Doctor Doak intently observed both shuffling, thousands of possible order for the cup's movement taken from the pattern it took before his eyes failed to keep up. Compared it to the first round of shuffling for the pattern. Cross referenced to known tricks and sleight of hands. Accounted possible change of pattern and possible obsfucation...
"It's under one of the two cups to the right, isn't it? If I may fancy a guess, the second from the right."
The goblin's snigger abruptly cut as he raised a metallic eyebrow and lifted the cup in question. Under it the pebble sat snugly, glimmering under sunlight.
"Well! Stuff me in a sack and dump me to the lake, it's actually down there!" The automata looked a bit down. "Figger' out you lot gonna fail once or twice more, but ya beat me fair and square. For the winner..."
He snickered, waving a hand. A halo appeared above Doctor Doak, spelling "Winner!" in fancy golden font. Another one popped above Dixie, gloomy black-purple halo spelling "Loser!". The third wave of hand opened the gate behind, not the slightest creak despite its size.
"Heh, I haven't been inside for a while. It haven't changed much." He stopped talking to have a fit of giggle. "Well? What are you waiting for, written invitation? Off you go, shoo!"