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Suit establishmen

Suit Establishment - how many entries?

Take this side-suit in a trump contract:

 
♦ 6 5 4 3 2
♦K J 9
 
Dummy
W   E
Declarer
 
♦A Q 10 8
 
♦7
Winning a trick may look far-fetched but on the expected 4-3 split as above (62 per cent), you can set up and enjoy a fifth-round length winner. You’ll lose the first round; you’ll get over to dummy (that’s one entry) to ruff a second diamond; you’ll get over to dummy (that’s a second entry) to ruff a third diamond; you’ll get over to dummy (that’s a third entry) to ruff a fourth diamond. And you’ll need a fourth dummy entry to enjoy the fifth diamond.

The number of entries required to set up a suit is equal to the number of ruffs plus one (to get back at the end). Take this side-suit in a trump contract:
 
♣ 8 6 5 4 3 2
♣ ??
 
Dummy
W   E
Declarer
 
♣ ??
 
♣ 7
You don’t know how the six opposing clubs will split. You’ll naturally hope for a 3-3 split but a missing even number of cards does not usually split evenly (3-3 is just 36 per cent). You can hypothesise.

If you have four dummy entries, you can set up clubs if they split 4-2 (lose a club; three club ruffs; back at the end to enjoy two long cards). If you have three dummy entries, you’ll need clubs to split 3-3. If you have just two dummy entries, I’m afraid you can forget about setting up dummy’s clubs for the lack of entries. I hope there’s a Plan B.
South Deals
None Vul
♠ K J 3
♥ J 4
♦ 7 5 2
♣ A 7 5 3 2
♠ 6 4
♥ K Q 9 5 2
♦ Q 9 8
♣ K J 8
 
N
W   E
S
 
♠ 5
♥ 10 8 7 6
♦ J 10 6 3
♣ Q 10 9 4
 
♠ A Q 10 9 8 7 2
♥ A 3
♦ A K 4
♣ 6
West North East South
      1 ♠
Pass 2 ♣ Pass 3 ♠1
Pass 4 ♠ Pass 6 ♠
Pass Pass  Pass  
  1. Forcing to game facing a two-over-one.

As declarer, you win West’s ♥ K lead and count 11 winners. The 12th can only come from dummy’s fifth club. This can be established if the suit splits 4-3, provided there are four dummy entries (three ruffs plus one). ♣ A, ♠ K and ♠ J are three entries. The fourth is more elusive — it’s ♠ 3 but only if you retain ♠ 2.

At trick two, lead ♣ 6 to ♣ A and ruff ♣ 2 with ♠ 7 (not with ♠ 2). Lead ♠ 8 (not ♠ 2) to ♠ J (both following — a 3-0 spade split would have prevented ♠ 3 from being an entry) and ruff ♣ 3 with ♠ 9. Both opponents follow, revealing the 4-3 club split: your plan will work.

Lead ♠ 10 to ♠ K, ruff ♣ 5 with ♠ Q and at trick eight (fanfare), you lead ♠ 2 to ♠ 3. You cash ♣ 7 at that’s 12 tricks and slam made. Only an unlikely opening spade lead, removing a dummy entry prematurely, would have scuppered the slam.