https://github.com/fifthist/Introduction-To-Probability-Blitzstein-Solutions/blob/master/src/chapters/1/sections/counting/problems/7.tex I got 267, I think you are missing when the games end with a draw or with a win and just bundle the two. https://math.stackexchange.com/questions/1285582/two-chess-players-a-and-b-are-going-to-play-7-games-there-are-three-possible I got confirmation here that 267 may be correct.
https://github.com/fifthist/Introduction-To-Probability-Blitzstein-Solutions/blob/master/src/chapters/1/sections/counting/problems/7.tex
I got 267, I think you are missing when the games end with a draw or with a win and just bundle the two.
https://math.stackexchange.com/questions/1285582/two-chess-players-a-and-b-are-going-to-play-7-games-there-are-three-possible I got confirmation here that 267 may be correct.