# Law of Averages and Coin Tosses **URL:** \ **Category:** Factual Questions\ **Created:** [September 27, 2001, 2:31am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046 "2001-09-27T02:31:08Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [October 1, 2001, 7:03pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/41 "2001-10-01T19:03:45Z")
> [@](#): > > \*Originally posted by Lance Turbo \* > **Flipping a fair coin 1000 times there is only a 0.8% chance of getting 5000 heads and 5000 tails.** 1000 should be 10000 in the above. ---
**Author:** ![cornflakes](https://avatars.discourse-cdn.com/v4/letter/c/9d8465/32.png) [@cornflakes](https://boards.straightdope.com/u/cornflakes)\ **Post date:** [October 1, 2001, 7:19pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/42 "2001-10-01T19:19:27Z")
> [@](#): > > \*Originally posted by Lance Turbo \* > **This was in a statistics book? Why would a statistics book make any conclusions based on a measley three trials using as many as three different coins?** No conclusions were made; the anecdotes were used to introduce the concept of probability. FYI, the book is _Introduction to the Practice of Statistics_, by Moore and McCabe, 1st edition. ---
**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:** [October 1, 2001, 7:45pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/43 "2001-10-01T19:45:06Z")
> [@](#): > > \*Originally posted by RickJay \* > The odds of incorrectly guessing 21 straight coin flips are one in 67,108,864. An amazing occurrence. You would have MUCH better odds of winning the Lotto 6/49. Huh? 2[sup]21[/sup] = 2,097,152 2[sup]26[/sup] = 67,108,864 Where ya get 26 from? ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [October 1, 2001, 10:07pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/44 "2001-10-01T22:07:46Z")
> [@](#): > > \*Originally posted by cornflakes \* > \*\*No conclusions were made; the anecdotes were used to introduce the concept of probability. FYI, the book is _Introduction to the Practice of Statistics_, by Moore and McCabe, 1st edition. \*\* Upon rereading your post I realize my error. Thank you for drawing it to my attention. ---
**Author:** ![ignatzmouse](https://avatars.discourse-cdn.com/v4/letter/i/b2d939/32.png) [@ignatzmouse](https://boards.straightdope.com/u/ignatzmouse)\ **Post date:** [October 1, 2001, 10:52pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/45 "2001-10-01T22:52:07Z")
But if we postulate that within un-, sub-, or supernatural forces, the probability is that the law of probability will not operate as a factor, then we must accept that the probability of the first part will not operate as a factor, in which case the law of probabilty will operate as a factor within un-, sub, or supernatural forces. Since it obviously hasn’t been doing so, we can take it that we are not held within un-, sub, or supernatural forces after all. This is a great comfort to me personally. ---
**Author:** ![Another\_Primate](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@Another\_Primate](https://boards.straightdope.com/u/Another_Primate)\ **Post date:** [October 2, 2001, 2:21am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/46 "2001-10-02T02:21:20Z")
> [@](#): > > \*Originally posted by zut \* > \*\*…investigating the occurance of the numbers: > > 1, 10, 18, 28, 30, and **18** > > \*\* Why 1? She liked one. 2 is the number she didn’t pick. Sue the confused. I’m sure I’ll find out you’re tricking me somehow… ---
**Author:** ![Another\_Primate](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@Another\_Primate](https://boards.straightdope.com/u/Another_Primate)\ **Post date:** [October 2, 2001, 2:31am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/47 "2001-10-02T02:31:36Z")
> [@](#): > > \*Originally posted by Futile Gesture \* > \*\*There are ways to fix the way a coin toss ends up. Technical term for this is ‘cheating’ > > It’s a combination of being very practiced in how you flip the coin and in looking at it as it lands. \*\* What? Why would I cheat to provide a result that would make my daughter cry? If I could have cheated, I would have succeeded in showing her that she was NOT unlucky in coin tosses, which is what I was aiming at? And, a coin toss is called in the air – what does one do, wait until it’s called and somehow wiggle the air or the ground? Sue p.s. Oh, maybe I get it. You think that maybe Casey, at six years old, was able to figure out how to cheat, and then wanted to cheat in order to call coin tosses wrong 21 times in a row so that 15 years later I’d mention it on the SDMB. Yeah, that’s it. Well, she’s smart. And, doggone, was she a good actress. I really bought into those crocodile tears. Nope. She was smart enough even then to realize that if she could figure out a coin toss in the air, and her mom used it to decide who could choose what we’d have for lunch, or who could be the last one out of the shower at the Y, that she should keep it to herself so she could always win. ---
