Distribution Symbols and Signals

Bruce Watson, St. John's, Newfoundland

Every bridge hand of 13 cards has one suit with an even number of cards and three suits with an odd number or the other way round, one odd and three even. Voids count as even. For example, the hand pattern 4-3-3-3 has one even, three odd; while 4-4-3-2 has one odd, three even. Whether the unique suit is even or odd determines the parity-type of the hand. A 4-3-3-3 hand has even parity-type, and a 4-4-3-2 hand has odd parity-type. The unique suit is referred to in a variety of ways in the literature. Helge Vinje, in his 1980 book, Defensive Play in Bridge, called it the one suit. Other writers have called it the single suit or singular suit. Here, it is called the unique suit.

We keep track of the parity-type and unique suit of a hand using a two-letter distribution symbol. The symbol for a 3=4=3=3 hand with even parity-type and unique suit hearts is EH. The first letter in the pair indicates the parity-type and the second letter the unique suit. Writing that a player is OS will mean that the player has odd parity-type and that his unique suit is spades. The symbols ES, OH, ED, OD, EC and OC have similar meanings.

It's worth noting that the same observation holds for a single suit distributed among four hands. Using spades as an example, there are only two possibilities. One player must have an even number of spades and the other three players an odd number in that suit, or it is the other way round with one odd and three even. Suits have parity-type also.

Vinje described a method whereby each defender, under certain conditions, could signal his original parity-type. We will review his idea, but the main purpose of this article is to present a new method for a defender quickly to recover declarer's distribution symbol as soon as the distribution symbol of the defender's partner becomes known.

In Vinje's distribution signal, if the opponents are playing in a trump contract he suggests that the signaling suit should be the trump suit. When declarer or dummy leads trump, a defender plays high-low with even parity-type or low-high with odd parity-type. This gives partner complete information when the actual unique suit is identified. Of course, it also gives declarer the same complete information. Against a notrump contract, Vinje suggests that the signaling suit should be the first suit bid and supported by declarer and dummy. If no suit has been bid and supported, the signaling suit is the first suit initially led by declarer or dummy. The defenders signal as before, playing high-low for even parity-type and low-high for odd. In this article, and when we use the distribution signal, the signaling suit against notrump is always the first suit led by declarer or dummy. That way, the opponents' systems do not dictate our defensive methods. For example, we don't need advance agreements regarding explicit or implicit support. In addition, declarer may not lead his side's bid and supported suit early enough in the play to be helpful.

Consider this deal where the defenders are using Vinje's Distribution Signal.

	NORTH ♠ 7 5 3 ♥ K 9 6 ♦ A 6 5 ♣ A Q J 3
		EAST ♠ K J 6 ♥ J 8 5 4 ♦ J 7 2 ♣ K 8 2

With both sides vulnerable, South passes as dealer and responds two notrump to North's one-club opening; North raises to three notrump.

Partner, West, leads a fourth best spade deuce. Declarer wins the third round with the ace, then plays a club to the jack, on which partner contributes the seven and you play the eight. Declarer returns to his hand with the diamond king (partner following with the eight) and leads another club. Partner plays the four, and you win with the king. What do you do now?

Partner has shown one even suit and three odd. With four spades, he must be 4=3=3=3, ES. That means declarer is 3=3=4=3, ED. Since declarer is a passed hand, partner has either the heart ace or both red queens. It looks as if declarer has only eight tricks, and the only safe return is a club. The danger is that partner might throw a diamond on the last club to protect the heart queen. So, on the fourth club, you should discard the diamond jack. Partner's diamonds must be queen-ten-eight or queen-nine-eight. He cannot be prevented from winning a diamond trick if declarer goes that route. Partner should also know then that you were EH. Here is the full deal:

	NORTH ♠ 7 5 3 ♥ K 9 6 ♦ A 6 5 ♣ A Q J 3
WEST ♠ Q 10 8 2 ♥ Q 7 3 ♦ Q 9 8 ♣ 10 7 4		EAST ♠ K J 6 ♥ J 8 5 4 ♦ J 7 2 ♣ K 8 2
	SOUTH ♠ A 9 4 ♥ A 10 2 ♦ K 10 4 3 ♣ 9 6 5

Once partner's parity-type and unique suit were identified, it was easy to deduce partner's and declarer's distributions. Reconstructing partner's hand, followed by declarer's, through normal bridge discovery is the approach Vinje takes in his book. It would be useful if there was a quick way directly to identify declarer's distribution symbol once we know that same information for partner. Somewhat surprisingly, there are ways to do exactly that. In his monograph Prism Signals (available free at http://prismsignals.com/PDFonline.pdf), John Sheehan describes one method using what he calls the prism of the hand. We present another method.

