back of the ticket. It’s printed there. ---
**Author:** ![Laggard](https://avatars.discourse-cdn.com/v4/letter/l/9de053/32.png) [@Laggard](https://boards.straightdope.com/u/Laggard)\ **Post date:** [February 16, 2012, 8:04pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/9 "2012-02-16T20:04:57Z")
> [@Rigamarole](#): > > You’d have to calculate the [expected value](http://en.wikipedia.org/wiki/Expected_value) of a ticket to determine the exact odds. Usually lotteries tell you exactly what the odds are somewhere in the fine print. > . THANK YOU for answering the question in an informative way. ---
**Author:** ![Laggard](https://avatars.discourse-cdn.com/v4/letter/l/9de053/32.png) [@Laggard](https://boards.straightdope.com/u/Laggard)\ **Post date:** [February 16, 2012, 8:06pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/10 "2012-02-16T20:06:37Z")
> [@Chessic\_Sense](#): > > Why would you have a 2:1 chance of winning $50? I assure you, you don’t. If you want to know the odds, look on the back of the ticket. It’s printed there. The ticket shows that there are 2:1 odds at winning $50. Of course. I assume what they print on the back of the ticket has to mean something and is not just some numbers they print just for the hell of it. You’re still better off taking the $50 cash? ---
**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:** [February 16, 2012, 8:13pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/11 "2012-02-16T20:13:58Z")
> [@Laggard](#): > > You’re still better off taking the $50 cash? As others have pointed out, if you were better off buying the lottery tickets, the state would be worse off selling the lottery tickets, and they wouldn’t be selling them to you in the first place. QED. They sell them to make money, not out of generosity. The only possible flaw in this argument that I can see is if they thought they could make money on winning tickets that people somehow neglected to cash in. ETA: You might be “better off” buying the lottery tickets if the entertainment value (or whatever) they provided to you made up for the expected loss in money. ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [February 16, 2012, 8:15pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/12 "2012-02-16T20:15:38Z")
> [@Laggard](#): > > The ticket shows that there are 2:1 odds at winning $50. Of course. I assume what they print on the back of the ticket has to mean something and is not just some numbers they print just for the hell of it. Can you scan the ticket or give us a link to the State lottery site? That doesn’t make sense. > [@](#): > > You’re still better off taking the $50 cash? No. I am honestly not sure what your difficulty is with this. The State makes a profit on the lottery. They take in more money than they give out. On average and most of the time, you will not yield more than $50 on $50 worth of tickets. The upside is better because you could win more but it’s not likely to happen. ---
**Author:** ![FoieGrasIsEvil](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/foiegrasisevil/32/16638_2.png) [@FoieGrasIsEvil](https://boards.straightdope.com/u/FoieGrasIsEvil)\ **Post date:** [February 16, 2012, 8:16pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/13 "2012-02-16T20:16:10Z")
Where in the world do they sell scratch off tickets that give you 2:1 odds of winning $50 with each $1 ticket purchased? I want in on that action! ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [February 16, 2012, 8:17pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/14 "2012-02-16T20:17:29Z")
> [@FoieGrasIsEvil](#): > > Where in the world do they sell scratch off tickets that give you 2:1 odds of winning $50 with each $1 ticket purchased? I want in on that action! Maybe it’s 2:1 odds on winning any prize but most of the prizes are getting your dollar back or winning another ticket. ---
**Author:** ![Laggard](https://avatars.discourse-cdn.com/v4/letter/l/9de053/32.png) [@Laggard](https://boards.straightdope.com/u/Laggard)\ **Post date:** [February 16, 2012, 8:20pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/15 "2012-02-16T20:20:07Z")
> [@FoieGrasIsEvil](#): > > Where in the world do they sell scratch off tickets that give you 2:1 odds of winning $50 with each $1 ticket purchased? I want in on that action! I was being sarcastic. I was being lead to believe that no matter what the odds you are always better taking the $50. Putting aside that the state is always going to come out ahead, are their odds that would make it the smarter bet to take the tickets? ---
