Do you mean that it's not true that "in one round, the collective wealth goes up 5%"?

I could agree with that.

(However, if you add "in expectation" it will be true for one round and for each round no matter how many rounds you run.)

For a finite population and starting wealth, the collective wealth will tend to 0 given enough rounds.

So 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.)

Yeah 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.

Maybe 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.