For better or worse, mathematics hijacks regular terms for their own ends. Sometimes this works alright and no one gets confused. e.g. rings in algebra vs. rings on your fingers. Other times it ends up confusing matters. Suppose that we had a bunch of possible outcomes {a, b, c, d, …} where each has probabilities {p(a), p(b), p(c), p(d), …}. Then the expected value is ap(a)+bp(b)+cp(c)+dp(d)+… Why choose that? Well, you can think of it as a kind of weighted average. (e.g. when you repeat the process an infinite number of times, averaging the results as you go) You can also think of it as a kind of center of mass in an analogy to physics. What you can’t do is actually expect the expected value. You are never going to get 0mil$*0.5+50mil$*0.5 = 25 mil$. This happens with other multi-modal probability distributions as well. Calling it the expected value makes people think that they can expect it, but you can’t. 
Oh well.
Personally, as (an increasingly applied) mathematician, I’d choose the $1mil. I could pay off my mortgage with that. The next real quality of life improvement would be to self-fund my research but $50mil is not enough; I’d still have to write grants.
