You should always, obviously, pick the idea that you believe in the most. Both because it's probably the best (assuming you have good judgement) and because it's the one you will be most motivated to work on.
The reason I wrote the post is that I've seen people hanging on to a project long after it was apparent to everyone else that it wouldn't fly. I've made that mistake myself. I don't want others to make the same mistakes I did if it can be avoided.
And math won't necessarily make you rich - but it might improve your chances :-)
your post here is better rational than the other stuff (although it was all well written).
I think it would be very useful to define processes by which entrepreneurs can better determine if they are hanging on too long. Processes that have more depth than just playing with numbers. Perhaps its simply soliciting more critical feedback from others at key points along the path?
It's a very interesting thought. The problem may be that there aren't really anyone in the vicinity of entrepreneurs that have an interest in saying that it probably won't work out: Investors lose their money, partners lose their partnerships, etc. And friends often tell you you're doing great in an attempt to spur you on.
It might be possible to set up some system that you can judge yourself by. Maybe a quiz that you can take every month that is developed by psychologists, entrepreneurs, and VC's with questions on your progress, motivation, financials, etc. Your score reflects your chances of success, and you can track it from month to month. That way you will see more clearly whether things are going well or to hell. It would be like with small children: If they are your own you don't notice how quickly they grow because you see them every day. People that only see them every month notice right away.
Maybe a simple approach would be an evolution of what people already do with "Ask HN: Rate my startup". But do it later in the game not just when you first launch?
There is certainly enough "distance" between many of the participants here to get open feedback.
The reason I wrote the post is that I've seen people hanging on to a project long after it was apparent to everyone else that it wouldn't fly. I've made that mistake myself. I don't want others to make the same mistakes I did if it can be avoided.
And math won't necessarily make you rich - but it might improve your chances :-)