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A finesse is a positional play of the cards providing a chance to win tricks with lower cards.  Finessing involves leading towards an honor (or honors) where an additional trick can be won if the honor being finessed against is in front of the honors begin led towards.

A direct finesse (aka a simple finesse) illustrates this concept.

  North:  ♠AQ  
West:  ?   East:  ?
  South:  ♠54  

If you lead the ♠Ace from North's hand, North's ♠Queen will not take a trick unless the ♠King is a singleton.  
To finesse against West for the ♠King, you lead a low spade from South's hand.  If West plays the King, you cover it with the ♠Ace and win 2 spade tricks.  If West plays a low spade, you play the ♠Queen.  If West has the ♠King, a 50% chance, you win 2 spade tricks.  A direct finesse provides a 50% chance to win a 2nd spade trick.

An indirect finesse (aka a lobbing finesse) leads a low card towards one or more honors, hoping the high honors are front of the honor.

  North:  ♠K3  
West:  ?   East:  ?
  South:  ♠54  

 

If you lead the ♠3 from North's hand, the ♠King will only take a trick if the ♠Ace is singleton.  If you lead a low spade from South's hand, the ♠King will win a trick when West holds the ♠Ace, a 50% chance.

The holding below is similar.  Cashing the ♠Ace and leading towards the ♠Queen wins a 2nd spade trick when the ♠King is singleton or when East holds the ♠King.

  North:  ♠A83  
West:  ?   East:  ?
  South:  ♠Q54  

If you have enough honors, you can take a pushing finesse, leading an honor, hoping to trap the missing honor(s).

  North:  ♠A32  
West:  ?   East:  ?
  South:  ♠QJT  

 

Leading the ♠Queen, provides 3 spade tricks if the ♠King is onside with West, a 50% chance.  Below, North-South's spade holding is weaker.  They don't have the ♠10.  Leading the ♠Queen, will not win 3 spade tricks, even if the ♠King is onside.  

  North:  ♠A32  
West:  K96   East:  T875
  South:  ♠QJ4  

 

West can cover the ♠Queen (or Jack), promoting East's ♠10 to a winner.  You need to hope for a singleton ♠King to win 3 tricks.

Finessing against 2 honors is called a double finesse.  

  North:  ♠AQT  
West:  ?   East:  ?
  South:  ♠874  

Leading a low spade towards North finesses against the King and Jack.  If West plays an honor, North covers.  The finesse can be repeated against the remaining outstanding honor.  This line of play wins 3 tricks when the ♠King and Jack are onside, a 25% chance, 2 tricks when the ♠King and Jack are split, a 50% chance, and just 1 trick when East holds both the ♠King and Jack, a 25% chance.

The holding below is also a double finesse.  South leads a low spade towards North's hand.  If West plays the ♠King or Queen, North covers.  Otherwise, North finesses against the ♠King and Queen.  This line provides 2 spade tricks when West has the ♠King and/or Queen, a 75% chance.  Just one spade trick is available if East has the ♠King and the ♠Queen, a 25% chance.

  North:  ♠AJT  
West:  ?   East:  ?
  South:  ♠432  

 

In the holding below, North-South have just 2 of the top spades.  Declarer needs West to hold both the ♠King and Queen to win 2 spade tricks, a 25% chance.  South lead a low spade.  If West plays the King or Queen, North plays the Ace.  South will subsequently take a lobbing finesse towards the Jack, hoping West has the remaining King (or Queen).  

  North:  ♠AJ5  
West:  ?   East:  ?
  South:  ♠432  

 

Add the ♠9 to North's hand, as shown below, North-South's chance for a 2nd spade trick rises to almost 38%.   Instead of playing West for the ♠King and Queen, a 25% chance, you can play West for either the ♠King-Ten or ♠Queen-Ten, a 37.7% chance.  South leads a low a spade.  If West plays low, North plays the 9, finessing against the King, Queen, and Ten.  If East wins the King or Queen, South will repeat the finesse hoping West has the remaining King (or Queen).  

  North:  ♠AJ9  
West:  ?   East:  ?
  South:  ♠432  

 

Here are some additional articles on Finessing:

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