There's a variant of this puzzle which you can find in a few places online where the goal is to get the largest check--to maximize the chance that you get the largest check; in other words, assume you only get to keep the check if you choose the largest; the solution strategy is to examine the first 37 checks and remember the largest value there, and then go through the remaining checks and pick the first one that exceeds the remembered value; it turns out there's about a 37% chance of success. (The general solution is to find the max of the first N/e = N/2.71828.)
I can't actually find a description online for how to get the largest expected value if you're allowed to keep the money from whichever check you keep.
I woke up this morning and lay in bed for a while, mulling over my life, and thinking about one of my regrets. As I mentioned in my "101 things about me", there are two things I really regret. One of them I don't think about too often, but this one I think about all the time.
I wish I had a time machine and could go back and kick my ass nine years ago. I was chicken about escalating a friendship that was obviously slowly turning into a relationship. Circumstances changed slightly, and my stranger-phobia got in the way, but if I knew then what I know now, I could and would have worked through that. Instead, the situation got painful for me and I backed out of it; she started dating somebody else, I moved away, she moved on to another guy whom she married.
It's too bad, though; N, it seems, will be around 8, and she was in the fourth envelope I opened.