Bridge

Hopes that we would be able to restart social bridge at the club were, like so much else in this extraordinary year, soon replaced with certainty that this would not happen until 2021 at the earliest. In the meantime though, there are lots of opportunities to prepare for that. The rest of this article is intended as a broad introduction targeted at those who might like to take the game up; and follow this link for a quick review of on-line bridge options, for both novices and experienced players. Words in bold type are terms with specialised meanings, defined in the text.

A BEGINNER’S GUIDE TO THE GAME

Most of us have played whist at some point in our lives. It’s a very old game – at least five hundred years ago, the word ‘trump’ (from the French tromper, to defeat) came into use to describe a key development in it, even though the first known book codifying the rules dates only from the eighteenth century. The idea was that one suit would be nominated in rotation to triumph over the rest. A trick comprises four cards played in sequence, won by the strongest card on display, and a game is made up of 13 tricks. The player on the dealer’s left leads first and may play any card. Each player clock-wise in turn plays a card, following suit if possible. If a player cannot follow suit, she may play any card. For each subsequent trick, the player who won the preceding trick has the right to lead. The rules are simple: you and your partner (who sits opposite you) try to win more tricks than your opponents. The game can be played socially or competitively and has spawned many variants. The name ‘bridge’ is believed to be derived from a Russian word, which described one of them.

Contract Bridge (the title initially used to differentiate it from earlier and simpler versions) evolved around the turn of the 20th century in North America. Bridge differs from whist in two key ways: first, the card-play is preceded by a bidding auction in which each bid must top any prior one, and the first positive bid must be to take at least seven tricks. If all four players pass, the hand is re-dealt. The suits are ranked in alphabetical order, each topped by a bid of no-trumps, which as its name suggests, is a contract without any trump suit. It is abbreviated to NT, and the four suits plus NT are referred to as the five denominations. So if the last bid was to take say eight tricks in hearts, it is outbid by a later player venturing to take eight too in spades or NT; but since hearts outrank both diamonds and clubs, she must bid to take at least nine tricks in those suits. The first six tricks accrued by the winning side attract no score; and in bridge-speak a bid of One Club means a commitment to try to take one scoring trick (i.e., seven in all); and it is outranked by a bid of One Diamond and so on all the way to Seven spades and finally Seven NT. That’s a very rare bird to see. The person on the side winning the auction who first mentioned the denomination of play is called the declarer.

The second difference is that after the first card is led by the player sitting on the left of declarer (unlike whist where the lead rotates with the deal), the second hand is placed face-up for the other three players to see. It is called the dummy, because it is played by declarer, not the partner. So, other than on that first lead, play is made with sight of half the outstanding cards.

It was very quickly apparent that there had to be some agreed meanings attached to bids, and that they were in effect a conversation with very few words to describe a very large potential number of hands. And that bidding process rested on an explicit and commonly understood basis for evaluating your hand. The two objectives are to measure the hand’s trick-taking potential, and its ability to limit losers. These are not simply the opposite sides of the same coin. Take these two hands for example, assuming spades are trumps and a club is led.

Hand 1

 

AKQJ104
AQ943
J2

 

Hand 2

 

AKQJ104
AJ94
Q32

I hope you can see fairly readily that Hand 1 is considerably stronger, even though the two share the same range of high and low cards. But look a bit deeper: Hand 1 is stronger for two separate reasons. Having only two diamonds, it will not lose any more tricks than that in the suit thanks to the long trumps; and having five hearts including some attractive high cards rather than Hand 2’s four, it will be much easier to generate a winner or winners from the long cards in the suit. I’d rate it about one to two tricks stronger. (Note, though, that if Hand 1’s hearts were A9432 and diamonds QJ, it would maybe be worth an extra trick half the time).There are some sophisticated hand evaluation systems that claim to measure these differences precisely but for most bridge players, me included, they are too complex. For that reason all but a handful of world-class players are better-off sticking to a simpler evaluation which starts with a numerical assessment of high-card power, then makes adjustments reflecting the length of the longest suit (or suits), and the shape of the hand.

