This is a little basic, but a conversation with Kedar taught me that it isn't as obvious as I thought it was. Here goes...
Standard Carding:
This means that when you play high, you are encouraging the suit and when you play low, you are discouraging the suit. These attitudes may be shown in the following situations:
1) When you partner leads an honour.
2) When you are playing immediately after declarer or dummy plays an honour.
3) When you are discarding. Not just the first discard, you may be interested in more than one suit.
Count is shown by playing high-low for even and low-high for odd, when it is obvious that count is more important than attitude for eg. when dummy has KQJxxx and declarer plays the king. You hold two low cards in the suit. Play the higher one first! Partner needs to know how many rounds to duck, and count is very important.
Upside down carding:
The problem with standard carding is that the high card required for encouraging might be too high for you to afford. So, upside down carding involves playing a low card to encourage and a high card to discourage. This is superior to standard carding because, when you need to discourage a suit, you generally have no problems in dropping even a 9 or a 10. You ought to rarely have trouble finding the right card to encourage or discourage a suit. The transition from standard to upside down carding can be a little awkward - habits die hard - but making it is worth the trouble.
Count is still shown the same way in standard carding, though you could of course invert that as well.
First discard:
ACBL rules permit dual-message carding on the first discard alone. Dual-message carding avoids the one problem that upside down carding has: when you discourage a suit, it may still not be obvious to your partner which of the other two suits you want. Two popular carding conventions for the first discard are:
Odd/Even: An odd card encourages and an even card discourages while simultaneously showing suit preference. For example, if you discard the 6 or 8 of hearts on a club lead, you are showing interest in spades, whereas the 2 or 4 of hearts in the same situation would show interest in diamonds.
Lavinthal: The suit of the discard is automatically discouraging while showing suit preference at the same time. So, discarding a low heart on a club lead shows interest in diamonds and a high heart in the same situation shows interest in spades. There is a variation of lavinthal called rolling or sliding lavinthal, but let's not get into that! Lavinthal is generally played only in NT contracts, because that is when you generally want to hang on to cards in the suit you are interested in.
I prefer playing upside down carding with odd/even for first discard (in suit as well as NT contracts), but some people find odd/even discards irritating because you may not find the right card to discard. I don't have a very strong opinion on that but I definitely feel that switching to upside down carding will improve your game.
Remember: it's not just the first discard that is important, you must watch all of your partner's discards - and when he is following suit as well, for that matter!
Cheers,
Prashanth.
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