Explanation of numeric experiment that approximates e? Recently I found this post on Reddit. It describes the following algorithm to find e: 


  Here is an example of e turning up
  unexpectedly. Select a random number
  between 0 and 1. Now select another
  and add it to the first. Keep doing
  this, piling on random numbers. How
  many random numbers, on average, do
  you need to make the total greater
  than 1? The answer is e.


This means that you need on average ~2.7 random real numbers to make the sum greater than 1.

However, a random number between 0 and 1 would on average be equal to 0.5. So intuitively I would think that, on average, only 2 random numbers would be required to have a sum > 1.

So where did I go wrong in my thinking? 

Update

I just figured it out myself: You need at least two numbers to have a sum > 1, but often you'll need three, sometimes you'll need four, sometimes five, etc... So it only natural that the average required numbers is above 2.

Thanks for the replies!
It is never possible to get greater than 1 on the first try, so the average must be strictly greater than 2.
Sorry, can't explain it either. It's obvious you need at least two random numbers to go greater than 1. And if the random numbers are on average .5 you'll need (edit) on average (/edit) maximum three numbers. So we end up in the range [2..3], but that's as close as I can get to e.  

While the method sure looks curious, it must be about the least efficient way ever to calculate e digits. A quick-and-dirty test program I wrote only gave 4 correct significant digits after a billion iterations. Or maybe Delphi's PRNG isn't perfect.