Source: Learning to Think
«I am inclined to think —,» said I.
«I should do so,» Holmes remarked impatiently. CONAN DOYLE
You have probably at some time had the experience of driving along and approaching a traffic light with the sun directly in your eyes. The sun Is so bright that you can’t actually see the signal, but you can see all the other can around you are going through the intersection. What color do you think the light is? Green, of course. You don’t actually know for certain that the light is green (although you’re probably going to find out the hard way If it isn’t when you enter the intersection). What you have done is to draw an infer-ence, or a logical conclusion, from the facts you have observed: the other can are going through, so the light must be green.
You can apply the same logic at the bridge table, particularly on defense. For openers you have to make the assumption that both partner and declarer are playing rationally! (Yes, yes, I know what you are thinking.) If either one makes a completely irrational play, you could find yourself making an even worse one! One idiocy can easily breed another — the bridge equivalent of driving through a red light.
Say you are defending a heart contract and you lead the 
K. You have the 
A, and you notice that there are ten clubs between your hand and dummy. Partner overtakes your opening lead and shifts to a club. There is an overwhelming inference that partner has a singleton club. If partner lets the K hold instead of overtaking and shifting to a club, there Is a negative inference involved: partner is unlikely to have a singleton club.
Here’s another that you should have no trouble with after the last chapter. You lead a low spade against a heart contract and dummy tables with trump support plus the AQI085; you have three little clubs. Partner wins the opening lead and shifts to a trump. The Inference Is that partner has the clubs locked up and that you shouldn’t worry about that suit. If a trump switch is possible, but partner does not shift to a trump, the negative inference is that partner does not have the clubs locked up.
Inferences are also available when dummy tables with a powerful suit such as KQI10(x) or AQI(x) and declarer shies away from the suit. The Inference is that declarer, not partner, has the missing honor.
The following inferences related to discarding were discussed in detail in Chapter 7 of Eddie Kantor teaches Modem Bridge Defense but bear repeating nevertheless:
1) If dummy has something like the 
AKJ(x) and declarer discards a small diamond from dummy, declarer cannot have the Q.
2) When dummy has trump support plus side-suit shortness, yet declarer draws all of dummy’s trumps or draws them after raring once or twice in dummy, the inference is that declarer has no more losers In that suit to ruff. The defenders can now discard that suit with impunity.
Inferences from the lead
Say you are defending a spade contract; clubs Is an unbid suit, a club is not led, and when dummy appears, you can’t see the A or the K. The Inference is that partner cannot have both of those cards (he would have led one). Either declarer has them both or they are split between the two unseen hands. To a slightly lesser degree you can take the same inference when the king and queen of a suit are not visible and not led.
Say partner bids a suit, you support the suit, and partner leads another suit. Why? There are four possible reasons. (I) Partner may have a suit headed by the AQ or the Al and fears leading the suit in case declarer has the king. However, If you have the ace of the supported suit or dummy does, there must be another reason. (2) Partner has a sequence lead In another suit. (3) Partner has shortness with a likely trump entry and is planning on putting you on lead In the supported suit to get a ruff. (4) Partner has forgotten the bidding.
Say partner has preempted. Most preempts contain side-suit single-tons and most partners will lead a singleton without even looking at the rest of their hand. If partner preempts and doesn’t lead a sin-gleton, the inference is that partner’s singleton, if she has one, Is In the trump suit. Unfortunately, sharp declarers are also aware of these inferences as well as the ones coming up.
Another lead inference: say dummy has trump support with expect-ed side-suit length, yet partner leads a trump. The Inference is that partner is strong In the side suit or else partner would not be play-ing a passive defense. If partner leads dummy’s bid and rebid suit, the inference is that partner has a singleton, otherwise the lead is too dangerous.
At notrump with no suits having been bid, partner leads the 2, fourth best, indicating a four-card suit. Early In the play partner turns up with a singleton diamond. The inference Is that partner’s original distribution was 4-4-14. Why? Because with a side five-card suit, partner would have probably led that suit.
When partner leads from shortness at notrump, the inference is that partner’s long suits has been bid.
Inferences from the Play
Many defensive inferences come from the cards played in the suit that has been led. For example, suppose you lead the 5 against a heart contract and are faced with this layout:
| AQ6 |
|
| K10853 |
If dummy plays the ace, the inference is that declarer has a singleton; with two spades, the finesse is the more likely play. Furthermore, if dummy plays the queen, there is an overwhelming inference that partner has the jack. If declarer has the J, declarer plays low from dummy. Wouldn’t you?
