The Morra Board Game requires a bit of mind-reading (or at least intuition).

About Morra-board, from BoardGameGeek:

From the instructions: Morra-board builds on an ancient game - renewing and varying it by linking it to a board. The old game on which Morra-board is based is in Danish called 'Klunse', in English 'Odds and Evens'. Each of the two players presents a clenched fist containing a few small stones, coins or matches - both players taking turns at guessing if the sum of the objects in the two hands is even or uneven. Players pieces move around the track based on how many total marbles the two players reveal. If the inner track has a marking on it, the piece advances. The goal is to be the first to advance all the way to the center.