# How many times do you have to flip a coin to ensure a heads **URL:** \ **Category:** Great Debates\ **Created:** [May 23, 2007, 11:06pm UTC](https://boards.straightdope.com/t/how-many-times-do-you-have-to-flip-a-coin-to-ensure-a-heads/405290 "2007-05-23T23:06:03Z")\ **Posts on this page:** 5\ **Page:** 6
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 25, 2007, 9:57pm UTC](https://boards.straightdope.com/t/how-many-times-do-you-have-to-flip-a-coin-to-ensure-a-heads/405290/101 "2007-05-25T21:57:05Z")
[QUOTE=Frylock] Wait. More points? I thought all line segments, lines, curves and areas had the same number of points. -FrL- [/QUOTE] Sure, all the nontrivial ones have the cardinality of the continuum. But the world is full of trivialities: clearly, the empty set has only 0 points and the North Pole has only 1 point, in contrast to the border of India with its infinitely many points. (Specifically, continuum-many, as opposed to, say, the set of points with rational longitude and latitude, which also has area 0, like all of these, but with only a countably infinite number of points) ---
**Author:** ![VinylTurnip](https://avatars.discourse-cdn.com/v4/letter/v/b2d939/32.png) [@VinylTurnip](https://boards.straightdope.com/u/VinylTurnip)\ **Post date:** [May 25, 2007, 11:27pm UTC](https://boards.straightdope.com/t/how-many-times-do-you-have-to-flip-a-coin-to-ensure-a-heads/405290/102 "2007-05-25T23:27:33Z")
[QUOTE=Shodan] You can’t flip a coin an infinite number of times. Regards, Shodan [/QUOTE] Well hell, that sounds like a _dare_! (Back in a while.) ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [May 25, 2007, 11:51pm UTC](https://boards.straightdope.com/t/how-many-times-do-you-have-to-flip-a-coin-to-ensure-a-heads/405290/103 "2007-05-25T23:51:10Z")
[QUOTE=Indistinguishable] Sure, all the nontrivial ones have the cardinality of the continuum. But the world is full of trivialities: clearly, the empty set has only 0 points and the North Pole has only 1 point, in contrast to the border of India with its infinitely many points. (Specifically, continuum-many, as opposed to, say, the set of points with rational longitude and latitude, which also has area 0, like all of these, but with only a countably infinite number of points) [/QUOTE] I totally misread your post. I thought you had said the border has the same area as the entire ice shelf up north around the north pole. And I just skipped the part about the empty set, thinking I had your point already. Sorry about that! -FrL- ---
**Author:** ![lekatt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lekatt/32/7269_2.png) [@lekatt](https://boards.straightdope.com/u/lekatt)\ **Post date:** [May 26, 2007, 1:14am UTC](https://boards.straightdope.com/t/how-many-times-do-you-have-to-flip-a-coin-to-ensure-a-heads/405290/104 "2007-05-26T01:14:13Z")
[QUOTE=kanicbird] Believe it or not this comes from all the talk about theistic and atheistic faith issues that have come up lately. Here is the premises: If you flip a infinite number of coins a infinite number of times you will get a infinite number of coins that will never come up heads. -but- If you flip any one coin a infinite number of times it will hit heads and tails equally. These 2 can’t coexist. [/QUOTE] Both statements are the same logic. In the first statement each coin will sometimes be heads and sometimes be tails. There are only more coins in the first statement than the second. Otherwise they are identical, and can coexist. Why am I discussing this? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 26, 2007, 1:22am UTC](https://boards.straightdope.com/t/how-many-times-do-you-have-to-flip-a-coin-to-ensure-a-heads/405290/105 "2007-05-26T01:22:18Z")
**kanicbird** is right to say that the two statements can’t coexist; the first statement implies that some coin never comes up heads. The second statement implies that every coin eventually comes up heads. Those two are very clearly incompatible. The rest of my response to that post is found [here](http://boards.straightdope.com/sdmb/showpost.php?p=8606425&postcount=41). The gist of it is that there aren’t good probabilistic grounds for accepting the first statement as a given, and, in fact, there are very strong probabilistic grounds for rejecting it in many cases. [Previous page](https://boards.straightdope.com/t/how-many-times-do-you-have-to-flip-a-coin-to-ensure-a-heads/405290.md?page=5)