Do you ever bid quite reasonably to a contract that turns out to be totally revolting?. In the first hand you arrive in 3NT and are faced with the 
2 lead (fourth highest) at trick 1. Of course you will need a lot of luck to succeed, but can you give yourself the best chance possible?
| West | North | East | South |
| Pass | Pass | Pass | |
| 1NT | Pass | 2NT | Pass |
| 3NT | All Pass |
It looks as though you need three things to work: a spade guess at trick 1 followed by successful finesses in diamonds and clubs. That seems to give you a depressing one-in-eight chance. However logical thought can improve your chances to almost double that.
Suppose you knew who held the 
K and 
K. Would that help you guess the spade position? Well, the opening lead suggests South started with five spades, and if he had both missing kings and the A he would have been quite likely to open the bidding with a third-in-hand 1.
For all practical purposes you do know who has the missing kings. Unless South has them your contract will fail! The purpose of bridge is to fulfil your contract, so there is no room for defeatist thoughts. You require South to hold these kings, so assume he does hold them. In that case North is favourite to hold the A so play the K at trick 1.
Of course often this will result in an dim undertrick when South has the A and North holds one of the the missing kings, but the important thing is that on the occasions when it is possible to fulfil your game contract you will do so! Now try to apply similar logic to the hand below, firstly after auction (a) has led you to a cautious spade part-score and secondly after a more aggressive auction (b) has landed you in the spade game.
Each time North leads the 
A and South signals with the Q, denying the K but signalling that the J is an entry to his hand. North duly leads a low heart to South’s J at trick 2 and South puts you to the test by switching to the 6
a)
| West | North | East | South |
| Pass | |||
| Pass | 1 |
Pass | 2 |
| 2 |
Pass | 3 |
All Pass |
b)
| West | North | East | South |
| 1 |
Pass | 2 |
|
| 2 |
Pass | 4 |
All Pass |
You must assume that North has exactly one of the missing club honours, otherwise it won’t matter what you do. Which one? The key lies in the diamond suit. If you knew who had the K it would be fairly easy to read the clubs, but the defenders have forced you to take a view in clubs before you could finesse diamonds.
In fact you should decide for yourself who holds the K.
After auction (a) the only danger to your contract is if South has the K, therefore mentally place South with this card. In that case North must have the A to justify his opening bid, so try the J at trick 3.
After auction (b) your only chance of success is to assume North has the K. In that case it looks as though South is more likely to hold the A to justify the raise to 2, so rise with your K.
Note that the logic with (b) isn’t fool-proof. What you can say is that just about ALL hands with South holding the A and North the Q would be bid this way, while some hands with North holding the A and South the Q might be bid differently. For example suppose North held:
72 AK1097 K5 A1085
Might he not bid a competitive 3 over 2?
Effectively, playing the J at trick 3 gives you the best chance of nine tricks, while the K is more likely to lead to either eight tricks or 10.
In the above examples you placed honour cards as necessary in order to maximise your chances of fulfilling your contract. The same principles apply when you consider the defenders’ shape. There is no point in playing for a distribution that has repercussions elsewhere which will lead to certain failure. How do you tackle the next hand on the lead of the K?
| West | North | East | South |
| 1 |
2NT | Pass | 3 |
| 3 |
Pass | 4 |
All Pass |
2NT shows at least 5-5 shape in the minor suits.
You might vaguely feel that you need a reasonably even spade break, but that is woolly thinking. North has at least ten minor suit cards, so if he has even two spades the hearts will be breaking 4-1, leaving you with four inescapable red suit losers. You require North to hold at least two hearts, so you must assume spades are breaking 5-1. You can almost write down North’s hand:
4 J9 AQ1073 KQJ65
Now we are playing the hand double dummy. Win the A. finesse the 10 at trick 2, cash the AK and continue with high spades, intending to ruff the 9. What if North’s singleton spade is the J? A small singleton with North is four times more likely than the singleton J so you would be unlucky.
Note that if North’s hand has 0-3-5-5 shape you might succeed in practice, but you will be defeated if North ruffs the 10, cashes two diamonds and leads a third diamond. South can ruff high to promote a second trump trick for the defence.