An important component of a bet like this: you should base the win/lose calculation on returns after accounting for fees. The index fund likely has fees that ar

An important component of a bet like this: you should base the win/lose calculation on returns after accounting for fees. The index fund likely has fees that are two orders of magnitude lower than the active fund. Otherwise, a random fund may beat a broad index just by chance. Warren Buffett's very similar bet was done this way.