**Author:** ![Qwertyasdfg](https://avatars.discourse-cdn.com/v4/letter/q/ecc23a/32.png) [@Qwertyasdfg](https://boards.straightdope.com/u/Qwertyasdfg)\ **Post date:** [October 2, 2001, 2:38am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/48 "2001-10-02T02:38:54Z")
**Another Primate** I don’t think he/she was accusing you of cheating. ---
**Author:** ![Another\_Primate](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@Another\_Primate](https://boards.straightdope.com/u/Another_Primate)\ **Post date:** [October 2, 2001, 2:46am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/49 "2001-10-02T02:46:39Z")
> [@](#): > > \*Originally posted by jmonster \* > \*\*Well, if you were to test your daughter’s powers yourself, you could make sure you’ll be able to afford the nice nursing home. \*\* First, I don’t believe in luck. Second, I know you’re just kidding – but, really, even if I were to get rich, I’m such a sucker for a hardworn handsome old handyman-type, I’ll have already spent that all on my fourth husband (who I haven’t met yet). Gotta count on your kids to bail you out in the end. -Sue ---
**Author:** ![Another\_Primate](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@Another\_Primate](https://boards.straightdope.com/u/Another_Primate)\ **Post date:** [October 2, 2001, 2:57am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/50 "2001-10-02T02:57:48Z")
> [@](#): > > \*Originally posted by Qwertyasdfg \* > \*\ ***Another Primate** I don’t think he/she was accusing you of cheating. \*\* I figured that since he quoted me, he was joking about the possibility of my cheating. So I did the “how dare you! I’m a sweet mother!” routine. Then, I read his again, after previewing but before submitting, and realized it was even funnier – he was joking that Casey cheated. I really never considered that he’d quote me otherwise, since the whole thread was about coin tosses. But maybe some people hit “quote”, instead of just “reply”, forgetting that the thread was all about coin tosses in the first place? (He shall apply to he/she; him shall apply to him/her, etc. I grew up with “he” and never felt demeaned by it, any more than by “mankind” or “human”.) –Sue ---
**Author:** ![Casey\_Primate](https://avatars.discourse-cdn.com/v4/letter/c/ba8739/32.png) [@Casey\_Primate](https://boards.straightdope.com/u/Casey_Primate)\ **Post date:** [October 2, 2001, 4:46am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/51 "2001-10-02T04:46:21Z")
Speaking of Probabilities… What do you think the probability is that Another Primate has fabricated this “Anti-precognative-ability-having daughter” story? I mean, what do we REALLY know about her anyway? And do you realize that her name is really just an anagram for Methane Airport??? Yes, that is right. Methane Airport chew on that for a while. Heck, I’m her daughter, and I’m not even sure I believe it. Do I really remember sitting on my bed in my pink room, and missing 21 consecutive quarter tosses? I was what, 6? 7? Or have I just heard the story so many times that it worm-holed its way into my memory banks as being real? 'Fess up mom. I really missed 3 in a row, didn’t I? Casey Primate ---
**Author:** ![jmonster](https://avatars.discourse-cdn.com/v4/letter/j/dbc845/32.png) [@jmonster](https://boards.straightdope.com/u/jmonster)\ **Post date:** [October 2, 2001, 5:15am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/52 "2001-10-02T05:15:36Z")
> [@](#): > > \*Originally posted by Casey Primate \* > Heck, I’m her daughter, and I’m not even sure I believe it. Do I really remember sitting on my bed in my pink room, and missing 21 consecutive quarter tosses? I was what, 6? 7? Or have I just heard the story so many times that it worm-holed its way into my memory banks as being real? > > 'Fess up mom. I really missed 3 in a row, didn’t I? You could probably turn this into a book, and maybe even a Lifetime Channel Movie of the Week. See if you can work in your mom hitting you with wire clothes hangers every time you got one wrong. 🙂 ---
**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:** [October 2, 2001, 11:54am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/53 "2001-10-02T11:54:42Z")
> [@](#): > > \*Originally posted by Another Primate \* > Why 1? She liked one. 2 is the number she didn’t pick. Whoops. I’m sorry, it was actually _2_, 10, 18, 28, 30, and **18**. I _did_ get it right on the actual ticket, I just mis-transscribed the number when I was reporting back. Make sure Casey knows that I know that two is a number that she _didn’t_ choose, and thus two is a number that I _did_ choose. ---
