Aggregating logic, intelligence and odds...

Outstanding Cards

"Outstanding Card" statistics are the probibiliy of trump-split with the opponent
Use below tables in absense of useful information from the bidding. Notes: on all the drop or finesse suggestion, the text assumes you have all the top honor (Ace or King)
 

Seven-Cards Fit

If you and partner have 7 cards, then the LHO and RHO have a total of 6 cards:
 
Split  Probability 
0 - 6 1.5%
1 - 5 15%
2 - 4 48%
3 - 3 36%
Drop or Finesse the Queen/King?
Finesse the Queen/King.

Eight-Cards Fit

If you and partner have 8 cards, then the LHO and RHO have a total of 5 cards:
 
Split  Probability 
0 - 5 3.9%
1 - 4 28%
2 - 3 68%
Drop or Finesse the Queen?
Cash the Ace first, then finesse the Queen.

Nine-Cards Fit

If you and partner have 9 cards, then the LHO and RHO have a total of 4 cards:
 
Split  Probability 
0 - 4 9.6%
1 - 3 50%
2 - 2 41%
Drop or Finesse the Queen?
Cash the Ace first, so any singleton Q and void can be observed immediately. Then play toward the King. If you still do not see the Q, then it is almost 50-50 (20 to 19) in favor to drop the Q

Ten-Cards Fit

If you and partner have 10 cards, then the LHO and RHO have a total of 3 cards:
 
Split  Probability 
0 - 3 22%
1 - 2 78%

Drop or Finesse the Queen?

Cash the Ace first, if both opponent have the suit then cash the King. If your LHO show a void the first time, you can finesse the Q.

Eleven-Cards Fit

If you and partner have 11 cards, then the LHO and RHO have a total of 2 cards:
 
Split  Probability 
0 - 2 48%
1 - 1 52%
Drop or Finesse the King?
If possible, play toward the A, using Q preferably (especially if J is hidden):
  • Your RHO may show a void. So, always 1 trick for opponent. No regret, no wondering
  • Your RHO could mistakenly/unnecessarily play K to cover Q
  • The singleton K may show up from your RHO
  • If you did not see the King, then drop (cash the Ace) - 52% vs 48% - almost similar odds

Further Reading: