You are conflating time-samples with ensembles. That lecture refers to finite time series which may be shown to converge for N < infinity. That’s fine.
I have not mentioned either of these things. You can find other finitist formulations of probability if you want.
You replied to a post about aces. For any finite number of chips and players (n_players > 23 starts to raise some questions), there are finitely many games of NLHE anyway.
