[AaronBrown]

I think you misunderstand what he means. Say you're just flipping a fair coin for $1, betting on heads each time at even money. Call your stake after the Nth flip, S(N).

Half the time, S(N) < S(N-1) because the Nth flip was tails. If that's not true, one time in four, S(N) < S(N-3) because the Nth flip was heads, but the two flips before it were both tails. If that's not true, one time in six S(N) < S(N - 5).

If you keep going forever, eventually you get to certainty that you are below your high-water mark. The probabilities add up to 1.

However, with Blackjack you have a positive expectation, so the probabilities add up to slightly less than one. It's only slightly less, because the expectation matters only in the long run; for the last 100 hands or so the probability is not much different from coin flipping.