That's really cool. An easy way to understand it is by thinking about bunching. Since you're only flipping until you hit the first matching sequence, on avera

That's really cool. An easy way to understand it is by thinking about bunching. Since you're only flipping until you hit the first matching sequence, on average you'll hit the more evenly distributed sequence more quickly than the bunched sequence. Multiple heads in a row are more bunched than transition sequences because, for example, a sequence of three heads in a row will include two sequences with two heads in a row. You can't do that with a transition sequence--it takes at least four tosses to get two identical transition sequences.