Sometimes your partner will lead a low card in a suit. What information can you glean from the lead? If you are defending against a no-trump contract, your conclusions are quite simple — your partner probably has led from a suit that is at least four cards long.

There is a little arithmetic ploy you can engage to figure something quite interesting. Here is how it works. Take the value of the card led when you know your partner has led the fourth-best card from her longest suit. For this example, the card is the 8. Subtract the value of that card from the number eleven. The result is the number three. That value tells you the number of higher cards in the remaining three hands — dummy, yours, and declarer's. You can see your hand and dummy, so subtract the number of cards you can see. The remaining cards are in the declarer's hand.

Opening Lead: ♥ 5

Okay, let's try this out in a real example. The contract and the hands are from a real game. Let's not criticize the auction or even consider if it is the best contract. Your partner has led the ♥ 5. Apply our little arithmetic formula and see what you can discover.

The ♥ 5 must be the fourth-best card in your partner's suit. Take the value of the card, 5, and subtract that value from the number eleven. The result is six. That is the number we are going to consider.

Answer the question, how many cards can you see that are higher ranking than the five? One higher-ranking card is the ♥ 9 in the dummy. You can also see three cards in your hand that are higher ranking than the ♥ 5, specifically, the ace, king, and the 8. You see four cards higher ranking than the ♥ 5 — one in dummy and three in your hand. Therefore, the declarer has only two cards higher ranking than the ♥ 5.

You win the trick with the ♥ K and play the ♥ A, winning the second trick in hearts. The declarer follows with the 4 on the first trick and the jack on the second. Your partner played her ♥ 3 on the second trick. You now know how many hearts were in each hand.

Since your partner led her fourth-best heart on the opening lead and then played a lower card on the second heart trick, you know she began with five cards in the suit. Therefore, the declarer has only one heart card left in his hand, and your partner has three more. You lead another heart to the third trick, allowing the declarer to win, and then you just sit back and wait for the roof to fall in on the declarer.

The full deal: