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Feature Articles
from monthly BCCM Newsletters

All articles by club members.

  Reverses by Steve Ault

Upon arriving at the Bridge Club for the first time, I was mystified by the four little contraptions set upon each table. I had never encountered a bidding box before. But with my renowned manual dexterity, I managed to master their operation in little more than six months. (There are those who claim I still haven’t mastered it.)

A few boards into my inaugural session I was dealt a typical weak two bid hand, but first I dutifully pulled out a stop card. RHO took all of a millisecond and then passed. “What gives?” muttered I. In days of yore, before the advent of bidding boxes, we would say “Skip bid” before jumping a level, and LHO was obliged to wait ten seconds before bidding. I called the director. Director shrugged his shoulders.

Some boards later, partner opened 1C or 1D. With 5 spades and 4 hearts I bid 1S, of course. Partner then bid 2H. And so, with 4 hearts and 9 points, I confidently bid 4H. Partner went down 2 tricks, having reversed with 12 HCPs. I was shocked. Just about 50 years had passed since it was explained to me why a minimum of 16 HCPs is required for a reverse.

It is the last of these three little episodes that shall be the focus of our presentation: reverses.

What is a reverse?

A reverse is not a highfalutin add-on convention or bidding system. It is basic to the game, just as basic as a strong jump shift rebid by opener. It can be said that a reverse is actually more fundamental to bidding than the Blackwood and Stayman conventions we all play and take for granted.

A reverse is a rebid on the 2-level by opener after partner’s 1 level response (including 1 NOTRUMP!!) of a suit of a rank higher than that of the suit of the opening bid. There are 10 possible reverse sequences (We assume here that our friendly opponents are not being obnoxious by fouling up the works with bids of their own.): 1C-1H-2D, 1C-1S-2D, 1C-1S-2H, 1C-1NT-2D, 1C-1NT2H, 1C-1NT-2S, 1D-1S-2H, 1D-1NT-2H, 1D-1NT-2S, 1H-1NT-2S.


The additional point count requirement for a reverse is the default for standard bidding, but thereare some who say, “I don’t play reverses.” If not, partner needs to alert opponents that the bidmay not have the additional values customarily required for a reverse. And, these partnerships should not at all be surprised by frequently finding themselves in trouble at the three level.

The reason for the higher point count requirement for a reverse is quite simple: responder mustbid on the 3 level to show a preference for opener’s first bid and longer suit. Let’s illustrate thispoint by taking the first example, 1C-1H-2D. The responder may have bid 1H with only 6 points and perhaps 4 hearts and 3 cards in the other suits. A club contract is desirable given the obvious 8 card fit or better, but to support clubs the bid has to be made on the 3 level. If the opening bidder has 12 or 13 points, well, good luck—you most assuredly will need it.

Opener’s first suit is almost always longer than the suit of the rebid. It can never be shorter. Thetypical distribution is 5-4, but more extreme distributions such as 6-5 or 6-4, etc., are possible. With the more extreme distributions, the minimum point count requirement is lowered if all the points are in the long suits. A 6/5 hand can reverse with 14 HCPs or even 13 with good spot cards (10s and 9s).

For contrast, let’s change the auction a bit. Instead of 1C-1H-2D, we have 1D-1H-2C, and let’s as-sume partner has the very same weak hand with 4 hearts. It looks like opener has at least 5-4 dis-tribution in the minors with longer diamonds. But this time the weak hand can support opener’s first bid, 5 card suit at the 2 level by bidding 2 diamonds. The reason: opener’s second bid suit isof a rank lower than that of the first. Here, there is no reverse.

After a two over one response, e.g., 1D-2C, the additional point count requirement for a reverse is lifted. Reason: responder must have at least 10 points and thus reaching the 3 level should not prove to be disastrous. Opener can bid 2H or 2S with minimum values.

We stated previously that a requirement for a reverse is for the first bid suit to be almost alwayslonger than the second. “Almost always” seems to imply an exception, and indeed it does. There isone kind of hand that is extremely difficult to bid unless one happens to play the Roman 2 Diamond Convention: a strong hand with 4-4-4-1 distribution. If the spade is the singleton and you open 1C or 1D and partner bids 1S, a 2H bid is acceptable. Some, however, prefer to open such hands 1NT if the singleton is an ace or king.

Standard bidding practice is for opener to jump shift with a least 18 or 19 HCPs. The upper range is about 21 HCPs with distribution not suitable for a NT bid. A jump shift is virtually forcing to game. Some play that it is 100% forcing to game. A reverse has a lower minimum (16 HCPs), butthe same maximum. A reverse is forcing 1 round but not necessarily to game. A bid that’s both areverse and a jump shift, e.g., 1C-1S-3H, has an entirely different meaning: instead of length, thebid shows shortness, either a singleton or void, plus a good hand with strong support in partner’ssuit. This bid is known as a splinter.

What to do after partner reverses

It’s time to reevaluate the hand. With 9 points or more, game or higher should be reached. Withless, game should be attempted only if the reversing hand has values above the minimum.

With less than 9 points the following options are available: bid partner’s first suit with 3; raise partner’s second suit with 4; bid 2NT; rebid your suit with 5 or more. Passing is not an option. Thereversing hand will probably pass with a minimum. With a stronger hand partner will continue to bid, either bidding game or inviting to game.

With 9 or more points one can bid 3NT or game in one of partner’s suits, jump to the 4 level withsupport in a minor where 3NT is not a good option, jump in your original suit with at least 6 cards, or bid the fourth suit. The forcing bid of the fourth suit can serve as a check back for 3 card support for your 5 card major, or it can be asking for a stopper for bidding 3NT, or it can be none of the above. Sometimes a forcing bid is needed to get partner to reveal more information about the hand.

What if you have a hand that has the correct distribution for a reverse but is too weak?

Look at the ten possible auctions that include a reverse. A 5 card minor could be rebid if it is half decent, partner’s 1NT bid can be passed, you can bid 1NT, and finally, partner’s major suit bid can be raised with 3 card support. As a rule, partner’s bid should not be supported with a holding ofonly 3 cards, but sometimes one has to make the best possible bid when there are no good alternatives available. Landing in a 4-3 major suit fit is sometimes the best option, especially if the hand with 3 trumps has a singleton or void.

