How long until we find out what happens when it reaches 0? Let's be pessimistic and assume that everyone wants to click it. There were 3.4 active accounts on Reddit last month. 700000 have clicked it so far, so there are 2.7 remaining. Assuming an upper bound of clicking it at 1 second remaining, we get ((2700000 users) * (59 seconds/user))/((60 s/min) (60 min/h) (24 h/day)) = 1843 days, or a little more than 5 years. Of course, it will be less than this. I'm not sure what the distribution of click times is, and it will definitely change as more people have clicked.
and doesn't include accounts that were registered before April 1st, but did not log on yesterday. This potentially could be a lot since it is relatively common to have more than one account on reddit.
