Ergodicity
Whether one person keeps rolling a 6-sided die for a long time, or a large number of people each roll a 6-sided die once, the average outcome (the expected value, 3.5) will be the same. Since both the time average for one person and the ensemble average across many people are the same, the process is ergodic.
Non-Ergodicity
A large number (ensemble) of people each playing Russian roulette once and one person repeatedly playing Russian roulette for a long time don’t lead to the same average outcome. For the people, ~83% survive the one round, while the individual’s average outcome of survival decreases with each round until it’s 0%. Since the time and ensemble averages are different, the process isn’t ergodic.
Note: Non-ergodic processes are much more common in the real-world (assuming you’re in it) than ergodic processes, hence the irony of disregarding it if you claim probability is important in decision making.
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