Problem hands

With minimal opening values, holding a 5 card minor and 4 hearts and doubletons in the other two suits, opener bids the 5 card minor. Partner, with a weak hand holding 5 spades and 4 hearts, responds 1 spade. Opener is too weak to make the reverse bid of 2 hearts, so either a rebid of the minor suit or 1NT are the remaining options. Partner, with a weak holding, cannot introduce a new suit at the 2 level, which is a forcing bid, and therefore must pass. Thus, the desired contract of 2 hearts is missed.

Things can get really dicey when opener is holding a 6/5 hand that wants to reverse but is too weak. The solution here is to treat the hand as if it were 5/5 and open the higher ranking 5 cardsuit. With the rare 7/5 hand, you’re really in a quandary.

  Overcall Bids by Bernard Garwood

An overcall is a bid you make after the opponents have opened the bidding. For a suit overcall, the most important requirement is that you have a good 5-card suit. Points are secondary. With a good suit, you may overcall at the l-Level with as few as 8 points. It is always a good idea for you and your partner to have some form of agreement on your overcall bids as well as the responses to them. Do you have such an agreement?

The 1-level Overcall

A 1-level overcall can be made with very few points, but it shows at least a good 5-card suit. How many points needed? Many players use a range of 8 to 15 HCP*. A minimum of at least a 5-card suit is a must (plus some colour, i.e., honours, 2 or more).

Requirements for a 1-Level Overcall:

  • A good 5-card suit, with at least 2 honors

  • A good 6-card suit with 1 honor, or a good 7 card suit

  • 8 to 15 High Card Points̉

  • If you have 16+ HCP, you should “double” rather than overcall

The 2-level Overcall (Non-jump)

An overcall at the 2-level requires a better hand and a better suit.

Requirements for a 2-Level Overcall:

  • A good 5-card suit, with 3 honors

  • A good 6-card suit with 2 honors

  • 10 to 15 High Card Points

  • If you have 16+ HCP, you should “double” rather than overcall

*Some partnerships may want to agree on a higher point count range for overcalls, so you should consult with your partner on this. The main thing is that whatever your point range, each of you is aware of the points indicated by a particular overcall bid.


So, you don't need many points to overcall and you also notice that in addition to a good 5-card suit, some honours are required within those cards. But the points within any given hand are not always distributed equally. In some holdings your points may be nicely divided throughout all four of the suits, but in other holdings, you may find all, or most of your points are in just one suit. If that is the case and it is your overcall suit where most of your points are located, then the quality of that suit is even more important when you are deciding whether or not to overcall. In those cases you should use the Suit Quality Test (SQUAT or SQ test) to help you decide whether to over- call or not.

This is sometimes called the “Squat” test, or “Squat” rating, since that term provides a clever andinteresting memory aid to help visualize and remember it.

The Squat Test measures suit quality / strength and whether the suit is strong enough to bid at a given level. Useful just about whenever suit quality is a relevant criterion, it is useful for pre- empts, weak twos and overcalls.


Number of Cards in the suit + honours in that suit

Count the number of cards in the suit and then add the number of honors in that suit. The answer is the SQ, or Squat rating, of that suit. For example, A-Q-7-4-2 has 2 honors and 5 cards. 2 + 5 = SQ of 7. The 10 is counted as an honor when the Jack is also held but only if the two are com- bined with a Queen or higher. A holding of J-10-9-7-6 is only an SQ rating of 6 while the K-J-10-9 -7 is an SQ of 8.

The SQ should equal or exceed the number of tricks for which you are bidding. A contract of one of a suit (seven tricks) requires an SQ of 7. A holding of K-J-9-5-4 has an SQ of 7

(2 honors + 5 cards). That is good enough to overcall at the one-level (assuming you have enough extra strength) but not strong enough for a two-level overcall. With an SQ of 6, such a suit is not good enough for an overcall even at the one-level.

You may insist on a suit as trumps if you have a suit with an SQ of 10, For example, suppose you hold:

  ♠ A 3  K Q J 10 6 4   8 7  ♣ Q 3 2   Hearts = SQ10; 6 cards + 4 honors

Consider these four (4) holdings when your RHO opponent opens the bidding:

1. ♠ K 2   K Q J 10 9    9 8 7 6  ♣ 7 6    SQUAT = 9  

2. ♠ A K 5 4 3   J 3 2   8 7 4  ♣ 6 5      SQUAT = 7  

3. ♠ J 9 5 3 2   7 4 2   A K  ♣ K Q 4      SQUAT = 6  

4. ♠ A J 10 5 4 3   7   J 10 3 2  ♣ 4 2    SQUAT = 9


It should be pointed out that the Spade suit occupies a special place in these situations due to the power it holds.

Let’s look closer at those hands in an actual deal:

Holding 1

Dlr: South
Vul: N/S
♠ 8 7
  A 8 6 2
  A 5 2
♣ K Q 9 8
♠ K 2
  K Q J 10 9
  9 8 7 6
♣ 7 6
  ♠ 10 9 5 4
  K Q 10 4
♣ 5 4 3 2
  ♠ A Q J 6 3
  7 5 3
  J 3
♣ A J 10

You are West South has opened 1♠ .

You have only 9 HCP, with most of the points in your heart suit - and an almost perfect Heart suit with a Squat rating of 9, which says you could overcall at the 2-level here.

Consider: You are not vulnerable. The opponents are.

Overcall 2  ! You may find a fit with partner but if not, at least your partner will know what to lead if North ends up playing the contract in no-trump. This is the same bid you would have made had you been the opening bidder.

Additional Note on Suit Quality: Another reason for being concerned about suit quality is that if you do not get the contract, your partner is probably going to lead the suit in which you overcalled! As a general rule, don’t overcall in a “trash” suit.

Holding 2

Dlr: West
Vul: All
♠ A K 5 4 3
  J 3 2
 8 7 4
♣ 6 5
♠ 8 7
 K Q 9 4
 J 6
♣ A Q J 8 2
  ♠ 9 6 2
 A10 8 6
 Q 10 5
♣ K 4 3 
  ♠ Q J 10
 7 5
 A K 9 3 2
♣ 10 9 7

You are North West, your RHO, opens the bidding with 1♣ .

