(OT) mathematicians-discover-prime-conspiracy

[Marcio Barbado, Jr.]

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 <peter at digitalbrains.com> 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.
>
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