There is a very accessible "numberphile" video which I think is closely related to this, about playing the odds on predicting elements of a nominally-random coi

There is a very accessible "numberphile" video which I think is closely related to this, about playing the odds on predicting elements of a nominally-random coin-flip sequence using the expected run length. https://www.youtube.com/watch?v=tP-Ipsat90c https://www.youtube.com/watch?v=tP-Ipsat90c