Your hand is not high in points (8) but with a SQ 7 rating in your nice Spade suit, it is an easy overcall of 1♠ here, which blocks East’s 1  response.

Overcall 1♠ .

East may then “double” (negative), to show 4  . Your partner, south, should then support your Spades. SEE: Responding toYour Partner’s Overcall, below.

If East-West does manage to get to 3, then North-South would do well to go to 3♠ , losing 50, or 100 if doubled.That’s better than giving away 140.

Holding 3.

Dlr: West
Vul: None
♠ J 9 5 3 2
 7 4 2
♦ A K
♣ K Q 4
♠ A 6
 A K 9 5 3
 J 9 4
♣ J 8 3
  ♠ K 10 4
 Q J 10 8
 Q 10 8 5
♣ 7 2 
  ♠ Q 8 7
 7 6 3 2
♣ A 10 9 6 5

You are North not vulnerable, West has opened 1  .

Your Spade suit is awful. - Do you overcall? A Squat Score of 6 is not enough for even a l-level overcall.

But, remember we mentioned the special nature of the Spade suit and while here it is weak, the rest of your hand is good, with 12 HCP in the other three suits.

An aggressive player here, not vulnerable, while not proud of his spades, would overcall 1♠ , for even if no fit is found, he is somewhat protected by the strength in the other suits.

If North does overcall 1♠ , East could make a pre-emptive raise to 3   showing a fit that includes 4 trumps. Three hearts will make and 3♠  would go down -1. But even if they double, losing -50 or -100 is still better than allowing East-West a score of +140 for their 3  . In general, when the opponents have an 8 or 9 card fit between them, then your side also has a fit somewhere. If your suit is Spades, then you have the upper hand and can make sacrifices at a lower level.

Holding 4.

Dlr: West
Vul: E/W
♠ A J 10 5 4 3
♦ J 10 3 2
♣ 4 2
♠ 8
 A K 8 4 2
A 8 5
♣ K 9 7 3
  ♠ 9 6
 Q J 9 6
 K Q 9 7
♣ Q J 5 
  ♠ K Q 7 2
 10 5 3
 6 4
♣ A 10 8 6

You are North. Your RHO, West, opens 1   The opponents are vulnerable.

You have a very weak hand but good playing strength in spades. Should you overcall? Squat score is 9 and so you could overcall 1♠ here.

But even better, if you and your partner play weak jump overcalls, then a 2♠  bid would be more disruptive and would also tell your partner (and opponents) more about your hand. The 2♠  bid here would be similar to a Weak-2 bid.

Make an overcall bid of 2♠ .

South, now knowing more about your hand shape from your 2S overcall, could easily go to 4 Spades here -- even 5 if necessary would be a good sacrifice.

As you can see, the choice to make an overcall bid is not always just a question of to do it or not. You may want to compete for the contract, or sacrifice, or maybe give your partner a lead- indicating bid, but any overcall you make is obstructive to the opponents. Factors such as vulnerability, points, hand shape, the spade suit, the Squat Rating, etc., all run through your mind when making a decision. You consider all these factors. That is part of the fun and interest of this game.


Weak: with 6 cards you should jump-overcall if you have a "weak two" kind of hand in any suit.

Strong: with a 6-card suit and 16+ HCP, double for takeout and then rebid your suit. (With 5- cards you'll need 18+HCP)

Very Long: with 7 cards double-jump-overcall if you satisfy all the preempting conditions

If you don't have these three situations, then a simple overcall is the right thing to do in each case.


When your partner makes an overcall, he is hoping to find a fit for his suit in your hand. Either you will have no fit - or you will. If you do have a fit, then factors such as the combined number oftrumps you hold, suit distribution and “dummy points” come into play. His overcall has given youa point range of his hand and if you should have a fit, then you can quickly come up with a point range of both of your hands combined. Many competitive bidding situations result in a partnership winning a partial score contract.

Here is a fairly easy guide to remember that can help you in your decision-making:

Try to remember the following:


For a 1 trick suit-contract

16 to 18

For a 2 trick suit-contract

19 to 21

For a 3 trick suit-contract

22 to 24

For a 4 trick suit-contract

25 to 27

For a 1NT contract

19 to 21

For a 2NT contract

22 to 24

For a 3NT contract

25 to 27



It is very difficult to compete if you and partner have no fit, so if you cannot support partner's suit it's usually best to pass his overcall. You should only suggest a suit of your own if it's likely to be superior to his – e.g. if he overcalls in a minor and you have, say AKQxx of a major. You may have a singleton in his suit . . .but he may well have a void in yours.


Then you can combine your points with those he is showing and get an initial idea as to the range of your combined strength. The guideline above is fairly easy to commit to memory. If you do have a fit with partner’s suit, then it is most important that you show this immediately, for if you delay, you may not have a chance later.

How you show a fit and your strength depends on whether or not your Right Hand Opponent (RHO) makes a bid (competition!) after your partner overcalls.

WHEN YOU HAVE A FIT (In competition, when both opponents are bidding)

a. Bid the opponent’s suit (cue-bid) if you have support and 10+ points.
Bidding has gone:   LHO       Partner        RHO        You
          1♠           2          ?

You are holding:  
♠   A K 9 8     K 10 9 7    9 8   ♣  9 7 2

Bid 3  , showing support and 10+ points.

b. Bid partner’s suit direct if you have support and less than 10 points.
Bidding has gone:   LHO       Partner        RHO        You
          1           2          ?

You are holding:  
♠   K J 10 2     Q 9 8 3    9 7 2   ♣  J 8

Bid 3 ..... to the limit of the Law of Total Tricks. If you're not vulnerable, you can do this with a very weak hand. Caution if you’re vulnerable! If so, then you will want to have some HCP.

The Law of Total Tricks (LOTT) says that you and your partner can generally bid with a fair amount of safety to the level equal to the total number of trumps between you. That is, if partner overcalls one Spade and you are holding 4 spades, that is a total of at least 9 between you, which is enough for a 3 Level bid.


a. Bid your normal responses:
   Bidding has gone:      LHO    Partner     RHO      You
       1♠        pass      ?
   You are holding:  
♠  A K 9 8      K 10 9 7      9 8    ♣  9 7 2

Bid 3 , showing 4-card support with 10-12 points.

