Suit Combinations

A-Q-9-2 opposite J-6-5-4. K-9-2 opposite Q-8-5-4. Nine cards missing the queen. Declarer meets these small problems over and over, and each one is a suit combination with a best way to play it that you can work out at home instead of guessing at the table. Of all the parts of card play, bridge suit combinations repay study most directly, because the right line depends only on the cards in the suit and on how many tricks you need.

A suit combination is the holding of one suit in declarer's two hands, studied on its own. The other suits are assumed to provide whatever entries you need, and the defenders are assumed to defend perfectly once they see what you do. The question is always the same. Which sequence of plays takes the required number of tricks against the largest share of the possible layouts of the missing cards?

Two things define the problem. One is the cards you hold. The other is the target, the number of tricks you need from the suit, and the same cards can have a different best line for each target, so a combination is never solved until you know what you are playing for.

Before the play starts, every way the missing cards can be divided between the defenders has an a priori probability. These are the figures most serious players end up knowing by heart.

There is a pattern in the table. When an odd number of cards is missing, the most even split is the most likely one. When an even number is missing, it is not. Four cards split 3-1 more often than 2-2, and six cards split 4-2 more often than 3-3, because there are more ways to deal the uneven split.

Each split is a total over several specific layouts. The 3-1 split of four missing cards covers eight of them (either defender can hold the singleton, and it can be any of the four cards), so each is about 6 percent. A singleton queen in a particular hand is therefore about a 6 percent shot, and a specific doubleton such as Q-J in one hand is about 7 percent.

Eight ever, nine never

The best-known result of these numbers is the rule for missing the queen. Holding nine cards missing the queen (four cards out), cash the ace and king. The queen falls when the suit splits 2-2 (40 percent) or when it is singleton (about 12 percent), about 53 percent in all. A finesse is about 50 percent, so the drop is slightly better. Holding eight cards (five out), the queen falls in two rounds only when it is singleton or doubleton, about 33 percent, and the finesse at about 50 percent is clearly better. Hence eight ever, nine never.

Treat the rule as a starting point, and drop it once the hand tells you more. A defender who has shown a long suit in the auction has fewer places for your queen, and a defender who has shown out of another suit has more. Once you have a count, play the odds of the actual hand, not the a priori table. The finesse guide covers how to collect that information.

Take A-Q-9-2 in North opposite J-6-5-4 in South. To make all four tricks you need West to hold the king and, in practice, the ten as well, because the defenders can make you guess the ten. The best start is the jack from South, which makes four tricks about 19 percent of the time. If you need only three tricks, the jack is no longer best. Cashing the ace or leading a low card first makes three tricks about 90 percent of the time, the jack lead about 87 percent. The jack commits a card that matters on the bad breaks, and when you can afford a loser those bad breaks are exactly what you are playing for.

The lesson goes beyond this suit. Decide how many tricks you need from a suit before you touch it. In a contract that needs only three tricks, the play that gives you the best chance of four can be a mistake. The same thinking is the basis of the safety play.

Restricted choice explains a decision that feels like a coin toss but is not. Hold A-K-10-9-x in North and four small cards in South, nine cards missing Q-J-x-x. You cash the ace and East drops the queen. On the next round, West follows low. Do you play the king, hoping East started with Q-J, or the ten, hoping East started with the singleton queen?

The singleton queen and the doubleton Q-J are almost equally likely before the play. But with the singleton East had no choice, while with Q-J East could have played either honor and would play the queen only half the time. So the queen appearing is roughly twice as consistent with a singleton. Finessing the ten wins about 65 percent of the time, close to two to one.

Plenty of club players distrust this the first time they meet it. The arithmetic holds all the same.

Combination tables and the suit solver describe layouts by naming what West holds, and East has the rest. "West K-x" means West holds the king and one small card, and the solver lists every such layout with its probability and whether your line wins it. Read the table as a checklist. Which layouts do you win, which do you lose, and is there a line that trades a rare loss for a more common win?

Here is a second combination to try. In K-9-2 opposite Q-8-5-4 the honors are split and the ace is missing, so whichever defender sits over an honor can capture it.

• Playing the suit before deciding the target. The best line for the maximum is often wrong when you need one trick less.
• Applying eight ever, nine never after the auction has spoken. A defender who has shown a seven-card suit is short in yours.
• Cashing a top honor too early. It can block the suit or remove the card you needed to finesse later.
• Treating a dropped honor as a coin toss. Restricted choice says the singleton is more likely than the touching honors.
• Forgetting entries. A line that needs to lead twice from South is worthless if South has one entry.

You can play any holding trick by trick against perfect defense in the Suit Trainer, and look up the best line for any target in the suit solver. Combinations also feed bigger techniques like the squeeze and the endplay, which create extra chances when a combination alone falls short.

What is a suit combination in bridge?

A suit combination is declarer's holding in one suit across both hands, considered on its own. Solving it means finding the line of play that takes the required number of tricks against the most layouts of the missing cards.

What are the odds of a 3-2 break?

With five cards missing, they split 3-2 about 68 percent of the time, 4-1 about 28 percent and 5-0 about 4 percent.

Why is a 3-3 split less likely than 4-2?

There are more ways to deal six cards 4-2 than 3-3. A 4-2 split happens about 48 percent of the time and a 3-3 split about 36 percent.

What is restricted choice?

It is the principle that a defender who plays one of two equal honors is more likely to have had no choice. If an honor drops on the first round, finessing against the other honor is about twice as likely to succeed as playing for both to fall.

Does the best line depend on how many tricks I need?

Yes. A-Q-9-2 opposite J-6-5-4 is best played by leading the jack for four tricks, but cashing the ace or leading low is better when you need only three.