The Rule of 11 is used for declarer play (or defense) at trick one. It assumes that the opening lead was "4th-best."
It is usually used at notrump, when the lead is assumed to be the 4th-highest card in the suit. By subtracting from 11, the declarer can tell how many cards higher than the card led are in the other three hands. For example:
J 9 7
|K 10 8 5 2|| |
A 6 4 3
When West leads the 5, South does the following calculation:
11-5=6. So there are 6 cards higher than the 5 in the three other hands (North, East, and South). South can see 5 of those 6 cards (the A,J,9,7,6). So he knows that East has only one card higher than the 5. He can then also use bridge logic. He can assume that with KQ10, West would have led the King. So, probably East's one card above the 5 is the King, Queen, or 10. South will probably play the 9 (or 7) from dummy, in the hopes that East's high card is the king or queen (twice as likely as the ten).
A defender can also use the Rule of 11. Say that partner leads the 7 in this situation:
K 6 5
Q 10 8 7
A J 9 2
Declarer plays low from dummy. What should East do?
Assuming 4th-best, East uses the Rule of 11 to get 11-7=4.
East knows there are 4 cards higher than the card led in the North, East and South hands. East can see all 4 of them (A,K,J,9). He knows that South has no card higher than the 7, and accordingly lets the 7 win the first trick so that West can continue the suit.
The Rule of 11 is reliable and easy to remember. Frankly, though, it doesn't come up very often. It is worth knowing, but don't expect to use it more than once every dozen sessions you play.