# Probability/argument with g/f **URL:** \ **Category:** Factual Questions\ **Created:** [October 9, 2003, 1:45am UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393 "2003-10-09T01:45:55Z")\ **Posts on this page:** 13\ **Page:** 2
**Author:** ![Eleusis](https://avatars.discourse-cdn.com/v4/letter/e/f4b2a3/32.png) [@Eleusis](https://boards.straightdope.com/u/Eleusis)\ **Post date:** [October 9, 2003, 6:45am UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/21 "2003-10-09T06:45:23Z")
She’s obviously right. It’s a lot less likely for 1,2,3,4,5 to show up, than _any other combination_. Don’t fuck with me. ---
**Author:** ![MartinL](https://avatars.discourse-cdn.com/v4/letter/m/ebca7d/32.png) [@MartinL](https://boards.straightdope.com/u/MartinL)\ **Post date:** [October 9, 2003, 7:38am UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/22 "2003-10-09T07:38:53Z")
Although the matter seems settled to me from a mathematical point of view, maybe this will help to convince her (inspired by **Eleusis** ’s post). For any given drawing it is much more likely to result in some “seemingly random”, non-consecutive numbers to be drawn than a “nicely ordered”, consecutive set of numbers. The reason is that considering all the possible outcomes, there are so many more non-consecutive possibilities. So when you choose, say, 5-12-19-23-28-41 (If these numbers are drawn next week, will I get a share? 🙂 ) your chances for winning are the same as when you choose 1-2-3-4-5-6, but with the non-consecutive guess you have a much higher chance to get the feeling ‘Hey, I wasn’t too far off, maybe next week I’ll be lucky!’ There is a high chance that every week your girlfriend can say: ‘We did not win the lottery, but at least I got it right that the numbers are non-consecutive, you missed even that.’ Consider this: Pick a number from 1 to 6 at random, then roll a die. You pick always 1, your girlfriend may choose from 2-6. Of course the result will be in her range more often than in your ‘range’, but you will have just as many direct hits as she will have. ---
**Author:** ![KenGr](https://avatars.discourse-cdn.com/v4/letter/k/ecc23a/32.png) [@KenGr](https://boards.straightdope.com/u/KenGr)\ **Post date:** [October 9, 2003, 8:04am UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/23 "2003-10-09T08:04:39Z")
I suggest you just tell the gf she’s right, you were being stubborn and pigheaded and you’re sorry for doubting her. It won’t be true, but if she actually believes the probability changes she’ll probably buy that too. Then go straight to the bogus internet news story about fellatio preventing breast cancer. ---
**Author:** ![Eleusis](https://avatars.discourse-cdn.com/v4/letter/e/f4b2a3/32.png) [@Eleusis](https://boards.straightdope.com/u/Eleusis)\ **Post date:** [October 9, 2003, 8:15am UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/24 "2003-10-09T08:15:57Z")
Thanks a lot **KenGr**. Now we can’t show this thread to our wives (to prove their stupidity), lest they know the fellatio story is “bogus”. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [October 9, 2003, 10:18am UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/25 "2003-10-09T10:18:11Z")
By the way, there are 49 balls in the UK lottery, not 48. But based on the widespread confusion on here, I think I’m gonna start picking 49 as oone of my numbers, as nobody else seems to know it exists! 🙂 ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [October 9, 2003, 12:54pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/26 "2003-10-09T12:54:01Z")
Ask her if you throw a die twice if ‘1 then 2’ is as likely than the other 35 outcomes. If she says not, it’s fairly easy to model with a lot of time or a computer. (Or you may be able to convince her in this simple case.) When she’s convinced ask about ‘1, then 2, then 3’ throwing three times. Say ‘How long does a sequence have to be before it magically breaks the universally accepted laws of probability’ I think the confusion arises because ‘1,2,3,4,5,6’ is as likely as ‘13,29,5,23,19,44’ but not as likely as ‘some collection of numbers with no apparent patterns’ which is how we naturally look at it. ---
**Author:** ![brainfizz](https://avatars.discourse-cdn.com/v4/letter/b/da6949/32.png) [@brainfizz](https://boards.straightdope.com/u/brainfizz)\ **Post date:** [October 9, 2003, 1:04pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/27 "2003-10-09T13:04:45Z")
There’s one other factor here that you’re not considering. If someone else has the same numbers as you then if you win the jackpot, the money is split between the winners. So, the best numbers to have will be those that you think nobody else will have. Statistically, more money is won by “Lucky Dip” winners (people that have the computer choose for them) than by people that choose their own numbers, since people will often choose birthdays, lucky numbers, ages, etc. ---
**Author:** ![jjimm](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@jjimm](https://boards.straightdope.com/u/jjimm)\ **Post date:** [October 9, 2003, 1:10pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/28 "2003-10-09T13:10:19Z")
I’ve always thought that the fact that a sequence is as likely to come up as any other combination of numbers is a perfectly brilliant way of illustrating why the odds are so appalling. ---
**Author:** ![Scuba\_Ben](https://avatars.discourse-cdn.com/v4/letter/s/278dde/32.png) [@Scuba\_Ben](https://boards.straightdope.com/u/Scuba_Ben)\ **Post date:** [October 9, 2003, 2:20pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/29 "2003-10-09T14:20:23Z")
> [@](#): > > \*Originally posted by Kinthalis \* > [BWhat I was talking about is that the odds become greater against a particular sequence the more possible numbers (or balls, dice, etc) you toss into the equation. > > If you roll 1 6-sided die you have a 1-6 chance of rolling any particular number. But what happens when you toss 2 dice? the chances of you getting a particular sequence of numbers there (say, two 1 ones) is now much less. And so if you keep adding dice the chances of a particular sequence coming up become less and less likely. \*\* That depends on the circumstances. As described, the probability of rolling a fair 6-sided die twice and getting the result {1, 1} is 1 in 36. Note, though, that the probability of rolling {1, 1} GIVEN that the first roll is {1} is 1 in 6. This is called “conditional probability;” the probability of an outcome given a starting condition. Likewise, given a condition where the first two rolls were {1, 1}, the probability of obtaining the sequence {1, 1, 1} is still 1 in 6. For a lottery drawing, where the odds change due to not replacing the drawn balls, the probability of any particular sequence of 6 numbers drawn from a pool of 48 is 1 in 48!/42!. Given the first five drawn balls, the probability of any particular sixth ball is 1 in 43. ---
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [October 9, 2003, 2:30pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/30 "2003-10-09T14:30:58Z")
> [@](#): > > \*Originally posted by brainfizz \* > \*\*Statistically, more money is won by “Lucky Dip” winners (people that have the computer choose for them) than by people that choose their own numbers, since people will often choose birthdays, lucky numbers, ages, etc. \*\* No, you fall into the same trap as the OP’s gf – the reason why there are more Lucky Dip winners than “chooser” winners is because there are more Lucky Dip tickets sold than “choosing” tickets. IIRC, the sequence 1,2,3,4,5,6 is played by tens of people everyweek, if the numbers do ever come up, it’ll be interesting to see their faces when they realise they have to split the jackpot 50 ways. ---
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [October 9, 2003, 2:34pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/31 "2003-10-09T14:34:11Z")
Actually, **brainfizz** , I see you say more _money_ is won, not more _wins_, so I take it back, you are in all probability correct – optimal strategy, is of course, not to play, but failing that you should aim to pick sequences unchosen by others. ---
**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:** [October 9, 2003, 3:55pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/32 "2003-10-09T15:55:22Z")
You can tell your girlfriend that she gave the right answer, just to the wrong question. 🙂 Given six randomly chosen numbers, it is far less likely that they will be consecutive than that they will not. This is because there are far fewer ways of choosing a sequence of six numbers in a row than there are of choosing six numbers that aren’t all in a row like that. But of course, any particular choice of six numbers is just as likely to appear as any other particular choice, whether the numbers are consecutive or not. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [October 9, 2003, 4:21pm UTC](https://boards.straightdope.com/t/probability-argument-with-g-f/206393/33 "2003-10-09T16:21:03Z")
> [@](#): > > _TGU wrote:_ > No, you fall into the same trap as the OP’s gf – the reason why there are more Lucky Dip winners than “chooser” winners is because there are more Lucky Dip tickets sold than “choosing” tickets. I think his point was, that even if you normalize it to the ratio of people playing each way, the Lucky Dip (we call them Quick Pick) winners win more money, for exactly the reason you stated in your second paragraph. [Previous page](https://boards.straightdope.com/t/probability-argument-with-g-f/206393.md?page=1)