Lavinthal
A suit is being led and you are out of the suit, and so have to find a discard.
Throw a card from a suit in which you have no interest. You can throw any card from this suit right? Either a high one or a low one. This will depend on which of the other two suits you want your partner to lead when he gets in. A High card asks for the higher of the other 2 suits, and a low card asks for the lower.
Spades are being led and you have a discard to find. Your Diamonds are 9.6.3. Throw the 9 if you want a Heart, or the 3 if you want a Club.
Odd/Even
Sometimes it is difficult to find the right card to discard, so to make life easier, Odd/Even discards were invented. This is just a development of Lavinthal.
ODD
ANY odd card you discard shows you like the suit.
EVEN
An even card shows you do not like this suit……so leaves 2 other suits right? Which two? NOT the suit being led (you have no cards in this suit) or the suit you are discarding an even card from. So is the even card high or low? Your choice: Higher of the other 2 suits or the lower?
Let me give example. Hearts being led, you have none. You discard a spade.
3 of Spades (or ANY odd spade)…… shows a liking for spades.
4 of spades……….calls for Clubs (lowest of other 2 suits
10 of Spades……..calls for Diamonds (Highest of other 2 suits.
Give this some thought. To signal a suit, you can signal with an odd card of the suit, OR an even card of another suit. Gives you options in case you do not have a suitable odd or even card.
Sometimes, and only sometimes, it is helpful to let partner know how many of the suit you hold. I am referring of course to following suit in defence.
The prime example is when an otherwise entry-less dummy holds a long suit headed by the KQ. You play before dummy, and hold precisely 2 cards. Start a "peter" this is the play of high/low.
Partner holding the ace will know how many times to hold up, in order to kill the dummy. There are other times too when it would be helpful to signal to show an even number by Petering.
However don’t get into the habit of always signalling without any thought. It may help declarer as well.