There are a wide variety of discard conventions two of which were discussed on a Tuesday session.
Discard conventions (NOT signals) are only used on the very fist discard made by a player.
McKenney is widely used in the UK and indicates a preference for one of the two remaining suits.
By the two remaining, it means not the suit being led, nor the suit being discarded.
So for example, discarding a diamond to a heart lead excludes anything to do with hearts or diamonds.
A LOW discard requests that the lowest of the remaining two suits is led.
A HIGH discard requests that the highest of the remaining suits is led.
In the above example, discarding a low diamond to a heart lead requests a club lead when appropriate. Discarding a high diamond to the heart lead requests a spade lead when appropriate.
The advantage on McKenney is that it gives the discarder the option of different suits to discard and still suggest the same suit is required.
If a club lead is required in the above example, either a low spade or a low diamond would give the same indication.
If a diamond lead is required to the heart lead, either a high spade (showing the higher of diamonds or clubs) or a low club (showing the lower of spades and diamonds) could be discarded.
Although this may seem complex at first sight, the way to remember is that only two suits are relevant. Ignoring the suit led and ignoring the suit required, inspect the remaining two suits for a suitable discard.
The disadvantage occurs when no suit preference is required, or discarding a high card would be inappropropriate. In this case there needs to be a partnership understanding as to what a neutral card should be e.g. 5, 6 or 7 could indicate no preference.
Dodds is used in East Anglia but not widely used elsewhere.
Discourage ODD card.
Discarding an odd card from a suit indicates that the suit is not to be led.
Discarding an even card from a suit indicates that the suit should be led when appropriate.
The main disadvantage is that to encourage a suit, the discard is from thast suit. In cases showing a shortage, this would be no problem in a trump contract suggesting that a continuing lead may end up in the signaller ruffing a card.
e.g. If the discarding player has a singleton even card, discarding it may lead to a ruff if partner is ab;e to lead that suit.
The other disadvantage is that, when discouraging a suit there is no indication as to which of the other two suits should be led.
e.g. Discarding an odd diamond to a heart could mean a club or spade lead.
To overcome this, the discard should be colour relevant.
Discarding an odd diamond (red) to a spade lead would request a heart.
Discarding an even diamond (red) to a spade lead would request a diamond.