“It’s a lava lamp, Mom! I swear!”

You can get a 66% chance of being right if you turn on a switch and check the room. If the light is off you guess between the other two. For example, you are going to test switch 1 and if it is off you guess switch 2.

Reminds me of the Monty Hall problem except in that problem the game show host has an action to take which effects the odds.