High card strength is usually measured by counting each Ace as four points, King as three, Queen as two and Jack as one. There are thus 40 high card points (HCP) on offer, and on average each hand will have ten of them. The original rule-of-thumb was that a hand needed to contain 13 HCP to open, and more than that to venture into NT. That was because players knew from experience that unless you could limit your losers (and without a trump suit that’s harder) your winners had a bad habit of being engulfed by those held by opponents. NT contracts typically need 21-22 HCP between the hands to win seven tricks, 23-24 to win eight, and 25 or more to win nine. You must remember though that this is a guide, not a guarantee. An instance of this, which can occur fairly frequently, is where one hand has a real powerhouse but partner is very weak. For example, opener and partner pick up the following:

 

Hand 3

Opener Partner

AKQ

J109876

AQJ

32

A5432

Q6

KQ

J102

 

That’s very nice indeed, 25 HCP opposite 4. But if this hand is played in NT, it will rarely make more than eight tricks, losing a top club, the King of Hearts, and three diamonds. It makes ten to twelve tricks in spades of course but who, holding dummy’s hand, is going to disagree with a partner bidding their socks off in NT? This may be an extreme example, but it contains a much broader truth. If you had to rely solely upon face-cards to take your nine tricks against any lead, the minimum to get the job done is several more than 25. Quite a few 29-point, and some 30-point, combinations will struggle to take nine tricks. The reason that the benchmark is lower is that with an NT distribution, high cards perform another function: they stop opponents from developing length winners until you have developed and cashed yours. What they have done is to allow you the time to make the extra. And you won’t do that without the trick-taking potential of lower cards. The higher the spots, and the more you have in the suit, the easier that is.

In a suit contract, a third factor, shape, comes into play. Imagine, for example, that your hand contains only three suits: five spades, five hearts and three diamonds. A 5-5-3-0 distribution happens about once in every 110 hands you pick up. That’s a liability in NT, because the opponents can put you under pressure by leading the void suit. You can’t trump it, and have to discard potentially helpful cards. In a suit contract, by contrast, the void – especially in a suit bid by opponents – is a source of strength, because their high cards can be beaten by your low trumps. Here are a few examples to underline the importance of these factors.

Hand 4: which of these is the best suit, assuming you need five tricks for your NT contract?

A: AKQJ2     B: AKQ432    C: AKQJ9    D: AQJ1032    E: AQJ5432

Believe it or not you can work this out quite quickly from first principles, and you don’t need to be a whizz-kid at probability theory. But to do so you need to turn the problem on its head. Instead of wondering how to quantify the chances of success, consider the conditions for failure. In fact, you can quickly see that none of these hands can guarantee five tricks, and all may fail if one opponent holds five cards in the suit. But set down how they fail.

 

Fails if one opponent holds five cards from

Which include

Suit A

8

any five

Suit B

7

any five

Suit C

8

the ten and any four

Suit D

7

the king and any four

Suit E

6

the king and any four

 

I hope you can readily see that C beats A and D beats B, because the added requirement that the five opposing cards include one in particular makes C and D less likely. So we are left with C, D and E. Think about the analogous situation of tossing a coin. If I asked you to land heads five times, would you prefer six, seven or eight attempts? So even though it lacks the high-card power of the other two, E beats D (thus B) which beats C (plus A). I am not suggesting incidentally that you sit down and do this laborious task every time you are faced with a choice of what to bid: but just to take the key message that both high-card strength and length are important, and that one assists the other with the top cards preventing the opponents winning tricks while shortening their holdings so that your lesser cards become winners.

Here is a harder set of choices. Which of these hands would you prefer as the trump suit?

Hand 5:      A: AKQJ2      B: AQ6543

Hand 6:      C: AKQJ2      D: 1098765432

In the first of these, suit A must make four tricks and will make a fifth quite often. Suit B could in theory make just one trick, and five tricks will be an infrequent outcome. Here, the edge contributed by one more trump is much smaller than that contributed by having three more top cards.

In the second case though, the three extra top cards of suit C are outweighed by the four extra trumps of suit D. If you’re interested in the sums, D must always make five tricks 100%, and has a 50% chance of making seven or more!

From this point on, we will introduce another bit of bridge terminology. Hands are normally labelled with the four cardinal points of the compass, and represented in print with North at the top, West-East aligned left and right in the middle, and South (North’s partner) at the foot. Let’s now array potential trump suits C and D as the best suits of partners West and East and imagine that East is second to bid after North, as dealer, passed.

