This Week in Bridge
(489) Combining Chances as Declarer
© AiB Robert S. Todd
Level: 5 of 10 (2 of 6) robert@advinbridge.com
General
One of the “expert tricks” to being a good declarer is to not settle for only one chance of making a contract. When we see that a contract can be made if the cards lie one way (call it layout A) and we see another way to make the contract if the cards lie another way (call this layout B), then often the best line of play is not to guess between layout A or B, but instead to find a way to combine our chances and to make the contract if either layout works! Combining chances effectively has a lot to do with the order in which we explore our options, not counting on only one layout. Let’s look at some examples of how to improve our declarer play by combining our chances.
Choosing Between Two Finesses
When we need one additional trick to make our contract and we have a choice of two different finesses to take, we are faced with a classic situation of figuring out how to combine our chances instead of strictly making a choice between the two.
Example 1
♠ AKJ xxxx
♥ AQ xxxx
Consider the two suits above. We have 3 sure tricks from these suits (♠AK and ♥A). If we need one additional trick to make our contract, then we should not choose between taking the ♠ finesse and the ♥ finesse. Instead, we should combine our chances by first playing for the honor to drop in one of the suits, hoping to avoid a finesse, and if that fails, we take the other finesse. Both finesses have about the same chance of working (50%) but the Queen doubleton is much more likely in our 7-card ♠ fit than a stiff King in our 6-card ♥ fit. The best line of play is to play the ♠AK to see if the Queen falls doubleton (onside or offside), and if not, then take the ♥ finesse.
Two Types of Finesses
We generally refer to a finesse as a play that is leading up to a card (usually an honor) and hoping to score an additional trick by finding a missing card being where we want it to be, called being onside. This is a traditional finesse where we lead up to honors and hope to win an extra trick without giving up the lead.
Example 2
xx AQ
xxx AKJ
Here we lead up towards the honors and try to produce an extra trick (two or three tricks) without giving up the lead if the finesse works (the missing honor is in front of our other honors.)
An alternate type of finesse is one that produces an additional trick by leading up to an honor, but is likely to give up a trick even if the finesse works and the honor is onside.
Example 3
xxx KJx
Here we lead from the xxx up towards the KJx. If both the Ace and Queen are onside, then we get two tricks (by playing the Jack). If one honor is onside, we get one trick (by usually playing the Jack the first time and later leading up to the King), and if neither honor is onside we get no tricks.
Example 4
Axx Qxx
In this situation, we lead away from our Ace and towards the Queen. If the King is onside, then we score a second trick with the Queen, and if the King is offside then we only get one trick (our Ace).
In both of these last two examples we must give the opponents a chance to gain the lead in order to execute our finesse. The first type of finesse did not need to allow the opponents to gain the lead in order to try the finesse. This is an important distinction that can affect our choices if we cannot afford to give up the lead.
Combine Two Finesses of Different Types
When we can afford to give up the lead only one time then it is important that we choose our finesses in a correct order.
Example 5
♠ 93
♥ Q53
♦ AKJ3
♣ 8743
♠ AK
♥ A876
♦ Q876
♣ AQ6
Here in 3NT we have 2♠, 1♥, 4♦, and 1♣ for 8 sure tricks. We can get our 9th trick from either the ♥ finesse (leading up to the ♥Q) or the ♣ finesse (leading up to the ♣AQ). On a ♠ lead we still have another ♠ stopper, so we can afford to give up the lead one additional time. If we try the ♣ finesse first and it fails, then our last ♠ stopper will be knocked out and we will not be able to lead a ♥ towards the Queen. In this line of play we will go down even if the ♥K is onside, because LHO will take the ♥K and run the ♠. But instead, if we lead a ♥ towards the Queen first, then even if that loses and our last ♠ stopper is dislodged, we will have time to try the ♣ finesse – combining our chances of making the contract.
Since one type of finesse is certain to lose the lead and another type of finesse may not, it is best to try to one that is certain to give up the lead first if we can afford to do so!
Combining Finesses with Other Chances
Another type of situation where we have two ways to produce an extra trick is when we have a finesse and a suit that can set up if it splits well for us. Let’s look at how we combine our chances in this situation, instead of choosing between these two options.
Example 6
♠ K3
♥ AKQ5
♦ 7654
♣ JT8
♠ QJ
♥ 932
♦ AK83
♣ AK4
Declaring in 3NT on a ♠ lead, we cannot afford to give up the lead. We have 8 tricks (1♠, 3♥, 2♦, and 2♣) and we can get an extra trick, without giving up the lead, from either the ♥ suit or the ♣ suit. We can get our extra trick from the ♣ finesse working or from the ♥ suit splitting 3-3. Here we want to not just choose between these two options for another trick but find a way to try both. In this case, we can test the ♥ suit and see if it splits 3-3 without giving up the lead. If that fails, then we can try the ♣ finesse (cashing the ♣A first, just in case the ♣Q is singleton). If we try the ♣ finesse first and it fails, then we will go down, even if the ♥ suit splits 3-3.
More Complicated Combining Chances
Sometimes we may even try to combine our chances amongst a large number of possible options, giving ourselves a way to make the contract if any of a number of good things happen.
Example 7
♠ K3
♥ AKQ5
♦ J765
♣ JT8
♠ QJ
♥ 932
♦ AK83
♣ AK4
This is the same hand from the previous example, only adding the ♦J in the dummy. This allows us to make the hand if any of the following things happen, provided that we try things in the correct order:
♦Q falls doubleton or singleton.
♥ split 3-3.
♣Q falls singleton.
♣ finesse works.
By trying for the lines of play that do not risk losing the lead (usually, suits splitting well or honors falling) then we can combine these chances and fall back on the finesse last, which risks giving up the lead and allowing the opponents to run the ♠ suit.
Conclusion
Finding the best line of play as declarer requires a lot of experience and precompiled knowledge about what things have the best chance of happening, but one of the ways you can greatly improve your declarer play is to find ways to combine as many chances as possible so you are not picking between two choices when you are not forced to. Another important thing to notice when you are combining your chances is that the order matters. First, you must know if it is safe to give up the lead to the opponents because you have control of all the suits. Second, you must understand which options are 100% safe to try without giving up the lead (testing suit splits, seeing if an honor drops), which options risk giving up the lead (traditional finesses), and which options always give up the lead (leading up to an honor like the King or Queen). When faced with a variety of options for how to make a contract, try constructing a line of play that allows you to try as many as possible so that you can make your contract if any one of these lines of play work.