I haven’t thoroughly tested so this is more or less just anecdotal but quite a few times this has happened in my games and I have yet to see it fail. But if you don’t know what your opponent picked from suspicious alchemist just rope your turn and the game will automatically pick the right card.
Super OP tech.
Edit: it is actually random although the amount of times my opponent goes afk or is seemingly disconnected after playing alchemist is rather uncanny