Corollary: An optimal predictor need not adapt at switches

The memoryless predictor $B(X_t)$ has expected accuracy $3/4$ at all times, including windows selected solely from an independent switch schedule. For nonempty early and stable windows with this selection rule, its population early-to-stable accuracy ratio is one.

High accuracy and a ratio near one therefore do not establish inference of the active rule or successful rule updating.

Proof. Theorem thm:ceiling applies conditional on each admitted schedule and at every selected time. The predictor does not use a hidden state or switch history.