Some excellent critiques have been provided in this thread already but I would like to offer a different perspective.

In programming terms, the switching argument (see original link) is incorrect because it does not typecheck. And it does not typecheck because variable A is used out of its scope when writing down the (5/4)*A expected value.

Indeed, variable A is tied to a specific random outcome and so it simply does not make sense to refer to it in an expected value ranging over this same outcome.

Trying to formalize the argument in a proof assistant makes the mistake clear and obvious. However, the ambiguity of the English language makes it possible for such typing errors to sneak in undetected.