Misunderstanding the St Petersburg Paradox

I talked to Andrea last night. Turns out I misunderstood what the St Petersburg paradox was.

• I thought it was that accepting an infinite series of 50/50 bets to double or go to 0 leads to an infinitely small chance of a non-0 outcome.
• She says it’s actually that if you have an infinite number of trades, you never cash out your winnings and instead just end up trading and trading.
• Chat GPT and wikipedia say it’s about expected outcome calcs leading to different answers than what people will actually do (the original paradox was about bets in money, not utility, so risk aversion makes sense given diminishing marginal returns).

Of the three interpretations, I find none particularly convincing.

• The fact that an infinite series of 50/50 bets leads to an outcome space where value is very concentrated in one tiny part of the utility space isn’t particularly interesting. Whether making that choice is sane or not depends entirely on the agents utility function and risk attitude. (If presented with multiple options with the same EV but different degrees of variance, what would the agent prefer)
• Being trapped forever in trading is silly. If trades take time then the disutility of a trade is something you need to account for. If they don’t you don’t. Also, the word “trade” here doesn’t have the same meaning as “trade” in real life. It’s not a commercial transaction  but the act of choosing from among a few options. The idea that you’re wasting your life by trading instead of touching grass isn’t really sensical. You’re either saying that people shouldn’t waste time making choices or that trade-bot 3000 who exists only to transact should have a different utility function. Both are silly.
• The oldest version of the paradox dealing with real money trades is dissolved by the realisation that money and utility are not interchangeable at a 1:1 ratio. For the vast majority of people, money has steeply diminishing marginal utility. Hence it makes sense to be risk averse even when offered trades that are EV positive in $ terms.