This diagram leads to the inevitable question any defender trying to locate a missing honor must ask himself: If declarer has the missing honor, would declarer be playing this way? If the answer is no, then partner has the missing honor.
Now you try it:
| A62 |
|
| K10853 |
Again you are on lead versus a heart contract and you elect to lead a low spade. Dummy flies with the ace; who has the queen? Piece of cake. Partner. If declarer has it, declarer plays low. Later in the hand you can even lead a low spade over to partner’s queen if you need partner on lead for one reason or another.
What about this one?
| 10953 |
|
| KQ64 |
Hearts are trumps and you lead the K, which holds, partner playing the 2. What do you make of this? Partner normally encourages holding the jack or the ace when you lead the king. On the other hand, if declarer has AJ, he takes the trick since the ten in the dummy ensures a quick second spade trick, not to mention the nine. Who’s gone mad? Nobody. Partner probably has J2 and cannot afford to drop the Jack; or she has A2 or AJ2 and doesn’t think it is right to over-take. In any event, partner has one or both of the missing honors.
How about this?
| Q106 |
|
| J 5 |
Diamonds are trumps and you lead the J which rides round to declarer’s ace. What do you make of this? Declarer must have the K. If declarer did not have the K, wouldn’t declarer cover the J with the Q?
And this:
| Q5 |
|
| J962 |
You lead the 2 against a notrump contract, dummy plays the queen, partner the king, and declarer the ace. Who has the 10? Almost certainly partner. If declarer has A10x(x), declare gets two sure spade tricks by playing low from dummy. (However, if declarer has A10 doubleton, declarer might play the queen from dummy.)
And now a big league inference:
| Q5 |
|
| K1084 |
Partner leads the 3 against a notrump contract, no suits having been bid, and dummy plays low. What do you make of this? If declarer has A(x) or xx(x) declarer plays the Q from dummy, so scratch those holdings. Declarer must have the J and partner the A. If declarer has Jxx, declarer cannot be prevented from taking a spade trick: however if declarer has Jx, you can run the entire suit if you make the proper play of the K.
Partner seldom underleads aces on opening lead against a suit contract. Therefore, when partner leads a suit and you cannot see the ace, assume declarer has it and play accordingly.
| KJ54 |
|
| Q96 |
Partner leads the 3 against a club contract. If dummy plays low, insert the 9. The 9 figures to drive out the ace. Partner should have an honor for a low card lead and that honor figures to be the 10. If spades are not led originally, but later In the hand partner shifts to a low spade, now there is a good chance that partner does have the A.
After having led from the top of an honor sequence, your second card in the suit can lead to valuable defensive inferences.
| A754 |
|
| KQJ9 |
You lead the K which holds. Your second play should be the lower or lowest of your remaining equals, the jack. The play of the jack shows the queen but denies the ten.
There is no calculating the number of tricks lost in the following position from players who don’t play this way:
| 743 |
||
| Q |
K86 |
|
| ??? |
Say partner leads the Q against a notrump contract. You signal with the 8, and partner’s queen takes the trick. Now partner continues with the J. Which spade do you play?
Do not overtake with the king to unblock for partner; partner is unblocking for you! Partner’s play of the J denies the 10. If partner has QJ10x(x), partner continues with the 10, not the J. Partner’s actual holding is QJ9 and declarer’s A1052.
Similarly:
| K63 |
||
| Q |
A872 |
|
| ??? |
Partner leads the Q against a suit contract which holds, as you signal encouragement with the 8. Partner continues with the J, dummy covers with the K, and you win the A. Who has the 10? If partner has read this book, declarer has it. If partner has the QJ10(x), partner continues with the 10, not the J.
Leading equal honors out of order (lower-higher) also leads to inferences. For example, if you and partner have agreed to lead the ace from AKx(x) against suit contracts, and you lead the king and then the ace (out of the normal order), the inference is that you have a doubleton. Here is another example:
| 10432 |
||
| A976 |
KQ |
|
| J85 |
Say spades is a side suit at a trump contract and early in the hand partner shifts to the Q and then continues with the K. Since partner has played spades ‘out of order’, the inference is that partner has a doubleton. If there is a danger that the third spade trick can be lost, overtake and give partner a ruff.
When declarer initiates a suit, inferences also abound. The catch is to be able to pick up on them.
| 63 |
|
| Q1054 |
At a heart contract, dummy leads a low spade, partner plays low, and declarer’s nine fetches your ten. What do you think is going on? Declarer cannot have the AK and play this way, and partner cannot have the AK and duck the trick. Ergo, the top spade honors are divided.
