[irchans]

I had some fun with the article's claims. It claims that

"In the history of the universe or in it's foreseeable future, no two decks of cards have ever been or will ever be in the same sequence (unless artificially so arranged )."

and it goes on to claim

"In other words, you would run out of atoms in the galaxy before you run out of different sequences in a deck of cards."


The first claim is likely to be true, but it is possible to imagine a situation where it is false. The truth of the second claim is hard to determine.

Here is my reasoning,

If you have an experiment that has n possible results, each of which are equally likely and you repeat the experiment Sqrt[n] times then there is approximately a 40% chance that there will be a match. (For n large, the probability is about 1-e^(-0.5).) For n = 52! (approx 8*10^67), the probability of a match is 50% after about 1.05*10^34 deals. (To get this number I used the approximation

prob of getting a match ~= 1 - E^(-(m^2*(m + n))/(2*n^2))

for m experiments with n possible results.)


So, to get a match we need about 10^34 deals. This is unlikely, but if humans continue to play poker and colonize 10,000 galaxies, then we could get a match. Assuming each person shuffles 1 deck per year on average, then we get

10000 galaxies
* 10^10 planets per galaxy
* 10^10 humans per planet
* 10^10 years

= 10^34 deals.


As for the number of deals exceeding the number of atoms in the galaxy. The number of atoms is about

(mass of galaxy in grams)*( Avogadro's Number)

which is

6*10^11 * 2*10^30 * 1000. * 6 10^23
= 7.2*10^68.

This is about 10 times more than the number of deals.

I think we can conclude that if you have a poker probability result that you are going to put in an article, it would be best to check your result first by posting it to the 2+2 fourum. (2 missspellings intended [img]/images/graemlins/tongue.gif[/img] )