"Civilization Revolution" does this.
Say the player loses a 75% roll, then attempts another identical 75% roll. The game will actually give you better odds for the second roll. I think it's silly -- the game basically lies to you about your odds on the second attempt.
Sid Meier talked about it at length in this video: http://www.youtube.com/watch?v=bY7aRJE-oOY. It starts around 18:25.