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>>The expected win is infinite because very rare scenarios have huge payouts.

Not quite. The expected win is infinite because of the one single scenario where the games continues on an infinite basis.

The average win is approx $46 if the bankroll is all the money in the world.

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Thinking about the one single scenario where it goes on forever, as if it were an event unto itself, is misleading imo -- by that reasoning, in that scenario, you would win an infinite amount even if you were only getting paid $1 on each flip. But the EV is clearly not infinite for that game. The increasingly huge rare payouts are essential to the EV calc.

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