 

Hand 7 West East
AKQJ2 3
J 1098765432
A32 765
A432

 

If East is a slave to HCP, she will pass because she has none. West will then bid her spades. Even if North enters the fray, West, with 19 of the 40 points available, will probably prevail in 1S or 2S. The maximum tricks available are seven or eight depending on the layout and the lead; East’s nine hearts are of no use at all.

But if East is a knowledgeable player, she will open this hand by bidding 3H – even without a single face-card because she sees that 5-trick guarantee and odds-on 7-trick potential. A savvy West will then think: partner has at least seven hearts for that bid, and my high cards in the other three suits put a huge stop to any winners elsewhere; while that Jack could be priceless given the undoubted length opposite. By contrast, I won’t find it easy to set up the hearts to discard my five losing cards in diamonds and clubs. No-brainer: bid 4H. This contract is odds-on to succeed, even if the opponents can cash their three top hearts separately, which is improbable; in fact it will normally make 11 tricks. You aren’t very likely to pick up a nine-card suit any time soon, but the general message applies: long suits are always useful in trumps, but as side-suits they may be useless unless they are both long and strong. Next is another example of the power of the short suit we saw earlier.

Hand Shape: would you rather declare a contract to take eight tricks in spades with Hand 7 or Hand 8 after partner has signalled a weak support for the suit, but not much else?

 

Hand 8 Hand 9
AJ9876 AJ9876
Q32 KQJ32
KJ
K7 K7

 

The two trump suits are identical, so it’s all about the three side-suits. You might reasonably conclude that the powerful heart suit in Hand 9 makes this a no-brainer, and you would be right. But this fails to reflect another reason to prefer it. Hand 9 offers few opportunities for clever defence to wreck your plans. With Hand 9, there are only two cards that the third-in-hand player can hold that will win the first trick, the Aces of clubs and hearts – and each promotes an extra winner in declarer’s hand. Admittedly, the defence could win the heart and switch to clubs, exposing declarer to two club losers; but only at the price of establishing the heart suit, and guaranteeing no further minor suit losses. Eight tricks are effectively in the bag, and a ninth is likely. By contrast, there are four cards that will win against Hand 8, and all of them would allow the development of two losers in a minor suit. Imagine the nightmare scenario: the lead is a heart, won by the King, followed by a switch to a low diamond, resulting in two losers. Then a second heart is led, won by the Ace, and a club is tabled, leading to a further two losers. Then to cap it all a third heart is led – and ruffed! You set out expecting to mop up eight tricks with spades as trumps, and the defence just cashed the first seven against you. This ability to avoid losers is every bit as vital as that to develop winners.

So to sum up: you evaluate your hands based on a combination of HCP, trump length, and hand shape. A knowledgeable bridge teacher (follow this link) will guide you through this much better than me, but if you are hesitant to proceed too quickly, here’s my view. When I learned the game, bidders were much more cautious, and would stick to the HCP basis of evaluating hands; today, an average club-player will modify the HCP system by adding points for both length and shape. My recommendation for those starting out on the game is to do so sparingly though: learn to walk before you run. Uprate your strength by a point when your longest suit has at least six cards or your two longest suits combined have at least ten cards; or (and not in addition to that) add one point for a singleton or two for a void. But be warned: you must down-rate your hand as well. If you have a void in partner’s bid suit that’s a potential problem; and if you hold a singleton K or Q in the opponents’ suit, kiss goodbye to those points before adding one for the singleton. For those starting out, a simple rule of thumb is not to open the bidding in a suit with fewer than 13 adjusted points, and not to adjust the point-count in NT contracts. As the responder to partner’s opening bid, your threshold figure is six HCP similarly adjusted. More needs to be said about bidding in due course, but let’s conclude by introducing a few basic card-play techniques plus a card-play challenge.

The goal of the player is simple: to maximise winners and minimise losers. These steps will secure you extra tricks. They do not require lots of knowledge, just a bit of common sense and the ability to count!

1 EXTRACTING THE OPPONENTS’ TRUMPS BEFORE THEY CAN USE THEM This is the single most important habit to acquire as declarer. Until you are experienced enough to identify the minority of occasions when you can and should delay doing so, you should seek to remove all opposing trumps, leaving the field clear for your remaining ones.