  Take-out Doubles by Jim Peukert

A take-out double is exactly what the name implies: “Partner, take me out of this double by bidding something...anything.” Since the double is not for penalty, partner must bideven with the worst hand imaginable, with one important exception: if there is an inter-vening bid by the opposition, then partner is “off the hook” and can choose to bid if andonly if he has something to say, like 7 points or more and an okay suit.

The range of High Card Points (HCP) for a take-out double is 9 or 10 at the low end all the way up to 22 or 24 at the high end. In contrast, the point range for an overcall is 8 to 16. That upper range difference, namely 17 to 24 HCP is important: once an opponent has bid, a take-out double is the only way to show that range. By simply overcalling, your partner will assume that your hand is not particularly strong, and with a bust hand he can actually pass your overcall. The double on the other hand is positively forcing, and you can feel secure that doubling with your 20 HCP hand will not be passed out by partner, and you will have the opportunity to show a really big hand at your next bid.

When do you bid a take-out double?

A take-out double is used following a bid by an opponent. It need not be your right hand opponent (RHO), but it is normally bid at the first opportunity. Ideally, it says to partner that you can support any of the other three suits, and particularly the other major suit if the opponent has opened in one of the majors. The absolute perfect distribution for a take -out is 4-4-4-1, with the singleton being in the opponents’ bid suit. With the perfect distri-bution, the person bidding the take-out needs only about nine or ten high card points. As the distribution becomes less perfect, say 4-3-3-3, then one should have more like 13 or 14 points.

With some exceptions, a take-out double should not be used if the bidder has a 5 or 6 card suit. Rather, instead of doubling you should simply overcall. But an exception to this is if the person doubling has 17+ high card points (HCP). In this case the bidder should double and then on the next bid introduce a new suit. Conversely, with minimal HCP theperson bidding the double should not bid a new suit: either raise partner’s response orpass. The other exception is when the opponent has opened with a major suit, and the person making the take-out double wants to show four cards in the other major. (If he had five cards, he would overcall rather than double.) In this case he could also have a five card minor, but, again, with this kind of shape not being ideal, the point count should be at least an opening hand.

Where is the partnership going with this?

It usually winds up in a part score, but one that the partnership might not have found without using the take-out double. The opponents have at least one opening hand, or 13HCP, and even if opener’s partner has zero, the absolute maximum our side can have is 27. So though it is possible that a game is in the offing, it’s not likely.

The key points to remember when considering a take-out double are the shape of your hand and your point count. It is important to keep in mind that the only way to show partner a really big hand after an opponent opens the bidding is to make a take-out double and to bid a new suit on your next bid. It is equally important to remember that youmust respond to your partner’s take-out double. You may be reluctant with a 1 HCP handto say anything, but keep in mind that your partner is very likely short in the opponents’ suit, and to pass would be to “convert” the take-out to a penalty double. If you have fiveor six or the opponents’ suit, you can consider this, but a penalty double at a low level isusually not wise.

Responding to a take-out double?

A take-out double is forcing for one round, so partner must respond even with zero points. The logic of this is that the opponents would have no trouble making a one bid doubled, and this would probably give them a high board. And when we have that zero point hand,

bear in mind that the opponents may have a good chance at bidding and making a game,so it is not likely that we will be caught “holding the bag” with our zero-point response. It is best for responder to favor bidding a major suit with at least four cards, even if he has a better minor suit.

If responder has either 8 HCP with a good suit or 10 HCP with a so-so suit, he should respond with a jump bid in his best suit. If he has 12 points or more and a decent suit, he should make a double-jump bid. Note that if the two hands have a great fit, then game can be bid and made with a combined total of only about 20 or 21 HCP, and it may be one of those cases where neither of you had enough points to open.

When is a double for penalty rather than take-out?

This is largely a matter of partnership agreement. Doubling at the four-level or above is usually for penalty with the possible exception of doubling a pre-empt at the four level. Again, you must have a partnership agreement to define when the double is take-out and when it is for penalty. Some partnerships include the three-level to double for penalty, but this can be dangerous by doubling the opponents into game and at the same time giv-ing them a “blueprint” of how to play the hand.

Do I ever pass a take-out double with no interference?

Yes. If your hand has a “stack” (5 or 6) of the opponents bid suit, and no biddable suit ofyour own, you can pass and thereby convert the take-out double to a penalty double. Also, converting to a penalty double should come with at least 7 or 8 HCP. Beware that yourpartner will be fuming until you actually set the opponents’ bid. A general rule is that theweaker your hand, the more necessary it is to respond to the take-out double.

Assuming there is interference, and I pass, what does it mean if my partner doubles a second time?

Although this is, again, dependent on partnership agreement, usually the second double is for penalty, and it is likely that your partner has a big hand sitting behind opener.

If I open, my left-hand opponent overcalls, and my partner doubles, is this still a take-out double?

Yes, but it is more specific than a take-out over just one bid. It is a “negative double,”and it implies that the person doubling has four cards in each of the unbid suits, and at least 8 HCP. If the suit bid by the opponent is a major suit, then the person doubling definitely has four of the other major, but maybe not four of the other un-bid minor suit.

“I hope I have answered some of your questions regarding take-out doubles. If you have any others or (heaven forbid) disagreement regarding what I have written, please send an email to the newsletter and I will respond. If I am found to be wrong on a given topic (which is not unlikely) I will try to use my accident to build sympathy for the error—this is wearing thin, so voice your complaints soon.”


  Support Your Partner by Andrew and Pippa Hooper

You probably learned as a beginner that you need 4 cards in a suit to support partner unless you know partner’s suit is 5+ cards. This is not the whole story. Read on.

Whenever you open one of a minor suit and partner replies with one of a major suit, your best option is likely to be raising partner’s suit when you hold a minimum hand, 3 card support and a side suit shortage.

As Opening bidder you open 1♣ on any of the following hands:


♠ Q102 ♠ K73 ♠ K73 ♠ KQ106
 AK84  85  1075  1075
 54  AQ7  AQ7  J5
♣ A864 ♣ K9653 ♣ K965 ♣ AK96


Partner responds 1♠ on Hands A, B and C. What should opener rebid?

