Sorry for digging this back out:

Consider the situation: There is Prize P for submitting a design for a bridge that meets certain criteria (location, budget, etc.)

An engineer looks at the situation, and says "The expected time T to find a breakthrough for design such a bridge, conditional on it being possible, is worth ten times the prize P. I estimate a 25% chance that it is possible given the harsh constraints. However, if I had worked on it for time A without success, I will update to a less than 10% chance that it is possible given the constraints."

I think there /might be/ a reason to work for slightly more or less than A before aborting, but I think the calculus makes the proper undershoot approach zero; the proper value of trying includes the cost of time that it would take you to determine that it isn't likely enough to be possible, times the chance that you would spend that time before aborting.

Which ends up turning the decision into a straight-up Value of Information/Cost of Information calculation, which implies that people should spend lots of effort ($10k equivalent) pursuing goals with pP ( -log(P) )in the 2-4 range if those goals have payoffs in the $1m-$1b range.

Once I have time to integrate the conclusion here into the portion of my psyche that thinks it insane to chase a payoff with less that a single-digit chance of the jackpot, I suspect that I might end up owning a business.