A way to identify an ergodic situation is to ask do I get the same result if I:
The observed behavior of people making economic decision often deviates from what traditional economic theory would predict as optimal.
Thus the reason (under traditional economic reasoning) that someone doesn't participate in a positive expectation, but non-ergodic game is because they are "conservative" or "scared" as opposed to "aggressive" or "brave"
Now, let's step back and look at economics through the lens of ergodicity. Start with an economic decision with no uncertainty: Ergodicity
You may choose between a job that offers $12,000 per year or $2,000 per month. Which do you pick?
Everyone picks the $2,000 per month job, not because it is the larger amount (it isn't) but because it leads to a higher growth rate of wealth.
We care about our ROI when we make taking a job or making an investment, not how the average person does.
In maximizing the expectation value, expected utility theory assumes that individuals can interact with copies of themselves in parallel universes. If you could make a million copies of yourself and each copy played Russian Roulette for $1 million each round, then there is one version of yourself that would get extremely lucky and make a ton of money. But reality doesn't work that way. We do not live spread out across a multiverse. We live one life, through time. Ergodicity Multiverse Reality
It's not so much that some people are more aggressive or conservative, it's that people behave differently depending on the game are playing.