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And if you're allowed to make bets of an infinite size, which casinos restrict in part to defeat this strategy (as well as manage their risk).

Though even if you are allowed to make infinite bets, most people have finite money to bet with.

Thanks for the name "Martingale", I had wondered what this was called since an old gambler I met on a contract about 10 years ago described 'his' system.

After a quick wikipedia rabbithole, I now grok the St Petersburg paradox, which is fascinating - https://en.wikipedia.org/wiki/St._Petersburg_paradox - but mostly tells me that the 'expected value' is not a good measure of whether you should bet on something, because games can be constructed in such a way that the expected value is infinite, but the chances of you even getting your stake back even at a $16 buy in are 1/8...

the St. Petersburg paradox also reminds me of Pascal's mugging: https://en.wikipedia.org/wiki/Pascal's_mugging

So much so that I think they are likely to be different narratives around more or less the same phenomenon!

If you have an infinite amount of money, you already own the casino.