Suit Break Odds

Four missing cards split 3-1 more often than 2-2, at 49.74 percent against 40.70, and that surprises many players who expect the even split to lead. The table below lists every division of two to eight missing cards, each with its a priori chance. Five missing is the case most declarers want, and there the 3-2 break comes in at 67.83 percent.

An odd number of missing cards tends to split as evenly as it can. Five missing break 3-2 about two times in three, 4-1 at 28.26 percent and 5-0 at only 3.91.

From four upward, an even number tends to split unevenly. Four cards favor 3-1 over 2-2, and six cards favor 4-2 at 48.45 percent over 3-3 at 35.53. The reason is counting. There are four ways to give one defender three of the four cards and six ways to give each defender two. The 3-1 can go either way round, though, which makes it eight against six before the vacant places are weighed.

The two defenders hold 26 unseen cards, 13 each. For a given split the arithmetic counts the ways to deal the missing cards in that proportion and the rest of each hand around them, then divides by all the possible deals of those 26 cards. The chances for each number of missing cards add up to 100 percent.

A priori means before any information arrives. Once a defender has shown length in another suit, or shows out, the vacant places change and so do the odds. A player who has bid a long suit is less likely to hold length in yours.

The figures tell you what a line has to beat. A 5-0 break at 3.91 percent is worth guarding against only when the safety play costs nothing in the normal case. A 4-0 break of four missing cards, at 9.57 percent, deserves far more respect. For a missing queen the same numbers decide finesse or drop, and full holdings are worked through in suit combinations.

What are the odds of a 3-2 break in bridge?

A 3-2 break comes up 67.83 percent of the time when five cards are missing. The 4-1 break follows at 28.26 percent and the 5-0 break at 3.91.

Is a 2-2 or a 3-1 break more likely?

The 3-1 break is more likely, at 49.74 percent against 40.70 for 2-2. From four missing cards upward, an even number usually splits unevenly.

How often do four missing cards break 4-0?

Four missing cards break 4-0 in 9.57 percent of deals, roughly one time in ten, split between the two defenders.

Do suit break odds change during the play?

Yes. The table shows a priori odds. Every card a defender plays or shows out on, and every suit bid in the auction, shifts the chances of the remaining splits.