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by waveBidder
1045 days ago
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the St Petersburg paradox is also a problem of ergodicity, since every single player loses with probability 1 over time, even though the "space average" is net positive. No need to invoke messy reality to solve the paradox. the exponential example is just much more useful, since there are plenty of systems easily described by compound growth |
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> We have thus arrived at the intriguing result that wealth averaged over many systems grows at 5% per round, but wealth averaged in one system over a long time shrinks at about 5% per round.
Wealth averaged over many systems doesn’t grow by 5%. It shrinks just like the average. The EV calculation is just wrong. For any finite starting wealth between the players and the bank, there is a number of iterations where the EV turns negative.
If you say, well let the starting wealth be infinite, I say, okay? If you have infinite dollars there are a lot of tricks for making infinite more dollars. It doesn’t work in the real world.