[EricBurnett]

The expected value of an infinite series of coin flips centers on 0. Sure, you might get lucky, but you can't leverage that as a strategy to ratchet up value. That's the point about luck in the non convex case.

To your mining example, that's where prospecting comes in. Use your knowledge to make checking candidate locations cheaper (increasing convexity) - knowledge of geology to approximate likelihood, improvements to technology to determine if gold exists, etc. Then go check as many candidate mines as possible. It's much more cost effective to have a lot of shallow mines than it is to extract every ounce all the way down to the crust from a single mine.

[adrianN]

If heads is 1 and tails is 0 then the expected value is 0.5. The expectation really depends on what values your random variable can take.

[EricBurnett]

That's not the non convex case though (as e.g. 1 and -1 is). You're right that chance can be convex; the premise of the article is that that's the property of interest, and that randomness alone isn't sufficient.