OK, now I need to argue with myself: regardless the overall distribution of choices, each individual choice has a 50/50 chance of matching the result for each particular trial. So I’m not sure I see why it matters to stick with one result over randomly switching.
You were right to be confused, because the teaser was misspecified. It should read:
Acin’s experiment generates an “up” or “down”, each occurring as they may. When is guessing “up” every time better than switching guesses between “up” and “down”?