**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:** [October 2, 2001, 12:05pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/54 "2001-10-02T12:05:50Z")
> [@](#): > > \*Originally posted by Casey Primate \* > Heck, I’m her daughter, and I’m not even sure I believe it. Do I really remember sitting on my bed in my pink room, and missing 21 consecutive quarter tosses? I was what, 6? 7? Or have I just heard the story so many times that it worm-holed its way into my memory banks as being real? > > 'Fess up mom. I really missed 3 in a row, didn’t I? And here’s **Casey Primate** herself. Criminey; I thought **Another Primate’s** story was, like, from 1999 or something and you were still seven or eight. I was actually worried that you might start crying again 'cause it looked like I wasn’t believing you with the one/two thing. Sheesh. I suppose my dream of exploiting your anti-precognitive talents for my own financial gain, by telling your mother what a _smart_ little girl she has, has gone up in smoke; being as you can actually think for yourself and all. ---
**Author:** ![Another\_Primate](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@Another\_Primate](https://boards.straightdope.com/u/Another_Primate)\ **Post date:** [October 2, 2001, 1:45pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/55 "2001-10-02T13:45:52Z")
> [@](#): > > \*Originally posted by Casey Primate \* > \*\* What do you think the probability is that Another Primate has fabricated this “Anti-precognative-ability-having daughter” story? I mean, what do we REALLY know about her anyway? > Heck, I’m her daughter, and I’m not even sure I believe it… I was what, 6? 7? Or have I just heard the story so many times that it worm-holed its way into my memory banks as being real? > 'Fess up mom. I really missed 3 in a row, didn’t I? > > - Casey Primate \*\* Well, if you’re someone pretending to be my daughter, you’re doing a damned good job. Spelling precognative with an A was right-on. (To quote Casey, “I know how to spell definately. I just don’t.”) Go to your room! Or go to the methane airport! Yes, I confess, you missed three in a row. And then you went on to miss another 18. This is a real story, and I will ask your great-aunt Barbara, your grandmother, Vickie, and all my sisters and brothers to dig through circa 1984 letters to provide proof. Would I lie to you? Particularly, would I lie in a story that makes me look like a cruel mother? Not. Now go give Eli a kiss for me, then study. Mom p.s. I love you. You’re a card. ---
**Author:** ![Another\_Primate](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@Another\_Primate](https://boards.straightdope.com/u/Another_Primate)\ **Post date:** [October 2, 2001, 1:51pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/56 "2001-10-02T13:51:13Z")
> [@](#): > > \*Originally posted by jmonster \* > \*\* > You could probably turn this into a book, and maybe even a Lifetime Channel Movie of the Week. See if you can work in your mom hitting you with wire clothes hangers every time you got one wrong. 🙂 \*\* Umm, no, **jmonster** – that would be every time she got one RIGHT. Mom ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 2, 2001, 9:00pm UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/57 "2001-10-02T21:00:34Z")
> [@](#): > > \*Originally posted by Doctor Goo Fee \* > \*\*Bell Curve. > > That would help to answer some of these probability questions. > > I’d explain it myself 'cept my memory of college stats class is f u z z y. \*\* What **Doctor Goo Fee** is referring to here is, of course, the central limit theorem, which could be used to answer the first question in the OP. I don’t see how it applies to the second, though. ---
**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:** [October 3, 2001, 11:50am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/58 "2001-10-03T11:50:28Z")
…but the impartial representatives of the State chose: 07, 14, 22, 41, 46, and **01** Not even close. So I guess you don’t have any anti-precognative powers. Ah well; a good scientific test is a good scientific test regardless of the positive or negative results thereof. ---
**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:** [October 4, 2001, 1:18am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/59 "2001-10-04T01:18:37Z")
Wow, **zut** , do you realize that the odds of them picking that number were only one in 23688288? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 4, 2001, 1:38am UTC](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046/60 "2001-10-04T01:38:13Z")
> [@](#): > > \*Originally posted by Chronos \* > \*\*Wow, **zut** , do you realize that the odds of them picking that number were only one in 23688288? \*\* Therefore, we can conclude that they didn’t actually pick that number. 😉 [Previous page](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046.md?page=2) [Next page](https://boards.straightdope.com/t/law-of-averages-and-coin-tosses/84046.md?page=4)