With hands A and B your rebid should be 2♠. Your partner needs to understand that the single raise of a major in this sequence can also mean 3 support cards and a doubleton or a singleton. Neither of the above hands is suitable for a 1NT rebid and bidding clubs again should show a 6 card suit.

With hand C the recommended rebid is 1NT. You have 3 support cards, but no shortage. Failure to raise partners major suit strongly implies that while you may have 3 support cards you do not also hold a side suit shortage.

How should responder continue after opener has bid 2♠?

With a minimum hand:

Pass and learn to play a Moysian Fit. The 4-3 fit is named after Alphonse Moyse Jr 1898-1973.

With an invitational or better hand:

With 4 cards in your major you will probably prefer to play in NT if partner is supporting you with a 3 card suit. You can find out by bidding NT or other sensible bid at the appropriate level.

These bids mean: Partner, if you have 4 card support for my major suit please bid it again. Otherwise pass or bid NT.

With a 5+ card major, bid or invite game in the major suit. You do not need to know if partner has 3 or 4 card support.

Opposite hand D, partner responds 1.

You have 3 support cards and a doubleton – but on this hand you should now bid your spades as you don’t want to miss a possible 8 card spade fit. As the auction develops further you should get a chance to show the heart support.

The concept of supporting with 3 cards when partner may hold only 4 is not new. It has been discussed extensively in bridge literature since 1924. Hands that lend themselves to this treatment come up several times each session. Hand A is board 14 from the August 3rd game, where those who rebid 1NT made 5 tricks and scored 30%. The 2♠ bidders scored at least 80%.

The defense against a Moysian fit is very interesting. When the short hand has 3 low trumps best defense is likely to be leading trumps, planning to remove the 3 trumps in dummy before declarer can use them for ruffing. When the short hand has high trumps, best defense may be to force declarer to use the high trumps for ruffs as this can promote a trick for a defender holding 10xxx, Jxx or Qx in trumps. These are opposite defense strategies and you don’t know which (if either) is best until after you have made the opening lead and seen dummy.

  Restricted Choice in the Game of Bridge by John Bucher

The idea of Restricted Choice is an expert level tool used to make decisions about the location of a specific card. It was introduced to the general player in the '60s by Terrence Reese in his excellent book, "Master Play" (it was titled something else in the UK).

We understand ideas on multiple levels. The simplest level is just, "Okay, if I see this situation I should do this and that is the best that I can do."; a mechanical level of understanding. A level in the middle somewhere is to know what the general idea is. Maybe the highest level is to knowwhy the idea works and even being able to use that knowledge to predict other results. This paper attempts to share with you that highest level understanding of the idea of Restricted Choice, this is not an easy thing to do. My attempt to share with you includes some math but you can get the idea without the math if you want to avoid the numbers and just focus on the ideas. To help you do this I have separated out the mathematical statements as bold and italic.

In its simplest form, the idea is: "When a choice for a decision could be restricted, then the odds are that the choice was restricted." The usual way of illustrating the idea is to talk about what is called "The Monty Hall Problem". So, let's start with that.

Monty Hall was a famous TV game show host for a program called Let’s Make a Deal. He normally chose the contestant with the highest winnings at the end of the show and asked them if they would like to trade their winnings for a chance at the BIG prize. Now suppose you are that lucky contestant and Monty shows you three curtains; one curtain hides a Ferrari and the other two hide goats and he asks you to choose a curtain. You dutifully select a curtain. Now Monty opens one of the other curtains and shows you a goat. (It is important that you understand that Monty knows which curtain hides the Ferrari and would never open that curtain since that would spoil his whole spiel.) Now he asks you if you would like to trade your curtain for the remaining closed curtain. Should you trade?

Virtually everyone at this point responds, "It makes no difference, there are two curtains, the Ferrari is behind one of them, so it is a 50% chance for either." Surprisingly, it does make a difference; changing curtain will get you a Ferrari 67% of the time while sticking with your original choice of curtain will get you a goat 67% of the time.

This example illustrates what a restricted choice is; namely, if the Ferrari was behind one of Monty's curtains, Monty's choice of curtain to open would be restricted since he has a rule that he will not show you the Ferrari till the end. If the Ferrari was behind your curtain, his choice was not restricted, (each of Monty's curtains hold a goat, so he could open either). So, since his choice COULD have been restricted, the rule says the odds are that it WAS restricted and therefore the Ferrari is less likely to be behind your curtain than the remaining curtain. Another point about this example is that it is easy to verify. If you can find a person willing to play the part of Monty Hall, have that person choose three cards, one Ace and two deuces. The Ace is the Ferrari. Have "Monty" place these cards face down without your observation and then play out the game as described above. Each time after you select a card Monty must show you a deuce then allow you to make the decision of trade or not. Do this 100 times and trading with Monty every time will net you around 67 Ferraris. You're going to need a bigger garage. Stubbornly sticking to your choice will net you around 67 goats, you're going to need a farm.

If you are feeling a bit bewildered, you're not alone. There are math professors who will challenge you to a duel at dawn before they will admit that this idea is anything other than a parlor trick.

Now let's look at how this might apply to our game of bridge. There are many cases where Restricted Choice can be used. The usual example is the old "Nine never, Eight ever" rule. This tells us that when we have nine cards in a suit and we are missing the queen, we should play for the drop and when we have eight cards in a suit and are missing the queen we should finesse. More erudite web sites will add, "Unless, you are also missing the jack then you should use "Restricted Choice". Which means, if you play the ace or the king and one player drops the queen or the jack, since this play indicates his play might have been restricted (it would be silly to false card from queen small or jack small) you should assume his choice was RESTRICTED, i.e. the card he DID play was the only card he COULD play, a singleton, and therefore you should finesse his partner whenever possible.

This idea bothers many people. Why is it that the way a player plays his cards changes the odds? Consider this scenario. You have a nine card suit, you are missing the queen, jack, and two small. You cash the ace of the suit and west plays a small card, east the queen. You now lead from your hand towards dummy through west toward the king and ten. West again plays small, should you finesse? At this point there is only one missing card, the jack. Either west was dealt Jxx and east Q stiff or west was dealt xx and east QJ doubleton. There are 646,646 possible hands wherein east could have been dealt a stiff Q; there are 705,432 possible hands wherein east could have been dealt the doubleton QJ. Without further arithmetical torture one can see that without evidence to the contrary; east is more likely to have been dealt the doubleton QJ and therefore we should use "nine never" and play for the drop. But that is the opposite of what RESTRICTED CHOICE tells us to do. Why on earth??

