In bridge, missing QJxx in a suit, if the Q or J drops on the first round, it is better to finesse if possible on the second round if nothing else is known about the distribution. This is obvious to a mathematician, but the simple conditional probability is so difficult for the average person that bridge teachers have incorporated the principle into the qualitative "Rule of Restricted Choice", which says that if an opponent plays a card that can be from equals (such as the "quack" from QJ), it increases the probability that the other opponent has the second equal card.
In mathematics we often prove uniqueness before existence. The one thing I find appealing about Sudoko is that knowing a solution is unique can help in finding the solution.
