If partner leads low and dummy plays low, third hand plays high. This is not a signal. When partner leads high or dummy plays high so that third hand cannot win or try to win the trick, this is the moment for third hand to signal. The standard approach is to signal whether you like the suit led or whether you prefer a switch. In standard methods :
High card = Please continue this suit
Lowest card = Please switch to another suit.
High-then-low = Please play a third round.
These signals are not used by the player leading, only by the player in third seat.
You should obey partner's signal unless you know that it is correct to disobey.
In a trump contract, if partner leads an ace or a king, you should signal high-then-low with a doubleton if you want partner to continue so that you can ruff the third round. However, if you are unable to ruff or do not wish to ruff or you prefer a switch, do not play an automatic high-low with a doubleton. High-then-low asks partner to continue. If you do not want partner to continue, play low-high, even with a doubleton.
When you ask for a switch, you cannot indicate which suit you want Partner has to work it out from the bidding, the cards in dummy and the cards in hand.
You want a switch : Play your lowest card.
You do not want a switch: Do not play lowest.
If you play bottom from three or four rags, partner will (should) switch. If you feel it is better for partner to continue the suit led rather than break open a new suit, do not play your lowest. Even if partner's lead has not worked out well, it may be better to stick with that than to create a further loss with another suit.
When you play a middling card, partner will not be able to read it as your lowest You can follow with a higher card on the second round, low-then-high, saying, "I am not interested in a third round." High-then-low says, "Play the third round, please."
For example, suppose partner leads the ace and you have 8-6-5-2. Play the 6 if you are not keen on a switch and play the 8 next if you are not interested in a third round. If you would rather have a third round of the suit than a switch, start with the 6 and follow with the 5 or the 2. Do not confuse this with M. U. D. although the order of playing the cards is similar. M.U.D. is a method of leading a suit. It is not a signal. Signals are in third seat and you may choose to signal in the same order, but that is just a coincidence.
In this method, lowest is encouraging, high asks for a switch and low-then-high asks for a third round (exacdy the opposite of standard methods). This is a sound alternative approach preferred by many experts.
The standard high-encouraging is chosen for newer players who are more likely to notice a high spot card and read the correct message from it. New players tend not to notice low spot cards until they have had quite some experience. To make an impact, therefore, high-then-low may catch their attention.
At top level, reverse signals are superior because you are not squandering a high card when you wish the suit continued. If you have no interest in the suit led, you can usually afford to signal with a high card to show no interest.
In this method, when third player is not playing third-hand-high, third player 'gives count', that is, indicates the number of cards held in the suit led:
Bottom card = Odd number of cards in suit led.
High card = Even number of cards in suit led.
From this signal, partner can deduce the number of cards held by third hand and from this, the number of cards held by declarer in the suit led.
This is a mechanical method which replaces judgment with rote. It is decidedly inferior in many layouts and is not useful in deciding whether third player wants a switch or a continuation.
Again, third player signals only the number of cards held, but the method is the opposite of above:
Bottom card = Even number of cards in suit led
High card = Odd number of cards in suit led.
This is a better way of giving count since the top card of a doubleton is not wasted in a signal. Other than that, it is still a mechanical method which places no value on judgment or co-operation.
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