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I can see how this would compare to a casino that houses a game that perhaps only has a slight edge (say 5%). But the house has an almost infinite bankroll and thus can sustain long term risk, or one that is very close. But say some super rich tycoon comes along and decides to gamble in the millions. This is going heavily influence the house's bankroll even though the house has a thin edge on the player.

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This is a bad analogy. The casino scenarios have wildly different variance due to the difference in betting units. You don't get that choice in limit poker.

EDIT: The casino analogy, taken to limit poker, would be to move down in stakes so that your total variance decreases vis-a-vis your total bankroll.