Deal or No Deal
Since the range of possible values for cases is known at the start of each game, how much the banker offers at any given point changes based on what cases have been eliminated.  To promote suspense and lengthen games, the banker's offer usually strays from the expected value dictated by probability theory, particularly early in the game.  However it is not uncommon for the bank's offer to exceed the player's expected value very late in the game.