how many times have you run the script?

just 1000, but the results are pretty consistent if you try different numbers of iteration gist.github.com/c-johnson/91c9…

If you pick HHHT ex ante to compare with, the probability of getting it is the same as HHHH. It’s only if you pick the comparison ex post that the original claim is correct, for the same basic reason that a “garbage hand” in poker is more probable than a straight flush.

Technically, any five-card hand in poker is equally probable, but the equivalence class of “garbage hands” is vastly larger than the equivalence class of straight flushes. Likewise, things that “look like” HHHT—like HTHH or HHTH—are more numerous than HHHH or TTTT.

Ensemble vs. time average i think

YES. You're more likely to have a distinct appearance of HHHT first. But in an infinitely-long set of trials, you'll occasionally get HHHHHHH strings that dramatically let H catch up.

@meistrephilipos i am vindicated

Our biases and intuitions are the result of experience, but they are also the result of the forge of the greatest artifice of all: evolution.

OK, I didn't understand this at first, but now I think I do. Here's a painstakingly slow, careful, visual explanation of what I think is going on here. Let's start with this sequence: THHHHTTT

The first insight that helped me to understand this was that you're supposed to use a *sliding window* to evaluate the sequence, not a *jumping window.* If we use a *jumping window,* we see this: 1. [THHH]HTTT 2. THHH[HTTT] We see zero HHHH's and zero HHHT's.