Introduction to Bridge classes typically introduce students to the slogan “eight ever, nine never”. The “nine never” part of this slogan refers to the decision about whether to finesse for a missing Queen in this sort of position (you have nine combined cards in the suit):
You lead the three to the Ace (both opponents follow); when you lead the Jack from dummy, your right hand opponent (RHO) follows with the remaining small card. Is it better to finesse (hoping for RHO to have the Queen) or to play the Ace (hoping for LHO to have only the Queen remaining)? This part of the slogan (“nine never”) is misleading and sometimes suggests a poor choice.
Careful analysis demonstrates that when there is no other relevant information, playing the Ace stands to win 52% of the time, and finessing stands to win 48% of the time. Notice that 52 to 48 is almost a toss-up, so when there is other relevant information, strong declarers are quick to depart from the “nine never” part of the slogan.
For more information, see Real World Bridge 3: Declarer Play.