2 RUFFING IN THE SHORT HAND Usually, one of your hands, declarer or dummy, has more trumps than the other. When the short hand is exhausted of cards in a side-suit, any further leads in it can be trumped. This reduces the short hand’s trumps but does not reduce the tricks to be gained from the long hand.

3 The FINESSE Imagine that you are declarer sitting South, and that you have removed all of the opponents’ trumps, leaving two in your hand and one in dummy. Play them out and you have two more tricks; but you note that dummy has exactly two diamonds, AQ, and you have 432. Oh good; there is a fourth trick available in addition to your two trumps and a top diamond: a ruff in dummy of the third diamond. But play your cards right and maybe there’s a fifth as well. You could play the Ace then the Queen, hoping that the King falls on the first round of the suit. You have more chance of picking three winning numbers in the National Lottery. But don’t waste your money. There are much better odds right here. 50% of the time the King will be in West’s hand – so just lead low and cover whatever card West plays. As defender, you too can try for a finesse. Sitting after declarer and before dummy holding AQ in a side suit, you might surmise that when she does not bother with the finesse, it’s because she lacks the King, but it’s a guess. Great when it succeeds, but she may simply be keeping these as later dummy entries. Maybe you missed a better opportunity focusing on the wrong thing.

As declarer, things get better with other analogous layouts: say the dummy’s suit is AQ10, and as declarer you have 432. Now, played from the top, you have exactly zero chance of making three tricks, and less than 10% of making two, when either the King is singleton or the Jack is doubleton. But you can finesse twice instead, and the odds are that you will make all three tricks 25% of the time and at least two tricks 75% of the time. Much better odds! The defender has no guarantees of course, but the same logic applies: a declarer who spurns the finesse either doesn’t need it or doesn’t want it – and that alone may be a good reason to try when you are to lead playing after declarer, especially if you have no other appealing lead.

As declarer, you don’t have to precisely sandwich an opponent’s high card between two of yours: the logic applies in lots of different holdings. For example, if you have AJ10 in one hand and you lead twice towards it, you will of course lose to either the King or Queen, but you will only lose twice if they are both sitting on the left of the high hand – a 25% chance. So this two-shot finesse is actually a 75% bet for an extra trick. Another holding is where you are say missing the Ace, but hold K2 in one hand. Lead from it and you will lose two tricks every time; lead towards it and 50% of the time the Ace will be in the hand playing second – one extra trick, thank you.

In theory, these more complex finesse plays are equally available to the defence, but only at much greater risk. Declarer has the big advantage of seeing both her and her partner’s hand, so she knows that a finesse is on. For example when you see AJ109 on table, next to play after you, and declarer has avoided the suit so far, you must be tempted to place partner with KQ, and there are two potential tricks for the defence if you lead the suit. Or maybe you are singleton and like the thought of declarer running the lead round to the Queen in her hand – and for your partner to play the King and give you a ruff. Yes it would be nice, but what if partner’s only high card is the Queen? Left to her own devices, declarer might have finessed against you on the 50:50 basis that you might have the Queen, and lost the trick whereas if you lead she will clear the suit for no losers by playing the Jack for a free finesse. This sounds like arguing that the odds are stacked against the defence, and up to a point that’s true; but remember that usually the defence only need a few tricks to defeat the contract. Declarer has the bigger task of making enough!

4 The DROP. The beauty of the finesse is that the odds are so easy to work out. Unless you have good reason to think otherwise from the bidding or play of earlier cards, the odds of a missing card being in either of the hidden hands are 50-50. But sometimes better odds are available. Consider for example (N) AQ985 opposite (S) K76, where North is on lead. Missing J10432 you could play the finesse twice, hoping to find West holding both the J and 10. But that’s only a 25% chance; while reeling off AKQ gets all five tricks more than half the time. Yes, but…what if by chance, all five missing cards are sitting West? You make three tricks by playing for the drop, but five by finessing twice: that’s a massive gain which needs to be factored in, surely? Actually, no. If West has all five, you must still lose one trump unless she misplays, because you need three finesses, not two. In any case, the problem goes away with the last option:

