Source: BridgeGuys

This is a designation to describe a ruff with a trump smaller than one already played to the same trick. This principle is also referred to as Undertrump. There are several reasons why this play is valid, although unusual.

In order to avoid a trump surplus. This is also a Simple Trump Coup. An illustration follows:

 6 5 4 3 2 J 5 3 2 Q A 10 8 5 Q A K Q 10 K

South is the declarer and needs four tricks in Spades to fulfill the Spade contract. South, at this trick, plays a Club from the dummy, East covers, and South trumps with the  Ace. West must underruff in order to avoid a trump endplay, because if West discards the  Queen, then South will lead the  King forcing West to trump and lead a trump into the Spade tenace of South. By underruffing, South discovers that the contract is lost. By playing a trump, West knows that South is then forced to play his  King, which East will then win and when East continues with a small Diamond leading through the trump tenace of South, then South is in a losing situation and West collects a Spade trick. Even if South again trumps high, then West must also, on this trick, again underruff to secure the  Jack.

2. In order to avoid discarding winners in a plain suit. An illustration follows:

 9 5 7 2 J 10 9 3 A K 10 9 6 10 6 4 A K J 9 5 4 Q 7 4 3 Q J 7 4 10 3 6 5 2 Q J 8 2 A K 8 2 Q 8 6 A K 8 3 7 5

South is the declarer in a 5 contract. West leads  Ace followed by  King. East had signaled a high-low showing only two cards in Hearts, West continued with a small Heart hoping that South would either play a small trump or that East could overtrump. The problem was that East perhaps would have done better not to have signaled high-low since the declarer was sure to trump high with the  Jack on the third trick. East could not overtrump and this marked West as holding the  Queen. By creating a situation, whereby East may be presented with a discard problem later in the play, East solved this problem by underruffing on the third trick with 2. East did not leave his two black suits unguarded.

By inaccurate declarer play, the contract fails owing to the underruff, but by accurate play South could conceivably fulfill the contract by playing two high Spades, ruffing a Spade, and playing four rounds of trump would have squeezed East in both black suits. East would have to decide which black suit to discard leading to a perhaps error in judgment.

3. In order to have the ability to lead a plain suit at a later period during the play. This is also known as a Roberts Coup. An illustration follows:

 10 2 A Q 5 Q J 9 5 3 A Q J 10 5 K 8 6 4 A

South is the declarer in a Spade contract and requires three tricks to fulfill the contract. West is on lead and leads the 5, which East ruffs with the  Ace. The assumption by the opponents is that this action seems to secure two trump tricks by West, but on this trick South underruffs with 4. East is forced to return the  Queen, which South ruffs. South then leads the  Ace. West, faced with a decision, is forced to ruff with  Queen, otherwise South wins with 10. West prevents this action by trumping higher. South discards from the dummy and West is now forced to lead from his remaining Spade honor.

In the case that South does not keep the Ace to lead to the dummy, then South will be unable to cash four tricks to fulfill the contract. For example, if South leads a low trump then West will play the  Jack and dummy must follow suit. West then continues to play the  Queen which eliminates the 10 in the dummy and promotes the 9 held by West, thereby defeating the contract.

4. In order to avoid a premature squeeze. An illustration follows:

 Q J 10 A 4 3 2 A 4 3 2 9 2 A 5 Q J 10 Q J 10 A K Q J 10 8 7 6 8 7 6 5 8 7 6 5 8 7 K 9 4 3 2 K 9 K 9 6 5 4 3

Although West opened the auction with 2 No Trump, South, in the Pass-out Seat, decided, wisely or unwisely, to enter the auction by bidding Spades. North raised one level and the final contract was 4 Spades, undoubled. West leads the  Ace and South discovers immediately that East cannot have any values. After reviewing the dummy and winning the first trick, West decides to reduce the possible ruffing power of the dummy and switches to playing the  Ace and on the third trick the 5. South wins in the dummy and plays a second Club, which West wins. West switches to the Queen, which South wins in his hand with the King.

When South then leads a Club to ruff in the dummy with his last trump, East must underruff to defeat the contract. If East discards either of the red suits, then South will be able to establish either Hearts of Diamonds, depending on which red suit East discards, as a winner.

Another example follows illustrating the values of the underruff to prevent being caught in the wrong hand and discarding a card, which would prevent the fulfillment of the contract:

 A J 10 9 8 7 A Q 10 9 8 7 2 A K 9 Q J 7 6 4 Q 5 4 3 3 5 4 10 9 8 5 3 2 K J 6 5 4 Q J 10 8 7 6 3 2 K A K 6 2

South is the declarer and the final contract is: 6. The lead is: 3, which East recognizes as a singleton. South seems to be in an impossible contract even when presented as a double dummy. However, South plays low from the dummy, East also a higher Club, and South ruffs in hand. South then leads the  Queen. This play is decisive for South in this double dummy deal. If West plays the 9, then South discards the  Ace. If West plays a higher Spade, then South ruffs in dummy, returns to his hand with the  Ace, leads the  Jack, trumps if West covers, and returns to his hand with the  King to play the 10 to discard the  Ace. South then continues to play the Spades until West decidesa to ruff with the  Queen.

As soon as West decides to ruff with the  Queen, then South underruffs with the  Jack in the dummy. The dummy now holds only Clubs and West, on lead, is void in Spades, void in Clubs, has only the 5 against the 6 in the hand of South. If West leads a Heart, then South wins with the  King, pulls the last trump and runs the winning Spades. If West leads the 5, South wins with the 6 and has only winning Spades and the  King.