The trouble with all these "both ways are equal on average" scenarios is that when presented to people they are given (or often assume they are given) ONE chance at a loss or gain.

Yes, if they were deciding for a community (many people playing) or if they knew they had 1000 chances, then they may act "rational".

But most people are assuming one toss, one pick, one iteration. And so they are choosing rationally given that assumption (i.e. take the sure thing).