# HW5 by suchenfz

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```									HW5: The Finesse
The Finesse
We will now take a brief break from learning about bidding and look at a card-play
technique called the finesse. A finesse is a way to win tricks with cards that are not the
highest out in their suits. Let‟s look at the card position shown on the left. The top row
AQ                     of cards represents the dummy‟s holding in a particular suit. The
bottom row represents declarer‟s holding in the same suit. The
96                     question we are trying to answer is, “What is the best way to play
this suit to win the greatest number of tricks?” For the purposes of this and further card-
position discussions, we will assume that we have unlimited entries (high cards in other
suits we can use to get the lead into whichever hand we want) to either hand. One way to
play the above suit would be to play the Ace and then the Q. We will be able to win two
tricks in the suit whenever the King falls under the Ace. However, this isn‟t very likely
to occur. The King would have to be singleton in an opponent‟s hand for this to
realistically occur. Can we find a better way to play the suit?

What if, instead, we play the 9 or 6 out of declarer‟s hand first. If LHO (left-hand
opponent) plays the King, we can win the Ace and then win the Queen for two tricks. If
LHO plays any other card, what should we play? If we play the Ace, we will win two
tricks in the suit whenever RHO (right hand opponent) has the singleton King. If we
play the Queen, we will win two tricks in the suit whenever LHO has the King. The
former would require LHO to have started with an 8-card suit missing the King, and the
latter requires LHO to have started with any number of cards including the King. The
chance of the former occurring is very close to 0%. The chance of the latter occurring is
around 50%. The reason for this is that the King is in one opponent‟s hand or the other,
with roughly equal chance. Since LHO has already played to this trick, we can play the
Queen and win the trick any time LHO has the King. If RHO has the King, there is no
way we can win two tricks in the suit unless RHO leads the suit for us. The play of low-
to-the-Queen is called „finessing the Queen‟ or „finessing against the King.‟ We are
using a non-high card to win or promote a trick.
When finessing, it is generally right to play a small card towards the card with which we
are hoping to win a trick. Finesses are possible with many different card positions. Can
you identify the finesse(s) in each of the following situations?
(1)              (2)            (3)             (4)             (5)             (6)
K4               A97            AJ7             KJ4             AJT             KQ3

83               Q63            865             876             543             876
(1) and (2) are simple finessing positions. In (1), it is right to lead small to the King. If
LHO has the Ace, the King will win. If RHO has the Ace, we cannot win any tricks.
Thus, we are said to have one-half trick in this suit. In (2), it is right to cash the Ace and
then lead small to the Queen. Cashing the Ace has the effect of reducing the position to
(1). If RHO has the King or LHO has the singleton King, we will win two tricks in the
suit. If not, we will win one trick in the suit. Thus, we have one and a half tricks.

(3) is called a double finessing position. The right way to play the suit is to play small to
the Jack. This is a finesse against both the King and the Queen. We have a 25% chance
of winning two tricks. If LHO holds both the King and Queen, the Jack will win.
Otherwise, we can only win one trick in the suit. (4) is also best played as a double
finesse, although it is slightly different than (3). The right play is small to the Jack,
followed by small to the King. If LHO has the Ace and Queen, we will win two tricks in
the suit. If RHO has the Ace and Queen, we will win no tricks in the suit. If the Ace and
Queen are in different hands, we will win one trick in the suit. Thus we have, on average,
one trick in the suit. Playing small to the King and then small to the Jack is almost as
good a play as small to the Jack followed by small to the King. We will win one trick in
the suit whenever LHO holds the Ace and Queen, or whenever the Ace and Queen are in
different hands. We still cannot win any tricks in the suit RHO holds both the Ace and
Queen. However, we have no chance of winning two tricks in the suit. If LHO holds the
Ace and Queen, then the King will win the first round, but the Ace and Queen will win
the second and third rounds, rendering the Jack useless. Thus, small to the Jack initially is
the best play.
(5) and (6) are called repeated finessing positions. In (5), the best play is small to the
Jack or Ten, followed by small to the other one. This play will yield two tricks in the suit
whenever RHO does not hold both the King and Queen, and it will yield one trick in the
suit otherwise. Thus, we have one and three-quarters tricks in the suit. In (6), the right
play is small to the King, followed by small to the Queen (if the King wins). This play
will give us two tricks in the suit whenever LHO holds the Ace and one trick in the suit
whenever RHO holds the Ace. Thus we have one and a half tricks in the suit.

There are finessing positions where it is right to lead the card with which we are hoping
to win the trick. These are called promotion finesses. Look at the following positions:
(1)            (2)             In the two positions in the left, it is right to lead a card in
A65            K72             the honor sequence in declarer‟s hand. In (1), if LHO
plays the King, we can win the Ace and cash the remaining
QJT            JT9             tricks in the suit. If LHO plays low, we can play low from
dummy. If LHO holds the King, the honor from declarer‟s hand will win the trick, and
we can repeat the process. If RHO wins with the King, we could never win more than
two tricks in the suit. In (2), we lead the Jack, Ten, or Nine. If LHO plays the Queen, we
cover with the King. The Ace will win a trick at some point, but we have the other two
tricks in the suit. If LHO plays low or plays the Ace, we play low, hoping LHO holds the
Queen. If this is the case, we can win two tricks in the suit by repeating the promotion
finesse.

There are countless other finessing positions in bridge. In the next class, you will need to
be able to recognize and execute finesses in order to make your contracts.

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