**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\ **Post date:** [February 16, 2012, 8:26pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/16 "2012-02-16T20:26:06Z")
It’s always best to take the money. Any form of gambling has a house edge; lottery tickets have a very strong edge to the house. If you buy $50 of tickets, you will have some winners, but the odds are strong the totals will be less than $50. It’s not impossible for the tickets to be a better bet, but that’s very unlikely. ---
**Author:** ![Laggard](https://avatars.discourse-cdn.com/v4/letter/l/9de053/32.png) [@Laggard](https://boards.straightdope.com/u/Laggard)\ **Post date:** [February 16, 2012, 8:31pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/17 "2012-02-16T20:31:07Z")
> [@RealityChuck](#): > > It’s always best to take the money. Any form of gambling has a house edge; lottery tickets have a very strong edge to the house. If you buy $50 of tickets, you will have some winners, but the odds are strong the totals will be less than $50. > > It’s not impossible for the tickets to be a better bet, but that’s very unlikely. As your reward for answering this, I’ll give you either $50 or 100 $1 Lottery tickets. ---
**Author:** ![Enderw24](https://avatars.discourse-cdn.com/v4/letter/e/ba9def/32.png) [@Enderw24](https://boards.straightdope.com/u/Enderw24)\ **Post date:** [February 16, 2012, 8:33pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/18 "2012-02-16T20:33:14Z")
> [@Laggard](#): > > I was being sarcastic. I was being lead to believe that no matter what the odds you are always better taking the $50. > > Putting aside that the state is always going to come out ahead, are their odds that would make it the smarter bet to take the tickets? Well, yeah. If your odds of winning $X are 1 out of (x-1) or better, it’s better to buy the tickets. So if your odds of winning $50 are 1 out of 49 or better, you should buy the tickets. I think when you were talking to your friends and they said that buying a scratch off ticket is ALWAYS a bad bet, it’s not because they couldn’t think of a stupid hypothetical where it would be a good bet. They were saying it’s always a bad bet because here, in real life, it’s ALWAYS a bad bet. ---
**Author:** ![Bootis](https://avatars.discourse-cdn.com/v4/letter/b/e8c25b/32.png) [@Bootis](https://boards.straightdope.com/u/Bootis)\ **Post date:** [February 16, 2012, 8:40pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/19 "2012-02-16T20:40:45Z")
> [@RealityChuck](#): > > It’s not impossible for the tickets to be a better bet, but that’s very unlikely. With any lottery that pays out less than it takes in, with the situation as described the op, it is impossible for the tickets to be a better bet than the cash. The only way taking the tickets could ever be a better bet is if you knew the results of the tickets before taking them, or if the lottery inexplicably gave you odds such that the game payed out more money than it took in. Of course that scenario isn’t impossible. I could start a lotto right now and pay people 5 to 1 on tickets if I wanted to. To answer the OP’s question about what odds would make the ticket a better bet: it depends on the subset of odds within the game. Most games have,for example, a 5000 to 1 odds to get one prize,or a 30-1 odds to get another, and so on. So it’s impossible to give you a single “x to 1” answer for the whole game since it depends on all of the odds for the different prizes in the game. So the only answer you can get it: the odds required of a lotto to make taking the tickets a better bet than taking the money are odds that result in the lottery game paying out more in prize money than it takes in in ticket sales. ---
**Author:** ![Laggard](https://avatars.discourse-cdn.com/v4/letter/l/9de053/32.png) [@Laggard](https://boards.straightdope.com/u/Laggard)\ **Post date:** [February 16, 2012, 8:41pm UTC](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058/20 "2012-02-16T20:41:29Z")
> [@Enderw24](#): > > Well, yeah. If your odds of winning $X are 1 out of (x-1) or better, it’s better to buy the tickets. > So if your odds of winning $50 are 1 out of 49 or better, you should buy the tickets. > > I think when you were talking to your friends and they said that buying a scratch off ticket is ALWAYS a bad bet, it’s not because they couldn’t think of a stupid hypothetical where it would be a good bet. They were saying it’s always a bad bet because here, in real life, it’s ALWAYS a bad bet. And you my good sir get either $50 or 200 $1 lottery tickets. Choose wisely. [Next page](https://boards.straightdope.com/t/50-dollars-or-50-1-lottery-tickets/613058.md?page=2)