i totally didn't believe this, so i wrote a small script to test it, and 'lo --pic.twitter.com/suTIkc9sH1
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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.
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But a *sliding window* looks like this: 1. [THHH]HTTT 2. T[HHHH]TTT 3. TH[HHHT]TT Now we see one HHHH and one HHHT.
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The next important insight is that you can *double-count values.* In the sequence above, we counted the same three H's toward both an HHHH and an HHHT. This is important because it means that HHHH's and HHHT's can overlap.
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