When you have no cards left in the suit that's being played, and you can't trump, either because you don't have any, or the contract is no trumps, now's an opportunity to signal to partner, via your first discard, what suit you'd like them to switch to if they win a later trick. This will generally be an attitude signal. If you play high to encourage, play the highest card you can afford in a suit you'd like partner to lead, OR the opposite if you're playing low to encourage. Then, after that first discard, you still need to be careful of which cards you keep and which you throw away.
Declarer will try to make life hard for you by taking winners in their long suits, so you and partner need to cooperate in what suit to hold and what to discard. Usually when partner is discarding from one suit, you would throw cards of another suit.
Here are some tips to help you make better discards.
(1) If you see a long suit in dummy, even four cards, try to hold your length over that suit. In other words, do not discard from that suit if possible. Keep length over dummy. e.g. you hold: ♠J1086 and dummy has ♠AQ97, don't throw away a card of that suit as a discard. If you do, dummy's ♠7 may win a trick.
(2) If you hold a king and small cards, you need to retain at least one small card with the king to allow it to take a trick (♥Kx. If you started with ♥Kxx, you could afford to throw one away, but not two).
(3) If you hold a queen and small cards, you need to retain at least two cards with the queen to allow it to take a trick (e.g. ♥Qxx. If you started with ♥Qxxx, you could afford to throw one away, but not two).
(4) If you hold a jack and small cards, you need at least three cards with the jack to allow it to take a trick (e.g. ♥Jxxx. If you started with ♥Jxxxx, you could afford to throw one away, but not two).
(5) If partner has led a suit, hold onto at least one card in that suit, preferably two.
(6) If you have led a suit, do not throw away your small cards in that suit, as you may want to make tricks later through length .
(7) If a card could be an entry to your long suit, do not discard it. Hold onto it as long as possible.
On this hand: ♠ 73
♦ 87 ♦AQ93
South is declarer in 1NT
Partner leads their top hearts, and takes five tricks in the suit. On the third heart trick, you need to make a discard. You'd like partner to switch to a diamond, as you'll take two tricks there if played by partner through dummy’s ♦K.
So, playing low to encourage, the card you would discard is the ♦3, and playing high to encourage, it's the ♦9.
Sometimes you don't want to waste a card of the suit you want partner to play, because it may win a trick, so don't encourage in that suit; Discourage in another suit. It will send the same message. The main thing is that partner understands what you're trying to do!
Count Signals when Discarding
When the opponents reach a high level, e.g. slam, your discards can't be attitude, because declarer has all the missing high cards, so partner doesn’t need to give an attitude signal for any suit. Instead this is a situation for count signals. Partner must realise that you will need to know what to hold onto at the end of the hand in order to defeat the contract.
Discarding Losers on Winners
As either declarer or defender, sometimes you have winners in one suit and a different number of cards in the other hand in that suit. Playing that suit will allow you to throw away a loser or losers in another suit. Make sure the card/s you discard are actually losers, and that you are not throwing away the wrong suit
Test your knowledge
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