The properties of a very, very long sample path would be similar to the Monte Carlo properties of an average of shorter ones. The janitor in Chapter 1 who won the lottery, if he lived one thousand years, cannot be expected to win more lotteries. Those who were unlucky in life in spite of their skills would eventually rise. The lucky fool might have benefited from some luck in life; over the longer run he would slowly converge to the state of a less-lucky idiot. Each one would revert to his long-term properties.