I realized I needed to understand the "why" of this in order to satisfy my curiosity. As I read around, people kept mentioning Bayes Law as the reasoning behind this idea, but no one actually did more than just mention it. I need to know why! So, let's take a look at this idea.

The idea expressed by 'Bayes Rule' has been called by some of the most brilliant mathematicians of the twentieth century one of the most important ideas for logic and probability ever and compares its importance to the Pythagorean Theorem and its importance to geometry. (I.e. the sum of the squares of the base and height equal the square of the hypotenuse.)

Bayes Rule is considered to be bewildering by many but the basic idea can be understood rather easily. The idea behind Bayes Rule is simply that when you gain new information it changes the probabilities.

Computing simple probabilities is easy. Simple probability is about random, independent events. A random event is something that is no more likely than another random event. For example, when you flip a coin, it can come up heads or tails, and these events have equal probability. Independent means the events don't influence each other. For example, if I flip a coin and it comes up heads; that does not mean its next flip has any change in probability. When you have independent random events we need only look at which of those events we want to predict and how many possible events there are. The total possibility of events is called the universe of these events. For example, what is the probability that when you drew a card from a randomized deck of cards it was the ace of spades? There is one desired event (ace of spades) and 52 equally possible events in the universe of this event. So the probability is 1 out of 52.

The game of Bridge is all about probabilities. Most likely all the probabilities you are familiar with in your Bridge game are based on the deal. For example, which is more likely: 5 cards will split 3 and 2 or 4 and 1? We all know the 3:2 split is more likely, and that is because there are moredeals with 3:2 splits than with 4:1 splits. The deal is a random, independent event.

I stated that Bayes was about new information changing the probabilities. Information is another event, and if an event changes the likelihood of another event then those events are not independent. How do we compute the probability of dependent events? We use Bayes Rule. How does new information change probabilities? New information changes the universe of the event!

For the math oriented reader:

Dependent events create 'Conditional Probabilities' that are stated as the probability of one event (A) when we know that another event (B) has occurred. The probability of some event is written as p(some event). The conditional probability of event A when we get new evidence that B is true is written as p(A|B). Read this as "probability of A given B".

In our ace of spades example above, suppose someone tells you that they saw that your card was a black suit. Now the universe of events is only 26, not 52. So the probability that you drew the ace of spades when you have new evidence that your draw was a black suit is now 1 out of 26. Well, if it always was that simple, everybody would be a Bayesian expert. It IS all about the universe of possibilities changing, but it quite often is difficult to see just when and why and how that is happening. And this makes the results quite often very non-intuitive, like in the Monty Hall problem above, until one uses Bayes Rule to see the light.

Bayes Rule tells us that the probability that one event (call it A) occurs while another event (call it B) occurs is the count of events where A and B are both true divided by the count of all the events within the universe where B is true regardless of A.

For the math oriented reader:

Bayes rule uses probabilities, but they are proportional to counts, and can be interchanged if done so as to preserve the ratios. Bayes rule states: p(A|B) = (p(B|A) * p(A)) / p(B)

In English this is: the probability that A is true given that B is true, [p(A|B)], is equal to the probability that B is true given A is true, [p(B|A)], multiplied by the probability A is true, [p(A)], all of that divided by the probability that B is true, [p(B)].

In our ace of spades example above: The chance that we drew the ace of spades when we know that we did draw a black suit is the count of the cards where both of these events are true, which is just one event, divided by the number of events where it is true that the card has a black suit which is 26, in other words 1/26. As you can see the difference is that we reduced our universe from 52 to 26.

For the math oriented reader:

p(SAce|Black) = [p(Black|SAce)*p(SAce)] / p(Black) = (1/1 * 1/52) /(1/2) = 1 / 26

Let's take another look at the Monty Hall problem now. Call curtains two and three Monty's and curtain 1, ours. The probability our curtain has a Ferrari is 1/3, and that one of Monty's has a Ferrari is 2/3. Then Monty shows us one of his curtains has a goat behind it. How does this new information change our universe? Everywhere in our universe there is a goat behind at least one of Monty's! The A event always has B true and every event in the universe has B true, so there is no change to the probability and the chance Monty's unopened curtain has the Ferrari is unchanged at 67%. When evidence is either always true or always false, it does not change our universe of possibilities and therefore it does not change our probability. We didn't need to actually do any math to know that. A lawyer would call this kind of news, "moot".

For the math oriented reader:

p(MontyhasaFerrari | MontyhasaGoat) = [p(MontyhasaGoat | MontyhasaFerrari)*p (MontyhasaFerrari)] / p(MontyhasaGoat) = (1/1 * 2/3) / (1/1) = 2/3 = 67%

At this point you might be beginning to wonder how anyone could call this "rule" a great idea, let alone one difficult to comprehend. Before we go to the bridge example please indulge me as I show you a little bit of the power of this "rule".

Donald Trump wishes to provide EXTREME vetting for Syrian refugees trying to enter the U.S.A. So he invests billions of dollars to develop a lie detector machine which is very accurate. In fact, if the suspect is a terrorist, the machine will detect that with 99% accuracy. If the suspect is not a terrorist, the machine will detect that with 99% accuracy as well. Now the CIA informs Donald that half of one percent of Syrian refugees are in fact terrorists (0.5%). What is the probability that a refugee whom the machine claims is a terrorist actually is one? Donald feels quite confident that he will only have a 1% error rate, which is acceptable collateral damage. Is he right?

We want to know “What is the probability that a Syrian refugee is a terrorist when Donald's Test is positive?” So, our universe is now reduced to just those Syrians whom get a positive result. For achange let's use real numbers instead of percentages, the math is the same, but sometimes it is more revealing to use some example numbers. Let's say we get 200,000 refugees. That's going to include 1,000 terrorists (half of 1 percent of 200,000). And that will include 199,000 nonterrorists. So our new universe includes 99% of the 1000 terrorists (990) and 1% of the nonterrorists (1,990). So 990 + 1990 = 2980 Syrians test positive and 990 of those positives are actually terrorists. So, 990/2980 = about 33.2% of the positives are terrorists and the other 1990 are innocents and are now dwelling in Guantanamo. Not very good collateral damage numbers after all. We reduced our universe from 200,000 to 2,980 and the majority of those were nonterrorists because we started with 199,000 non-terrorists and only 1,000 terrorists. And America is great once again!

