CP9 - The Finesse
based on hope that a high card is held by one Defender, not the other
A simple Finesse has a 50% chance of success.

In an INDIRECT FINESSE
      a low card is lead from one hand
      towards an high card in the other,
      hoping to avoid being capture by Defender's higher card.
West
a. ♥ 7 4   > 2
  East
4 9 K
If North plays low, East plays his ♥K
West
b. ♥ 7 4   > 2
  East
4 9 Q A ♥
If North plays low, East plays his ♥Q
West
c. ♥ A 4   > 2
  East
4 9 Q
If North plays low, East plays his ♥Q
But with 8+ cards combined : lead the ♥A first.

In a DIRECT FINESSE
      a high card is lead from one hand
      towards a higher card in the other,
      hoping to capture Defender's high card.
West
d. ♥ 10 J   > Q
  East
4 7 A ♥
If North plays low, East plays his ♥4
If North plays the ♥K, East captures it with his ♥A
West
e. ♥ 9 10   > J
  East
4 6 K A ♥
If North plays low, East plays his ♥4
If North plays the ♥Q, East captures it with his ♥K

You need 4 of the top 5 (or 6) cards for the Direct finesse to be effective.

 
CP10 - The Double Finesse
A Double Finesse has a 75% chance of success
A Double Finesse can be either an Indirect or a Direct finesse.
You need to take the finesse twice whenever it loses the first time.
West
a. ♥ 7 4   > 2
  East
5 10 Q A ♥
If North plays low, East plays the ♥10, if it loses to the ♥J, a 2nd finesse is taken from West towards the ♥Q
West
b. ♥ .. 10 9   > J
  East
3 6 8 A ♥
If North plays low, East plays his ♥3, if it loses a 2nd finesse is taken from West leading the ♥10
West
c. ♥ 7 4   > 2
  East
6 J K ♥
If North plays low, East plays his ♥J, if it loses to the ♥Q, a 2nd finesse is taken from West towards the ♥K

A RUFFING FINESSE is a special kind of direct finesse
            leading a high card from one hand
            towards a void in that suit in the other.
                  When Defender plays low a loser is discarded
                  when Defender plays high his card is ruffed.
West
d. ♥ .. Q J   > K
  East
4 5 9 ♠ (trump suit)
      - ♥
   6 8 ♣ (losers)
If North plays low, East plays his ♣6,
if North plays his ♥A, East ruffs with the ♠4
West
e. ♥ .. Q J 10   > A
  East
4 5 9 ♠ (trump suit)
      3
   6 8 ♣ (losers)
West first leads his ♥A, removing East's singleton,
then West can execute a ruffing finesse