# Do These Numbers Look Random? A Mathematical Question. **URL:** \ **Category:** Factual Questions\ **Created:** [November 26, 2002, 1:48am UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809 "2002-11-26T01:48:47Z")\ **Posts on this page:** 11\ **Page:** 2
**Author:** ![Cheesesteak](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cheesesteak/32/3694_2.png) [@Cheesesteak](https://boards.straightdope.com/u/Cheesesteak)\ **Post date:** [November 26, 2002, 3:05pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/21 "2002-11-26T15:05:10Z")
Exactly true, Biggirl. By reducing the chances of having a possible jackpot heavily split, you increase the expected payoff of the wager. Let’s try it this way, if you buy 1 ticket for a $10M lottery and pick numbers that are also picked 100 times by others, you are essentially buying a ticket to a $100K lottery, but at odds worthy of a $10M lottery. The guy who picked randomly gets a possible payoff of $10M with the same odds, definitely a better deal. ---
**Author:** ![Biggirl](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biggirl/32/3294_2.png) [@Biggirl](https://boards.straightdope.com/u/Biggirl)\ **Post date:** [November 26, 2002, 3:10pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/22 "2002-11-26T15:10:05Z")
No, what you’ve done is decrease your chance of winning overall-- not increased your chance of hitting big. Your chance of winning with any set of numbers is exactly the same. Once you start eliminating numbers, your chances of winning decreases. Your chances of hitting big have not increased at all. ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [November 26, 2002, 3:42pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/23 "2002-11-26T15:42:13Z")
Biggirl: let me give you a practical example. There is a small lottery at my church with 100 people. You pick three numbers from 1 through 20. Everybody that has the winning three numbers will split the pot. We sell 100 tickets (1 per church member) at $1 each, so the prize is $100. Mrs. X, a respected member of the church, says “An angel came to me in a dream and says that the winning numbers are 5 12 17.” So half the people (50) buy a ticket with 5 12 17. I know that a lot of people will buy those numbers. If I also get those numbers, I will have to share the $100 with 50 other people. So I pick 3 10 19, which has the same odds of winning, but if I win, I won’t have to share with anyone, or only the few that also choose 3 10 19. I should **avoid** picking 5 12 17. ---
**Author:** ![aahala](https://avatars.discourse-cdn.com/v4/letter/a/a88e4f/32.png) [@aahala](https://boards.straightdope.com/u/aahala)\ **Post date:** [November 26, 2002, 3:52pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/24 "2002-11-26T15:52:38Z")
> [@](#): > > \*Originally posted by Biggirl \* > \*\* > Your chance of winning with any set of numbers is exactly the same. Once you start eliminating numbers, your chances of winning decreases. \*\* The first statement above is correct. The second isn’t. These are random numbers. You can eliminate certain numbers all you want, select numbers in any manner you want, but it has absolutely no effect on your chances of winning. Every combination of numbers are equally likely to be drawn. That’s what random numbers mean. ---
**Author:** ![Biggirl](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biggirl/32/3294_2.png) [@Biggirl](https://boards.straightdope.com/u/Biggirl)\ **Post date:** [November 26, 2002, 3:54pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/25 "2002-11-26T15:54:44Z")
I understand that picking numbers that no one else picks will make your winnings bigger-- if you win with those numbers. What I don’t see is how this _increases_ your chances of winning big. It doesn’t. You have the same chance to win with any combination of numbers. Your chances of winning have not increased at all. It is exactly the same. Now, if you take this to a national lotto where you play every week, avoiding certain numbers does not increase your chances of winning-- big or small. In fact, avoiding certain numbers all of the time _decreases_ your chances of winning because you have left out numbers that have every bit of a chance at being picked, thus decreasing your chance of winning-- especially in the long run. So, the chances of 5 12 7 being the winning number has the same chance as 3 10 9. If you pick 3 10 9 your chances of hitting _are exactly the same_ as if you picked 5 12 7. Your chances of hitting “big” are the same as your chances of sharing the pot. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [November 26, 2002, 4:05pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/26 "2002-11-26T16:05:25Z")
Suppose you have two choices to bet. Both ride on a coin flip, but if you bet $1 on coin A and you win you get back $2. If you bet $1 on coin B and you win you get back $10. Which coin will you bet on? The odds are exactly the same but the return is better on coin B. That is why it makes more sense to bet on less popular numbers. The chances of wining are exactly the same, but the distribution of winnings is not. Since gambling is based on statistics and odds, your return on investment is better when you bet on less popular numbers. You are correct that you are no more likely to have a winning ticket. But you are much more likely to have a ticket that wins more money. With that setup, why pick coin A? ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [November 26, 2002, 4:10pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/27 "2002-11-26T16:10:50Z")