For the math oriented reader:

p(terrorist | positive) = p(positive | terrorist) * p(terrorist) / (p(positive | terrorist) * p(terrorist) + p(positive | notterrorist)*p(notterrorist)) = (99%*.5%) / (99%*.5% + 1%*99.5%) = about 33.2 %

So at last, let's return to our bridge example mentioned above. This example is going to need some help to explain, so I am going to use a hand played recently at BCCM by that famous pair, Sherlock Holmes and Dr. John Watson. In the replay of this hand there is frequent mentioning of the number of hands with a singleton honor and the hands with two honors; these hands occur with frequency of 646,646 and 705,432 respectively; in order to simplify talking about these hands, Sherlock uses the proportionately correct numbers of 48 and 52 which will make it easier for everyone and still result in correct probability computations.

Sitting at a table in his favorite bridge club in the world, Sherlock Holmes studied the dummy as his partner Dr. Watson laid it out. There were about a dozen kibitzers surrounding the famous detective's table; about 6 sitting in chairs and 6 standing as there always is when Sherlock plays. The contract was 6 Spades, the opening lead a club. As Watson spread out four spades to the ace and ten, he began to cough. "UNGH, UnGh, Nung, naiine, unggh, neeverrr, ungh, ungh."

Sherlock looked up and said, "Dr. Watson, I'm glad you brought that up, pun unintentional, you might think I should play for the drop of the missing queen. You know we are missing it since we play Roman Key Card, and we have a 9 card fit. This would seem to dictate we follow the dictum "9 never 8 ever". My dear Watson, you are wrong. Unbeknownst to you I am also missing the jack. In this case, I must play the king of spades from my hand after winning this club lead and if no honor falls from the opponents, my only hope to avoid losing a trick will be to play for the 2-2 split where both missing honors may fall on my next play, the ace. However, if an honor does fall, then my correct play is to use the principle of Restricted Choice. Actually, that principle is a short cut for the actual computation which requires using Bayes Rule to find the missing card."

"I'm afraid I'm unfamiliar with that rule." said Dr. Watson.

"There is an excellent article on Bayes Rule in this month’s club newsletter; I am surprised youhaven't read it. It states, when you get new information, you can re-compute your probabilities based on that news." answered Sherlock. "In this particular case, about 81% of our universe of possibilities disappears when an honor falls under the king. Since the queen and the jack are equals, we can call either of them a 'quack'. Now when a quack falls under my king, I know that only two possibilities exist; either that player was dealt one quack or two quacks, since if he had any other card he would have played it rather than a valuable quack. This then is my updated universe of possibilities. It consists of all the possible hands which could hold a single quack, 96 of those, (48 for each singleton quack), and 52 hands which could hold both quacks. This is a total of 148 possible hands in my universe. So, the probability that this player started with a singleton quack is 96 out of 148, or 65%, and I should therefore finesse his partner for the other quack if possible."

"But, but..." interjected Watson, Sherlock aren't you ignoring valuable information?"

"What valuable information would that be, Watson?” calmly replied Sherlock. While the kibitzersbegan to buzz, obviously trying to guess the answer.

"I don't mean to be impertinent, Sherlock, but if you just think about it, no player can have theother singleton, you can only have one singleton in this suit, after all.” responded Watson whilethe kibitzers begin tittling. "So, if the player plays the queen, he either has singleton queen or doubleton queen and jack. As the odds are 52 to 48 that he has the doubleton, you therefore should play for the drop.", continued Watson as he looked up and gave a bashful little smile and a "weakish" wave to the crowd, as the kibitzers furor nearly rose to a roar.

"You can see that if you played all 148 possible hands and finessed every time you would win the finesse 96 times and lose the finesse 52 times, for a success rate of 65%, can you not?" queried Sherlock.

"Well, yes, but it still seems you are ignoring information." mumbled Watson.

"My dear Watson, you are wrong. All right, let's try and use that information and see what happens.", Sherlock cheerfully replied then continued, "We wish to know how often our player will hold the jack when he drops the queen under our king. If our player drops a queen then our new universe includes all of the 48 hands with a singleton queen and out of the 52 hands with the doubleton queen jack, let's see, will he play the queen every time? Our universe only includes those hands where the player played the queen under my king, but we have no idea how many hands that would be. We cannot compute our new universe or the conditional probability without thatinformation.” Sherlock continued. It is true that using simple probability the chance of a doubletonqueen is 52 versus 48, but this is a conditional event, so we must use Bayes Rule.

"Could we use the average, say half the time?" suggested Watson humbly.
"If you like." replied Sherlock with a sly smile and then added, “That means our universe now includes 26 of the 52 hands with doubleton queen jack and 48 hands with singleton queen, for a total of 74 and so we should finesse and expect a probability of success of 48 out of 74 or 65%; exactly the same rate as the quack case."

"So, that information is not useful, I guess.” feebly replied Watson.

"My dear Watson, you are wrong. Look around you. We are in the midst of a South East Asian sweltering jungle only a few kilometers from the Golden Triangle. The people in this bridge club are refugees from God only knows what or where. Interpol probably has records on everyone in this room. I would say that 95% of these players are pathological liars and that they would not be able to resist playing a false card at every opportunity. In this case, that would be the queen, since it denies holding a lower but equal card."

"Does that change things?" responded Watson, looking around the room slowly while attempting to avoid eye contact with the kibitzers who were mumbling and glowering at the pair.

Sherlock smiled broadly and answered in a calm voice, "Most assuredly, when a queen is dropped our new universe will have all 48 singleton queen hands and 49 of the 52 doubleton hands. So, if the player plays a queen, he will have the jack as well 49 out of 97 times or about 51% of the time, so we should play for the drop, not the finesse. However if he plays the jack, then our universe will include all 48 singleton jack hands plus only 3 of the doubleton queen jack hands, so he will have the queen as well as the jack 3 times out of 51 for a 6% likelihood. We will finesse his partner with a high degree of confidence. "

"I see, well done, Sherlock!" spoke Watson with a defiant look in his eyes aimed at the leering kibitzers.