If declarer has the king and partner the ace, declarer plays the king hoping to lose but one spade trick. Therefore, declarer cannot have the king: declarer has the ace and partner the king. If partner has given you count or the bidding has been revealing (say South had a chance to bid spades and didn’t), you also know how the spades are dividing.
| 64 |
|
| A83 |
Spades are trumps, dummy has side entries, and declarer leads the K. The inference is that declarer has the KQJ(10)x. With KQxxx(x), declarer would lead a spade from dummy.
Inferences from the bidding
The auction is, of course, a gold-mine of inferences, both from what they have bid and from what they haven’t. Suppose there has been an auction where both sides have been bidding, but no-one has mentioned hearts. Partner doesn’t lead a heart; dummy shows up with three hearts, and you have two. The eight remaining hearts should be split 4-4 between partner and declarer: if either had five hearts the suit would have been mentioned.
Declarer’s and dummy’s bidding can yield an amazing amount of Information, If you listen carefully. In the following auction:
| North | South |
| 1 |
1NT |
| 2 |
Pass |
Unless North is a weak player, he has six spades and is unlikely to hold four hearts. Dummy figures to have fewer than three spades. This sequence is even more revealing:
| North | South |
| 1 |
2 |
2 |
2NT |
| 3 |
3NT |
What do you know about the two hands? To begin with, North has a singleton club: anyone who bids two suits then supports a third figures to have a singleton in the fourth suit. What about South, who persists in notrump despite knowing of North’s singleton club? South is obviously well-heeled in clubs.
So if you had to lead from this hand:
Q42 J5 A742 J542 which card would you pick?
Many experts would opt for the J, a suit where partner is marked with four or five cards. If the opponents had as many as eight hearts between them, hearts would be trumps. They figure to have six or seven hearts, meaning that partner has four or five hearts. In addition, your Inferior club spots plus South’s insistence on notrump facing a known singleton club argue for another lead. The bidding also tells you that partner likely has a singleton diamond. A two-level response is generally made on a five card suit and North surely has three diamonds. Although partner Is likely to have four spades, spades is dummy’s long suit and your spade holding also argues against that lead.
Sometimes you can draw an inference about partner’s hand from the opponents’ bidding, and this can lead to a spectacularly successful defense. Suppose you have A5 6 10963 QJ10652 and the auction goes:
| North | South |
| 1 |
2 |
| 3 |
3 |
| 4 |
4NT |
| 5 |
6 |
| Pass |
What would you lead? The bidding tells you that partner has one diamond at most (with a diamond void partner doubles 6 asking for an unusual lead). Holding the ace of trumps you can envision giving partner a second-round diamond ruff. What about your singleton heart? Probably the worst lead in your hand. A singleton lead against a slam contract works out great if partner has the ace of the singleton suit or the ace of trumps. But you have the ace of trumps and partner can’t have the A — the opponents wouldn’t be in a slam off two aces after a Blackwood sequence! What about the Q? That would be a reasonable choice if the diamond ruff possibility wasn’t so compelling; lead a diamond.
Distributional inferences once the dummy comes down
Once dummy tables, you can often work out the declarer’s distribution by adding the number of cards dummy has in a suit to the number of cards you have in that suit and then figuring out from the bidding the distribution of the unseen hands in the suit. This little gimmick works particularly well In unbid majors.
Say partner, East, opens 1, South overcalls 2 and that ends the bidding. You lead a diamond and dummy has a doubleton heart while you have three hearts. There are eight hearts unaccounted for. If either partner or declarer had a five-card heart suit, the suit would have been mentioned. The conclusion is that hearts are 4-4.
Supported major suits may lead to simple inferences.
| Opener | Responder |
| 1 |
1 |
| 2 |
3NT |
| Pass |
Play responder for four spades. if responder had more than four spades, spades would be trumps. Skipping over mayor suits to rebid notrump also leads to distributional inferences:
| Opener | Responder |
| 1 |
1 |
| 1NT | Pass |
The inference is that opener does not have four spades.
To summarize: One reason bridge experts are experts is that they have the knack of making inferences quickly from the bidding, the lead, partner’s defense, and the way declarer is attacking the hand. Of course, having defended thousands upon thousands of hands doesn’t hurt either. The point is that you, too, can make many of these inferences; those that have been touched upon in this article plus many others you will be able to work out on your own.
Just don’t go through too many red lights!