First, there’s no ‘good’ reason to play the lotto - you’re basically going to lose money no matter what. If you are going to play, though, take the “random” numbers generated by the machine, because of the phenomenon many people have brought up here already - if you do win, you want numbers nobody else has picked. Those “random” number machines give you numbers nobody else has picked, when they can (at least in Illinois). ---
**Author:** ![aahala](https://avatars.discourse-cdn.com/v4/letter/a/a88e4f/32.png) [@aahala](https://boards.straightdope.com/u/aahala)\ **Post date:** [November 26, 2002, 4:42pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/28 "2002-11-26T16:42:34Z")
One last time Biggirl. What numbers you pick or your selection method will not alter your chances of winning, but that’s not the same claim as your chances of hitting it big. If there’s a 50M jackpot and you know 1 million have selected a specific number, I can tell you, a prior, the chances you will hit it big with that number. It’s not infinately small, it’s ZERO. $50 is not big. We can tell you that BEFORE the drawing. Your chances of hitting it big is greater if you select a less popular number–its ulitimate selection is exactly the same as all other numbers but the jackpot received will be greater. The chances of hitting it big with this number are extremely small, but greater than ZERO. Extremely small is greater than zero. ---
**Author:** ![clairobscur](https://avatars.discourse-cdn.com/v4/letter/c/839c29/32.png) [@clairobscur](https://boards.straightdope.com/u/clairobscur)\ **Post date:** [November 26, 2002, 5:12pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/29 "2002-11-26T17:12:28Z")
> [@](#): > > \*Originally posted by RickJay \* > \*\*Friends of ours solved this problem by simply picking the number 6-7-8-9-10-11 They were sure nobody else would try it, since they knew most people would (erroneously) believe that six numbers in a row was less likely than a more random-looking six number combination, and if anyone else did try it they’d likely start at 1. > \*\* I’m not convinced. There are quite a lot of smartass around, and I would suspect that many of them would pick consecutive numbers for the same reasons. Of course, there are much more people who wouldn’t pick consecutive number for the reasons you explained, but on the other hand, there are also way, way, much more combinations of non-consecutive numbers than combinations of consecutive numbers. With fifty numbers, there are only 44 possible different combinations of consecutive numbers. So, only a very low percentage of people acting like your friends would result in them having to share with a relatively large number of winners. If there’s, say, only 500 persons or so who follow the same reasonning, your friends will have to share the wins with a dozen of other winners. For this reason, I wouldn’t pick consecutive numbers. ---
**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\ **Post date:** [November 26, 2002, 6:19pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/30 "2002-11-26T18:19:47Z")
> [@](#): > > \*Originally posted by Biggirl \* > I understand that picking numbers that no one else picks will make your winnings bigger-- if you win with those numbers. What I don’t see is how this _increases_ your chances of winning big. It doesn’t. You have the same chance to win with any combination of numbers. Your chances of winning have not increased at all. It is exactly the same. I think you’re getting confused with semantics, **Biggirl**. **Arnold** et al. are _defining_ “winning BIG” as “making your winnings bigger,” exactly as you say above. Choosing unpopular numbers doesn’t increase your chance of _winning_, it increases your chance of _winning a bigger pot_; i.e., not sharing it with anyone else; i.e., “winning BIG.” > [@](#): > > In fact, avoiding certain numbers all of the time _decreases_ your chances of winning because you have left out numbers that have every bit of a chance at being picked, thus decreasing your chance of winning-- especially in the long run. Not true at all. As you yourself say, the chances of any given number combination turning up as the winner is the same as any other number combination. Consider: If I pick, say, 5 12 7 when I play, are my chances of winning smaller than anyone elses? What if I pick 5 12 7 _every single time_ I play? What if I pick 5 12 7 every single time I play because I superstitiously avoid all other combinations? In all cases, my chance of winning is the same as anyone else’s, whatever numbers the other person chooses or however he or she decides upon those numbers. Avoiding other numbers does NOT decrease my chance of winning. ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [November 26, 2002, 7:12pm UTC](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809/31 "2002-11-26T19:12:09Z")
Please ignore my post above. While I believed that the “Quick Pick” did only spit out numbers that hadn’t been taken already, and had the woman at my local White Hen as an (I thought) unimpeachable source, I decided to e-mail the lottery people anyway: “No, quick-pick is completely random-it does not know what set of numbers it picked last-it could pick some of the same numbers as the last pick or completely different numbers than the last pick-it is random.” So there is no guarantee that the numbers that you have generated for you are any less chosen than any others. [Previous page](https://boards.straightdope.com/t/do-these-numbers-look-random-a-mathematical-question/138809.md?page=1)