What is inference in bridge? Before entering into the details lets look at an example.
Let's start with a 'simple' hand. Bidding was South 1 No Trump, and North raised to 3 No Trump. West led 3♥.
North ♠ K 6 ♥ J 8 4 ♦ K 10 8 4 ♣ K 6 5 3
South ♠ A 6 4 3 ♥ K 7 ♦ A J 9 3 ♣ A 4 2
South can see 6 top tricks, and a winning ♥ K, and will need 2 additional tricks.
RHO wins the heart ace and returns the 9. You win the king and LHO follows with the heart 2.
Here's a defensive quiz where you can use the opening lead and the bidding to come up with the right play:
|Dummy (RHO):||Opening lead:|
How many clubs does he hold? Exactly 4 (because the lead shows that partner holds exactly 4 clubs).
How many diamonds? At least 4 (because he didn't raise spades).
How many hearts? Exactly 4. Declarer didn't open 1H, so he has fewer than 5 hearts. It appears that partner also has fewer than 5 hearts, since he surely would have led a 5-card heart suit rather than a 4-card club suit. The 8 hearts that you can't see must therefore be divided 4-4 in partner's and declarer's hands. (Note that you also have a clue that partner doesn't hold a heart honor. Since partner is 4-4 in hearts and clubs and he chose clubs for his opening lead, his clubs are probably stronger than his hearts.) How many spades? You've counted declarer's hand to be 4-4-4 in the other three suits, so that leaves him with one spade. That means partner has three spades with at least one honor.
Note that without a count, you probably wouldn't have expected opener to have a singleton for his 1NT rebid. Many players, however, prefer this approach when they have a 1-4-4-4 pattern. The alternative with this hand is to bid 2C (showing a minor two-suiter), which is also a distortion.
You can also add up the high-card points here. Declarer's minimum notrump rebid tells you he has 12 to 14 points. (If he had 15 pts., he would have opened a 15-17 1NT.) Add declarer's points to the 20 total points in your hand and dummy, and you can determine that partner holds from 6 to 8 high-card points.
Did you find the killing shift? It's right to lead a low spade at trick two. Partner wins the spade ace and returns a spade for down one. Your side will eventually score seven tricks -- three spades, the AK of clubs and the two red aces.
Declarer's hand was: Q KJ109 KQ106 Q1085 Partner's hand was: A43 8432 83 K972
Here's a deal where you can use a discovery play to collect extra information:
|Dummy: AQ9 765||Opening lead:|
So far, you know 9 of his 13 cards -- 6 hearts and 3 spades.
You've seen 10 of his high-card points -- the AKQ of hearts and the jack of spades.
Did he need the club queen to open the bidding? No. He could hold the diamond queen or QJ, which would give him 12 or 13 points.
Extra insurance -- the discovery play:
Before you make the critical play in the club suit, play on diamonds to gather more information about RHO's distribution. Cash the king and ace and trump one of dummy's small diamonds. RHO will follow to all three diamonds, so you now have all the information you need to take three sure club tricks. You may also see more of RHO's high-card points on the diamond tricks, but the most important information here is his distribution.
You now know 12 of RHO's 13 cards -- 3 spades, 6 hearts and at least 3 diamonds. That leaves him with a void or singleton in clubs, so you have a "marked" finesse. Cash the club ace, just in case RHO has the singleton queen. If the queen doesn't fall, finesse LHO for his known queen by leading a low club to dummy's 10.