Not sure if it's counterintuitive once tossing can be seen as abandoning inertia.
Marcio Barbado, Jr. On Fri, Mar 18, 2016 at 9:18 AM, Peter Lebbing <[email protected]> wrote: > On 14/03/16 10:37, Fulano Diego Perez wrote: >> https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/ > > So forgive me for the off-topicness, but something in the text caught my > attention: > >> Soundararajan was drawn to study consecutive primes after hearing a >> lecture at Stanford by the mathematician Tadashi Tokieda, of the >> University of Cambridge, in which he mentioned a counterintuitive >> property of coin-tossing: If Alice tosses a coin until she sees a >> head followed by a tail, and Bob tosses a coin until he sees two >> heads in a row, then on average, Alice will require four tosses while >> Bob will require six tosses (try this at home!), even though >> head-tail and head-head have an equal chance of appearing after two >> coin tosses. > > I did try this at home; only I wrote a Python script to do all the > tedious tossing and accounting. This is its output: > >> $ ./cointoss HH HT >> >> H T HH HT >> ---------- ---------- ---------- ---------- >> 59821 (49.9%) 60079 (50.1%) 6.044 3.990 > > > After over a million coin tosses, it takes 6 tosses on average until you > see two heads in a row, but only 4 to see head-tail. Obviously, the > script is attached. Supply the patterns on invocation, as shown above. > Any number of patterns of any length are supported (I think). Well, > strictly positive numbers and lengths :). > > Can someone point me in the direction of the solution to this > counterintuitive probability theory result? Any of a common name for the > property, a mathematical explanation or an intuitive explanation are > much appreciated! > > Anyway, to make up for the off-topicness, let's get slightly on-topic... > > To the OP: Please provide at least a short abstract of the text when you > post a link. That way people can tell from your mail what the text will > be about. > > With regards to the article, I'm surprised by the choice of words in its > title. Other than to draw in more readers, I don't see what place the > word "conspiracy" has in it. That's like saying 0 and 1 are conspiring > to be consecutive on the integral number line. Oh no, pretty much all > are computers are based on 0's and 1's and now they are conspiring! > Probably against us! Quick, we need neutral numbers without an agenda... > In my opinion, this title really devalues the article. "Three secret > ways to cope with prime conspiracy mathematicians don't want you to know > about" isn't that much further out. Oh, I hope that phrasing doesn't > tickle any spam filters... Ah well. > > Cheers, > > Peter. > > -- > I use the GNU Privacy Guard (GnuPG) in combination with Enigmail. > You can send me encrypted mail if you want some privacy. > My key is available at <http://digitalbrains.com/2012/openpgp-key-peter> > > _______________________________________________ > Gnupg-users mailing list > [email protected] > http://lists.gnupg.org/mailman/listinfo/gnupg-users > _______________________________________________ Gnupg-users mailing list [email protected] http://lists.gnupg.org/mailman/listinfo/gnupg-users
