How do you know what they really want? Take a closer look at the subreddit and things like an entire class system has developed over which number you get (if you've pressed at all.) Plus, who says the goal is to be the last person who clicks? Maybe the goal is to not click at all!
That's not the correct strategy for keeping the timer alive as long as possible. If everyone did that, then everyone would simultaneously press it the first time it almost-expires, and nobody would remain for the next time it nearly expires.
A better strategy is to pick a random time number that you wait until, biased towards the lower part of the range.