A 4-3 fit is called a Moysian, named after Alphonse Moyse. He was an editor of the Bridge World magazine and advocated them in certain situations. A decent explanation is available here. Richard Pavlicek shows a good example of a Moysian on his web site here.
Two friends of mine (Xwing and Kelstac) found a Moysian fit playing online at OKbridge. Often you have a singleton in one hand (making notrump undesirable) and you want to ruff that with the three-card suit. This deal was unique, however, as they ruffed with the four-card suit (hands rotated):
♠ A 9 5
♥ A K J 6 4
♦ A 5
♣ J 6 4
♠ Q J 7 ♠ 10 8 3
♥ 8 2 ♥ Q 10 9 7
♦ 10 8 3 ♦ J 4
♣ K Q 7 5 2 ♣ A 10 8 3
♠ K 6 4 2
♥ 5 3
♦ K Q 9 7 6 2
♣ 9
West North East South
Pass
Pass 1♥ Pass 1♠
Pass 2♣ Pass 2♥
Pass 3♠ Pass 4♠
All Pass
North-South were playing two-way Reverse Drury and so South couldn't bid her diamond suit over 1♥. North made the "expert" call of 2♣ at her first rebid and eventually the pair landed in 4♠.
West led the ♦3. Declarer won the ace and ducked a spade. The defense switched to the ♣K and another. Declarer ruffed and played the ♠A K. When that suit split, she was able to run diamonds and claim 10 tricks via six diamonds, two hearts and two spades. Making plus 420 was a 5.47 IMP pickup.
So, what if the defense started with a club at trick one? Deep Finesse says the contract can still be made. Declarer ruffs the second club, ducks a spade, ruffs a third club in her hand, cashes the ♠K, leads to dummy and draws the last trump.
You can see what all the pairs did if you click here.
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