[x1798DE]

The article is claiming that the guy can predict which things are going to succeed and which are going to fail, not make them succeed or fail. His evidence for this is that 50% of the time, he's right (e.g. [success, success], [fail, fail] are both success conditions for him). For him to be adding any information to the system, he has to get it right more often than either choosing randomly or using a fixed zero-information strategy (always bet fail/always bet succeed). You explicitly said that the joint probability matters, but then miscalculated the joint probability of him guessing correctly by random chance.

[brudgers]

I apologize for not making myself clear enough to communicate as effectively as might be hoped.