Yeah, which implies for any finite N eventually the average will collapse, once the lucky guy's luck runs out. The expected value prediction is only true over a

Yeah, which implies for any finite N eventually the average will collapse, once the lucky guy's luck runs out. The expected value prediction is only true over a long enough timescale for actually infinite N (I do wonder how this scales: I would intuitively expect that the time window scales with log(N), which implies even very large N will not last drastically longer, but I don't know if that's the case)