Bridge suit combinations
Choose the cards in one suit for you and dummy in bridge to see how to play the suit for as many tricks as possible, and how good the chances are.
The defenders hold Q 9 8 7.
Calculating…
Assumes unlimited entries and good defence. The chances apply before the bidding and earlier tricks have given clues about the cards.
How it works
The tool tries every way the defenders’ cards can lie and every way you can play the suit, and for each number of tricks picks the line that succeeds most often. You see only your own cards and the cards played, just as at the table.
The chance of each distribution is worked out with vacant places. With five cards out, the suit splits 3–2 67.8% of the time, 4–1 28.3% and 5–0 3.9%. Bidding and earlier tricks, which can change the odds, are not taken into account.
The defenders are assumed to play as well as possible against your line. They see all the cards and know how you plan to continue, so they cover, duck or false-card exactly when it fools you, but they choose at random between equivalent cards. The latter gives restricted choice: if a defender has played the queen, partner is more likely to hold the jack than the defender to have held both. The chance shown holds however the defenders choose.
As in the textbook tables, you are assumed to have unlimited entries to both hands and to lead to every trick yourself. The defenders never lead the suit.
The right line often depends on how many tricks you need. With ace, king, ten and two small opposite three small you lead towards the ten for five tricks but cash the king first when four will do, so the result is shown for each target separately, with the plan for how to continue depending on what the defenders play.
The results have been compared with two published suit-combination tables and agree within half a percentage point in 99 of 102 cases in one and 1,518 of 1,588 cases in the other. Where they differ, the table may contain an error, or the tool lets the defenders choose the card that is worst for you.
Combinations where the defenders hold many cards can take a couple of seconds to calculate.
How the defenders’ cards divide
The chance of each division when the defenders hold a given number of cards in the suit and nothing else is known. The figures use vacant places, the same method as the tool.
| Cards out | Division and chance |
|---|---|
| 2 | 1–1: 52.0%, 2–0: 48.0% |
| 3 | 2–1: 78.0%, 3–0: 22.0% |
| 4 | 2–2: 40.7%, 3–1: 49.7%, 4–0: 9.6% |
| 5 | 3–2: 67.8%, 4–1: 28.3%, 5–0: 3.9% |
| 6 | 3–3: 35.5%, 4–2: 48.4%, 5–1: 14.5%, 6–0: 1.5% |
| 7 | 4–3: 62.2%, 5–2: 30.5%, 6–1: 6.8%, 7–0: 0.5% |
| 8 | 4–4: 32.7%, 5–3: 47.1%, 6–2: 17.1%, 7–1: 2.9%, 8–0: 0.2% |
A few classic combinations
The chance of taking the maximum number of tricks, and one trick fewer, with best play. The figures come from the tool above, with unlimited entries and no help from the bidding.
| North–South | Tricks | Chance |
|---|---|---|
| A Q – x x | 2 | 50.0% |
| 1 | 100.0% | |
| A Q 10 – x x x | 3 | 24.0% |
| 2 | 76.0% | |
| A K Q x x – x x x | 5 | 67.8% |
| 4 | 96.1% | |
| A K J x x – x x x | 5 | 33.9% |
| 4 | 84.8% | |
| A K J x x x – x x x | 6 | 53.1% |
| 5 | 95.2% | |
| A K 10 x x – x x x | 5 | 13.6% |
| 4 | 82.0% |
An x stands for a small card.
The divisions hold before the bidding
The table above applies when nothing is known about the defenders’ hands. As soon as the bidding or the play reveals something, the chances change. If one defender has shown a long suit, the other has more room for the cards in the remaining suits, so a missing card is more likely to sit there.
The principle is called vacant places: each defender holds thirteen cards, and the places already taken by known cards cannot hold the card you are looking for. The tool assumes every place is free, which is right when you know nothing else.
Eight ever, nine never
The old maxim says that a declarer missing the queen finesses with eight cards in the suit and plays for the drop with nine. It holds in the common cases, but the margins are often slim.
With nine cards to the ace, king and jack the defenders hold four cards, and the queen falls when they split 2–2 or the queen is singleton. Playing for the drop then works 53.1% of the time against 50% for a simple finesse. With eight cards the gap runs the other way and is wider: best play gives five tricks 33.9% of the time, while playing for the drop works about 27% of the time. The tool works out the exact best line for each holding rather than following the maxim.
The tool and the published tables
Suit-combination tables appear in several classic reference works, and they generally calculate as the tool does, with unlimited entries and no help from the bidding. Where the tool differs from a table, the table may contain an error: one edition of a major bridge encyclopedia gave 51% for a holding where the correct figure is 58%. The tool also lets the defenders choose the card that is worst for you, and otherwise choose at random between equivalent cards.