> it can be shown that the gamblers wealth goes to 0 over suffiently large time scales with probability 1.
In real life, the time scales are not long enough and the number of N samples in one’s life is too small.
This is why retirees over age 60 are concerned with “sequence risk”. That is, you get unlucky VTI/VOO/S&P returns for 5 years, but you don’t live long enough for the average to come back to 8-10%.
Downside risk becomes more important than average return.
I have the same sequence risk when I gamble. I know the average is that I should lose, but I also know I'll never play enough in my lifetime to get enough samples. So I play games that are more likely to have sequences -- hand shuffled blackjack -- and more likely to win quickly and loose slowly -- the don't in craps.
In real life, the time scales are not long enough and the number of N samples in one’s life is too small.
This is why retirees over age 60 are concerned with “sequence risk”. That is, you get unlucky VTI/VOO/S&P returns for 5 years, but you don’t live long enough for the average to come back to 8-10%.
Downside risk becomes more important than average return.
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