5 COMBINATION PLAY. With that holding, you don’t play low to the King in preparation for two finesses. Just play the Ace first. Now, even when East has all missing five cards, you won’t lose the two tricks that would accrue to the opponents, because you know who has all the missing cards, and you still have a top honour in both hands. So you lead a low card through their holding, limiting your losses to one trick, because they must either sacrifice one of their high cards to drive out yours, or allow you to make a cheap trick with another low card played after their low one. That won’t happen very frequently, and so you follow up by leading towards the hand that only has two cards left. Most of the time, both players will follow, and your five tricks roll in when you play the King. The rest of the time, one or other player shows out. Quite often, you may still make all five tricks provided you were watching carefully! Of the five missing cards, only two, the Jack and ten, are potential winners, and it stands to reason that therefore some of the time that the suit splits 4-1, the singleton will be one or other of them; and that on half of those occasions, it will be East who was singleton. So you lead towards the King, East shows out, but you play the King anyway. Now you have one card left in the short hand, and your opponent has two – but you still have three in the long hand. So you know that when you lead, the opponent is caught. Go up or duck: makes no difference. You still make all five tricks! It won’t work every time, but it will work often enough to be worth the effort. I don’t suppose most of you are too bothered about the maths, but this table shows just how effective the combination play is.

 

AQ985 – K76

Finesse

Drop

Combination

Win all five tricks

25%

68%

74%

Win four or more tricks

75%

96%

100%

Win only three tricks

25%

4%

0%

Of course, there may be somebody out there who is as interested in the numbers as I am. Others can skip this paragraph! There are several on-line resources that will tell you the probabilities of all sorts of things in bridge. I usually consult https://www.bridgehands.com/P/Probability_of_Card_Distribution.htm. That tells you that five missing cards rate to split 3-2 68% of the time, 4-1 28% of the time, and the other 4% it will be 5-0. These are rounded to the nearest whole percentage point by me, which is more than adequate. So the drop is significantly better than the finesse when you are missing five cards, the largest of which is the Jack; but you improve even that by the combination play, if you are careful and clocking up what’s been played.

But it’s worth emphasising: knowing the numbers is less important than understanding the general principle. When you are able to cash a top card without reducing your subsequent options, do exactly that. You will get a possible warning of trouble ahead allowing you to change tack. Here’s another instance: you (N) hold say AK1084 in your hand and (S) J93 opposite. Now, the Queen will only drop when it is held as a singleton or doubleton and that is less than a one-in-three chance. But if you can, you should still play the Ace first because the combination play will save a loser every time that the Queen sits singleton in East’s hand. How irritating it would be to lose the finesse and then discover on the next lead that it would have dropped! The odds are, if you are interested, 33% for the drop, 50% for the finesse, and 53% for the combination play. So the last of these is not a massive gain, but why give away an edge to the opposition?

There are other more complex play techniques available but plenty of social players of the game will find these techniques are perfectly adequate to enable them to play to a decent standard once they are sufficiently practised.

Right, to finish, here is a card-play exercise, Hand 10. Declarer has the task of making eight or more tricks in spades. The opponents passed throughout the auction, which identified that both North and South were just a fraction short of the strength required for a game contract, and South’s shape persuaded her not to risk raising North’s 1NT response to her opening spade bid – a wise decision, since even 2NT might fail if the missing clubs are divided 5-3 and the suit is led at trick one. Instead she bid her second suit, diamonds, and North correctly bid only 2S, regarding her hand as a relatively poor nine HCP thanks to her flat shape and poor intermediate cards (eights, nines and tens, especially in longer suits, will generate tricks a lot more frequently than sixes and below).

So take over as declarer. When the first card is led, these are the 27 cards you can see:

 

North Dummy
J 10 2
A 9 8 4
6 5
A 7 6 5
♠3 led
South Declarer
A K Q 5 4
J 10 7
K Q 7 2
8

 

I’ll leave you with that, and a word of warning. This is not a manufactured hand, but one that I played recently. I led the low spade, and poor declarer play, caused by looking for overtricks in the face of what appeared to be a strong hand – it contains 24 HCP and declarer controls the top five trumps – resulted in failure. That declarer forgot that winning seven tricks when the target is eight will mean that the opponents – who made fewer than you – nonetheless won the hand. So don’t start by wondering how many tricks you might make. Concentrate on how many you can guarantee to make, no matter how the 25 hidden cards are distributed, and note down exactly how you plan to do it. Only once you have arrived at the answer to that can you then look at how to add more. Once you become more proficient, you will be able to do this quickly, but be prepared to take your time and make your practice thorough. It will make you a better player and increase the pleasure you get from the game.