A Complexity Four Example

This deal has complexity four, as described in the Introduction.

North/South can set up two clubs, three hearts, and two spades. East/West can set up three spades, one heart, three diamonds, and a club. The key, then, is timing.

If North/South declare notrump, the defense starts with a diamond to East, followed by a spade lead (spades cannot be effectively established by leading from West.)

If East/West declare notrump, the defense starts with a club. The best declarer can do is lead a spade to try to break up the communication between the North/South hands. South takes the ♠ K, and cashes the ♣ K.

			♠ A 7 5 ♥ J 9 7 2 ♦ 3 ♣ Q 6 4
♠ Q ♥ K 4 ♦ K 10 4 ♣ J 10 9 8 7						♠ J 8 6 3 ♥ 10 8 6 5 ♦ A Q 2 ♣ —
			♠ 10 ♥ A Q 3 ♦ J 9 8 7 6 5 ♣ K

What does East pitch? If East pitches a heart, then South can play the ♥ A and then the ♥ Q, setting up two hearts in dummy, along with the three tricks taken and the ♣ Q and ♠ A in dummy.

If east pitches a low diamond, south plays the ♥ A and the ♥ Q. West wins, but what does West play?

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If North/South declare diamonds, the defense starts with the ♣ A, then a heart shift. Whatever declarer does, he cannot avoid a heart loser, a club loser, and five seperate trump losers in a cross-ruff.

If East/West declare diamonds, North/South start with diamonds, keeping East/West from cross-ruffing diamonds.

If East/West declare clubs, North/South start with diamonds. The goal is to score four trump tricks via ruffs, in addition to a heart and two spades. Say declarer wins in the East hand, and cashes the ♣ A. Unfortunately for East/West, there is no entry to the West hand to continue clubs:

			♠ A 7 5 4 ♥ J 9 7 2 ♦ — ♣ Q 6 4
♠ Q 9 ♥ K 4 ♦ 10 4 ♣ J 10 9 8 7						♠ J 8 6 3 2 ♥ 10 8 6 5 ♦ A Q ♣ —
			♠ K 10 ♥ A Q 3 ♦ J 9 8 7 6 ♣ K

If a spade is led from dummy, South wins the king, gives North a diamond ruff, a heart is returned to South's ace, and North ruffs another diamond. North cashes the spade ace and then leads a spade at this position:

			♠ 7 5 ♥ J 9 7 ♦ — ♣ Q
♠ — ♥ K ♦ — ♣ J 10 9 8 7						♠ J 8 6 ♥ 10 8 6 ♦ — ♣ —
			♠ — ♥ Q 3 ♦ J 9 8 ♣ K

South ruffs high, and West can either pitch his heart king or underruff. In any event, the defense scores two spades, a heart, two low diamond ruffs, a spade ruff high, and North's ♣ Q.

If North/South declare clubs, the defense starts with the ♣ A, then a heart. Say South wins and leads a diamond, won by West. South loses a trump to the king in South, and North can get one diamond ruff, but declarer is held to two top trumps, a diamond ruff, two spades, and a heart.

What does complexity four mean? Essentially this means that none of the individual suits are parzero. For example, if we take the spade suit:

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

and construct a symmetric deal from this distribution:

			♠ A 7 5 4 ♥ J 8 6 4 3 ♦ K 10 ♣ Q 9
♠ Q 9 ♥ A 7 5 4 ♦ J 8 6 4 3 ♣ K 10						♠ J 8 6 3 2 ♥ K 10 ♦ Q 9 ♣ A 7 5 4
			♠ K 10 ♥ Q 9 ♦ A 7 5 4 ♣ J 8 6 4 3

this resulting deal is not par-zero.