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For a finite population and starting wealth, the collective wealth will tend to 0 given enough rounds.
by nhinck 3y ago
For a finite population and starting wealth, the collective wealth will tend to 0 given enough rounds.
- kgwgk 3y agoSo you say that it's false that "in one round, the collective wealth goes up 5%", right? However you agree that it's true that "in one round, the collective wealth goes up 5% in expectation", right? (I agree that "for a finite population and starting wealth, the collective wealth will tend to 0 given enough rounds ALMOST SURELY". The last bit is important though. Otherwise it's like saying that if you flip a coin enough times you will get heads - which is not exactly true.)
- nhinck 3y agoYeah I would say "in one round, the collective wealth goes up 5% in expectation" but "for a finite population and starting wealth, the collective wealth will tend to 0 given enough rounds" not almost, but absolutely.
- kgwgk 3y agoMaybe you're not aware but almost surely is a technical term - which makes the statement correct. Just like you cannot be absolutely certain to get heads if you flip a coin enough times even though it will happen almost surely.