# Shifting Forces

by Matthew Kidd

This is board 7 from the September 9, 2013 Monday afternoon game at the Soledad Club. South arrives in 2 after the brief auction 1 2 P P; 2.

The straightforward defense begins with the K, east encouraging, small to the A, and a forcing third diamond. How should declarer play?

Declarer has five hearts and two black aces. The eighth trick will have to come from the fourth rounds of spades, assuming a 3-2 break, or from something interesting happening in clubs. Since the eighth trick is slow, declarer needs trump to be 4-3; otherwise repeated forces will leave him with a trump loser in addition to the two diamonds, two spades, and a club that will be lost before the fourth round of spades is established. The 4-3 trump break is a 62% chance a priori. The 2 overcall and defense so far mark the defense with 5=3 diamonds. The diamond split breaks the symmetry of the 4=3 and 3=4 heart splits which are now 37.0% and 26.4% respectively and the total 4-3 chance is 63.4%, slightly better than the a priori odds. In general, known length in a side suit does not decrease the chance of the most favorable trump split very much and may in fact increase it if the side suit break is mild. Do not live in fear of the opponent’s side suit distribution! Even a 6-2 diamond split only pushes the chance of a 4-3 trump break down to 54.4%.

Obviously, declarer can not ruff the third diamond and simply pull trump because West will win a spade and cash the remaining diamonds. One of declarer’s options is to pitch a club on the third diamond, trading a club loser for a diamond loser. Now the 6 in dummy can ruff a fourth diamond. East will overruff to prevent declarer from immediately gaining his eighth trick. But declarer can overruff the overruff and remain in control provided East has the four card trump holding. Then declarer simply draws trump in three rounds and works on spades. West can only force once more with diamonds, after which the ♣A holds the line.

By the way, having assumed a 4-3 trump split out of necessity, the odds are now 7:5 (37.0% to 26.4%) in favor of East having the four card trump holding. You don’t need the 37.0% and 26.4% figures to work this out. If hearts are 4-3, East and West must each have at least three hearts. That means between hearts and diamonds, East has six known cards and West has eight known cards or conversely East has seven vacant spaces to hold the last trump and West has five, hence 7:5 odds.

When declarer bares his ♣A at trick three, West might try shifting to a low club to setup forces in clubs. Since declarer is subject to two more forces when spades are attacked, he must be careful not to draw trump no matter how strong his AKQJT may look. Instead, declarer should play a spade to the ace and another spade. West wins the second spade and forces with the ♣K but declarer simply plays a third round of spades in the position below and is protected against one diamond forces by dummy’s 6. Note that West has no more clubs to force with.

East can try to foil the club pitch by shifting to a low club at trick three. If declarer ducks, West will win and force with the Q. After the ♠A and a spade, West forces with another diamond. This force is protected by dummy’s 6 but the fifth diamond will do declarer in. Declarer needs both the forcing protection provided by pitching the club loser and by dummy’s 6. So declarer must go up with the ♣A at trick three and play the two rounds of spades. If West wins, cashes the ♣K, and forces with the Q, we are back to the preceding diagram. West can allow East to win the ♠Q instead but the blocked ♣K leads to the same result.

A clever West might foresee this blockage and throw the ♣K under the ♣A. but this does not succeed because it weakens the defensive clubs too much. Declarer can pull trump, retaining ♣J9x in dummy, and promote an eventual club trick by leading the ♣8 in this position.

East wins the club and forces declarer with his last diamond, as dummy discards a spade. Down to spades, declarer leads a small one. On a low spade from West, dummy inserts the ♠T and a club in dummy is easily established. On a spade honor from West, dummy plays the ♠A and continues with the ♠T. Either East gets thrown in with the ♠Q or sacrifices it only to see partner concede a spade to declarer at the end.

It may seem that the ♠9 and ♠10 are crucial but that’s not true. Suppose we swap the ♠9 and ♠5 in declarer and West’s hands.

Leading the ♣8 no longer works but a spade does. Dummy can duck whatever West plays with the result that the defense has to help declarer establish a club in dummy or the fourth spade in his hand. The spade duck forces whichever defender wins to commit to helping declarer in spades if a spades is returned or helping declarer in clubs if a club or diamond is returned. In particular, the defense can not split the difference by taking two spades and two clubs or two spades, a club, and a diamond as it could if declarer took the ♠A immediately. You can even let the defense have all the high spades except the ace and it still works out the same. It also works on the original hand.

On the straightforward defense of three rounds of diamonds, declarer can also succeed by ruffing the third round instead of pitching a club. Spades must be worked on immediately, for simplicity say the ace and another. If East wins the second spade and plays a club, declarer must rise with the ace and continue with spades, unless West drops the ♣K in which declarer must pull trump to avoid a club force at trick nine. If West wins the second spade, he can force with a diamond, dummy will ruff, and East will overruff. Things are simple if declarer pitches the losing club but he can also skate home by overruffing, drawing trump, and playing a third spade. The losing club goes on West’s last diamond and the ♣A allows the fourth round of spades to score.

Curiously the 2 contract fails if North is declarer. East can lead a low club and declarer is subject to a sort of Morton’s Fork. The defensive clubs are not weakened if declarer rises with the ♣A and works on spades. West gets to unblock the ♣K as a winner, instead of desperately trying to unblock in under the ace as above, before the defense cashes the K and A. After the two diamonds, East forces with a club and West gets in with another high spade and forces with the Q. The key difference is getting a club force. If instead declarer ducks at trick two, West takes the ♣K. No longer able to avoid one of the diamond forces by pitching a loser, declarer comes up a trick short; for example by three rounds of diamonds and diamonds again each time West is in with a spade.

Unlike the spade situation, the club situation is very delicate. East needs at least the Q-10 tenace for the opening club attack from his hand to succeed. If the ♣9 and ♣10 are swapped between North and East, declarer comes home by ducking the first club to the ♣K because East can only get one club in this end position where South is on lead after pulling trump.

Conversely swapping the ♣8 and ♣4 between the South and West hands, weakens South’s clubs enough that East can succeed by leading a diamond in addition to one of the two low clubs because West can successfully attack with the king from ♣K7 after say the A and K, and East can force later with the ♣Q, retaining the ♣T-8 tenace behind North’s ♣J-9. Swapping the ♣8 and ♣6 between the North and West hands such that three small clubs are rearranged restricts East again to a low club lead in order to succeed.

Hands where the double dummy analysis for a normal contract yields a different result at opposite sides of the table are often worth investigation. At least half the time the reason for the discrepancy is immediately apparent, for example the lead through a tenace rather than a lead to a tenace. But perhaps a quarter of the time something interesting lies in wait. Go forth and examine hands.