Some of the mutual-failure conditions in certain mini-games can invoke this. In Egg In Space, for example, if none of the players find the switch to Eggman's rocket, Eggman will escape from his prison while mocking you, leaving the entire group beside themselves.
Gamma's board victory quote is "Frog capture complete!"
If the number the AI chooses is larger than the number of spaces it takes to reach the Precioustone, they will turn around and go the opposite way no matter what.
On Hard Mode, the AI will often go to where the Precioustone will appear next rather than where it currently is. This makes them easier to deal with than on Easy Mode, where they go straight for the Precioustone that's out on the field.