# Wikipedia:Reference desk/Archives/Mathematics/2013 October 28

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# October 28

## Lottery tickets

When selecting numbers for a lottery, are the chances of winning any different when a person picks his own numbers for the lottery drawing, versus his having the computer system automatically select a random "quick pick" of numbers? Or is that a completely irrelevant factor in determining the chances of the person's ticket matching the winning numbers? Thanks. Joseph A. Spadaro (talk) 17:58, 28 October 2013 (UTC)

Chances of winning are the same but if the prize is split among the winners then it could affect your expected winnings. --RDBury (talk) 18:32, 28 October 2013 (UTC)
Agreed. So if you pick something obvious, like that day's date, your chances of winning are the same, but you are likely to have to split it more ways if you do win, so your average return on investment is less (although you can be confident it will be negative, in any case). StuRat (talk) 18:59, 28 October 2013 (UTC)
Thanks. So, in terms of the probability of winning (leaving aside the issue of how much you'd win, if you had to share the prize with others) ... the odds are exactly the same, either way. And there is no "advantage" or "disadvantage" to selecting numbers on your own, versus having the computer select the random quick pick. Is that correct? Thanks. Joseph A. Spadaro (talk) 19:11, 28 October 2013 (UTC)
Yes. All outcomes are equally likely. It doesn't matter if you use a computer, choose 1,2,3,4,5,6, etc. or take the last lottery draw and gamble on that happening again. Count Iblis (talk) 20:05, 28 October 2013 (UTC)
I disagree. I would expect Selection_bias to play a factor. You, as a human, are likely to be predisposed to pick or avoid certain numbers - therefore your selection is not random. Hopefully the algorithm doing the picking for you is well written... 196.214.78.114 (talk) 07:58, 29 October 2013 (UTC)
Selection bias has nothing to do with it, since every number has the same probability of being drawn as every other number does. So it doesn't matter what algorithm if any you use to select the number to play. Duoduoduo (talk) 20:01, 29 October 2013 (UTC)
I am sure that that scenario works out, mathematically, to be correct. It does seem so counter-intuitive, however. Joseph A. Spadaro (talk)
That counterintuitivenes comes from the extremely low probability of winning. The probability is so low that it is difficult to imagine this. But because every week someone wins and you have some winning sequence of numbers that looks rather ordinary, that makes it look like any ordinary looking sequence has a decent chance of winning. While you can still calculate that the probability is low, your intuition tells you that you do have a decent probablity, 1 in a 100 million is then interpreted by our brain as if it is a lot more than it really is. But if you consider that the probability for having last times draw is the same as any other draw, then that clashes with this intuition.
I don't participate in lotteries. I always try to explain that to people who are not good in math as follows. I ask them to imagine all the millions of lottery participants, only one of whom will be a millionaire, so it most likely won't be them. Then I ask where the money comes from to make that person a millionaire? So, do you want to spend your money to help make someone else a millionaire? :) . Count Iblis (talk) 20:49, 28 October 2013 (UTC)
I don't mind participating on similar grounds: lottery revenues are tax dollars that support various programs, with the added bonus that I might be a millionaire if I participate. 1 in 14000000, if I recall, but still, there's free tickets and 10 dollar prizes to be won, too. Mingmingla (talk) 01:16, 29 October 2013 (UTC)
You are better off gambling in the stock market, you should have invested \$100,000 when in early 2009 the Dow Jones index was around 7000 and Obama said that this is the time to buy some stocks. That would have been an almost guaranteed way to win \$100,000. Count Iblis (talk) 14:25, 29 October 2013 (UTC)
It depends on what it is that you are paying for/expecting. For a lot of people, the experience of picking numbers and waiting to see if they win appears exciting and enjoyable- it seems more enjoyable than a candy bar and costs about the same. I don't know many people who seriously believe they will win, it seems more like they are playing make believe with themselves- people have all sorts of controlled irrational behaviour because it's fun; haunted house, scary movies, flirting with people half your age, reading fiction, etc. would all be pretty damn boring if approached soberly. I don't see the difference between buying a lotto ticket and any of those things listed. /End Rant.Phoenixia1177 (talk) 06:26, 30 October 2013 (UTC)
The gambling industry (which likes to use the euphemism "gaming") always argues that all the money people are losing is worth it, due to their enjoyment of the experience, but go to the slots at 3 AM some time, and those people look more like addicted zombies than people who are enjoying themselves. StuRat (talk) 21:33, 30 October 2013 (UTC)
I agree that gambling can definitely be a problem, but im talking more about the occasional dollar nightly number- casino games are a different beast, theyre immediate and immediately repeatable (and casinos are dedicated to gambling, lotto tickets show up in convenience stores)Phoenixia1177 (talk) 21:40, 30 October 2013 (UTC)
I've also seen lottery players buying dozens of tickets at a time. Somehow I doubt if they get much of a thrill from that. StuRat (talk) 21:51, 30 October 2013 (UTC)
Is that the norm, though? Most people I know get a little psyched up about powerball amounts, etc. buy a ticket, or two, lose, laugh, and move on. I get a thrill out of eating a candy bar, but there are people out there who eat pathologically, that doesn't mean candy bars should be judged on that basis. --if it so happens that the norm is pathological buying of tickets, then I concede the point and admit I had the wrong impression, but I've never seen this outside of a few cases (and those cases involved people who appeared to have existing problems of other kinds).Phoenixia1177 (talk) 05:10, 31 October 2013 (UTC)
I'd guess that the majority of people who ever gamble are not addicts, but that the majority of money lost does come from those addicts. Therefore, the gambling industry is dependent upon their continued addiction. StuRat (talk) 16:04, 31 October 2013 (UTC)

Whereas it's true for a single line that a random selection and a choice have the same chance of winning it is different with multiple lines. Techniques like Lottery Wheeling can increase your chance of a larger win at the expense of reducing chances of a smaller win. -- Q Chris (talk) 18:59, 31 October 2013 (UTC)

I'm fairly surprised that no one has mentioned this (maybe I missed it? I didn't go over it with a fine-tooth comb). The problem with choosing 1 2 3 4 5 6 is that it's (by far!) the most popular entry in 6/49-type lotteries. That means, if it ever does hit, all the people that chose it are going to have to share the pot. So your buy-in is the same, but your expected payout is much lower, even though the probability of winning is the same as for any other combination. --Trovatore (talk) 03:42, 2 November 2013 (UTC)