As East in the above deal, when partner's unique suit was identified you knew West was ES, dummy was EC, and you were EH. In general, among the three unique suits, there can be exactly one, two or three different suits represented. In this case, three suits were represented: spades, clubs and hearts. You also knew three parity-types; namely, West's, dummy's and your own. Since all three were even, the parity-type division was 3-0. Now look at the table below. Each entry shows how to calculate declarer's parity type (does it match the majority type or is it opposite to that type?) and how declarer's unique suit compares to the unique suits among the hands with known types. Here, from the bottom row and third column of the table, you determine immediately that declarer is ED; that is, he has even parity-type (the same as the even 3-0 majority) and his unique suit is diamonds (the suit not represented).

Parity-type split:	2-1	3-0
Suits Represented:
1	majority (only suit represented)	opposite (only suit represented)
2	majority (suit represented once)	opposite (suit represented once)
3	opposite (suit not represented)	majority (suit not represented)

As an exercise, pick any full hand diagram in any bridge book or magazine. Cover one of the hands and determine the distribution symbols of the other three. Then use the table to find the distribution symbol of the covered hand. After doing a few of these, you will find that you no longer need the table.

Now defend against this spade game (neither side vulnerable):

	NORTH ♠ 5 2 ♥ K Q 5 4 ♦ A 7 6 ♣ 7 6 5 4
WEST ♠ 9 4 ♥ A 10 7 2 ♦ Q J 9 5 ♣ Q 9 8

South and North bid uncontested: one spade — one notrump — four spades.

You lead the diamond queen. Declarer plays low from dummy, while partner contributes the four and declarer the deuce. You continue diamonds, and it goes five, ace, king, three. Three rounds of trumps follow, on which partner plays seven, three, six in that order. You follow low-high and then discard a heart. Declarer now tables the heart eight and you need to have done your homework. You were OC, dummy OD, and partner was ED if the king of diamonds was doubleton. So, from the third row and second column of the table, declarer is OC, and his exact distribution is 6=2=4=1. You must duck the first heart lead to have any chance of defeating the contract. Declarer's actual hand included the eight-six of hearts and the singleton ace of clubs, but, alternatively, had he held the singleton eight of hearts and the ace-king of clubs, partner would have signaled low-high with his three trumps, telling you declarer was OH and 6=1=4=2. With either of these hands, declarer's options were to play for a strip-squeeze (which will succeed) or to go for a three-three diamond split. He can't try both. The distribution signal will not necessarily help declarer on the actual layout. He knows only that West has odd parity-type and East has even. West's odd suit could be diamonds and his partner's even suit could be clubs. But had declarer held the alternate hand, the distribution signal would have given the show away.

In this article, we are not making a case for Vinje's distribution signal either for or against. On one side, his signal does not appear to have a serious following. To begin with, declarer sees the messages that the defenders give each other, and on some deals he will be able to reconstruct the distributions of the defenders. Then, use of the distribution signal means loss of the common trump echo as well as the inability to give a less common suit-preference signal in the trump suit.

Beyond that, there are many deals where one or both defenders may be unable to signal parity-type. A defender may not have two low cards in the signaling suit, for example. Or, it may be far more important to give count in the first suit led by declarer or dummy. With no firm data, we estimate that you will have an opportunity to give the distribution signal on no more than half of the contracts you defend against.

On the other side, when the signal is used we suggest that an opening trump lead from two or three low cards should be the start of a high-low or low-high parity-type indicator. When a defender has three or more low cards in the signaling suit, it is possible to show both parity-type and unique suit. A way to do this is described in the Sheehan monograph. Also, the partnership will need to agree on some firm rules about when count has priority over the distribution signal.

Lastly, tempo becomes very important using the distribution signal. Defenders must be prepared to give the signal without broadcasting unauthorized information. Then, when the signal has been received, the defenders must work out declarer's distribution symbol and exact distribution without a significant break in tempo. The table in this article, committed to memory, may help with that.

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