The use of "almost certainly" when people talk about ergodicity economics drives me nuts - you can't actually bet an infinite number of times so the question about whether a (tiny) chance of a huge win is worth it is still relevant!
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I also think nobody (probably not even economists who used ergodicity as a technical assumption) ever believed that "this strategy has a high expected payoff" meant you were guaranteed a high payoff eventually - that would be a weird way to talk about probability!