After all this Sherlock Holmes finally played the king of spades from his hand, west followed low, and east played the jack. Next he played low towards dummy's ace ten, west played low again and Dr. Watson reached for the 10 with an almost smug look of pleasure in being part of the brilliance of Sherlock's logic. Before he touched the ten Sherlock called out, "My dear Watson, you are wrong!" Watson froze his hand hovering over the ten, "But, but ..." he whimpered.

Sherlock looked around the room smiling with the slightest of smiles and said, "Play the ace please, Watson, and I claim." The kibitzers began shouting at each other as Watson asked, almost choking as he did so, "Did you say the ace???" while slowly pulling it out and placing it in play. East then played the queen of spades with a look of irritation and barely concealed anger and stu-pefaction. The kibitzers began shouting at Sherlock, yelling “fraud”, “incompetent”, and similarinsults.

Watson shouted above the uproar from the kibitzers, "How? Why? What? I don't get it!"

Sherlock, answered in the same slow deliberate way he always did, causing the kibitzers to rapidly quiet down, "The correct play was to finesse, using Bayes Rule or Restricted Choice. The business about the players in this room being pathological liars was sheer guile; these are the sweetest people in the world. I needed to manufacture additional cases to further the explanation. We needed a top board and the 65% probability of the finesse wasn't good enough. I mentioned the article in the club newsletter so that a player who was not holding queen jack doubleton would not feel a great need to understand every word I spoke. If they wanted to learn about Restricted Choice they could read the article when they got home, however a player holding the doubleton queen jack would need to listen closely so they would know how to play to fool me into finessing their partner. And the insults would make them so angry that they would ignore me unless they desperately wanted to set me. When I saw East straining to understand all the cases I was listing, I knew he held the queen and the jack. It didn't matter to me which card he played I was always going to play him for the other honor."

"Well, you surely got us a top with all that brilliant planning, Sherlock!” spoke a grinning Dr. Watson.

With a slight sigh and a warm smile, Sherlock answered, "My dear Watson, you are wrong. We appear to have an average result. It seems the other players also bid 6 spades and made 7, by virtue of the "9 never, 8 ever" dictum.

"Well, you avoided getting us a bottom by virtue of 'the expert's curse'. I say man, bloody brilliant, your play." Watson answered while sharply nodding his head.

"My dear Watson, you are right.", Sherlock replied as the kibitzers all began to applaud.

For the math oriented reader:

"the quack case"

p(Q&J|dropQorJ) = p(dropQorJ|Q&J) * p(Q&J) / [p(dropQorJ|Q&J)*p(Q&J) + p (dropQorJ|QorJalone)*p(QorJalone)] = 100% * 52 / [100% * 52 + 100% * 96] = 52 / [52 + 96] = about 35%

"the 50% guess"

p(QJ|dropQ) = p(dropQ|QJ) * p(QJ) / [p(dropQ|QJ)*p(QJ) + p(dropQ|Qalone)*p(Qalone)] =?50%? * 52 / [?50%? * 52 + 100% * 48] = ?26? / [?26? + 48] = about ?35%?

"the pathological liar cases"

p(QJ|dropQ) = p(dropQ|QJ) * p(QJ) / [p(dropQ|QJ)*p(QJ) + p(dropQ|Qalone)*p(Qalone)] = 95%* 52 / [95% * 52 + 100% * 48] = 49/ [49 + 48] = about 51% :play for drop p (QJ|dropJ) = p(dropJ|QJ) * p(QJ) / [p(dropJ|QJ)*p(QJ) + p(dropJ|Jalone)*p(Jalone)] = 5% * 52 / [5% * 52 + 100% * 48] = 3 / [3 + 48] = about 6% :finesse other player


I recently saw a bridge quiz on the internet called "Test Your Bridge IQ". One of the questions was: holding A975 in dummy and KQ3 in your hand, missing 6 cards in the suit including the Jack and Ten, you play off the K, both follow, then you play off the Q; LHO follows, RHO drops the Ten. Should you finesse LHO for the Jack or play for the drop? The answer is to finesse; this is due to Restricted Choice. They mention that you probably don't know why you should finesse but you should give yourself partial credit for having good instincts if you did. You should use the Restricted Choice idea; you don't need to worry about all the numbers as was demonstrated by the quack case and you should give yourself full credit for knowing why.

  All About Movements by Steve Ault

We’re talking here about movements of the duplicate bridge variety, that is.

Earlier in the year the Club Committee decided to standardize the movement to be used for any given number of tables in play. This was done in response to complaints about some rather weird movements, the worst of which resulted in a pair having to sit out twice. Secondly, it was our intention to improve our games by employing movements that conform to the recommendations of authorities on the subject. And finally, for new scorers and directors, the list of options listed on the computer for possible movements is rather confusing and intimidating. Now, we just choose “STANDARD.”

So here’s how it works:

Howell for 6 tables or less. The Howell movement requires just about everyone to move, although sometimes we move in strange ways. For example, a 6 table Howell requires one pair to remain at the same table but alternate irregularly between N/S and E/W. During the Summer Session, when many members return home to enjoy their brief summers (no disrespect intended to our Australian comrades for whom everything is backwards or up-side-down), turnout at the Club dwindles so that more often than not we play a Howell movement.

Mitchell for 7 tables and up. And then, just as the tides ebb and flow and the seasons change, people return to Chiang Mai. Mitchell is rather straight forward: N/S pairs remain stationary, E/W pairs move up a table and boards move down a table each round. Sometimes we are informed there is a skip, i.e., E/W pairs move up two tables instead of one after a given round. But why is that? Skips are required whenever we have an even number of tables in play, and the skip always occurs after the round equal to the number of tables divided by 2. To see what happens if there is no skip just play out a movement of 8 tables for 5 rounds with E/W pairs moving up and boards moving down. On round 5 the E/W pairs will play the same boards they started with in round 1. Thus, a skip is required after round 4.

The literature on duplicate bridge movements recommends those that are well balanced and equitable, which translates into maximizing both the number of opponents played against and the number of times each board is played. Conversely, both the number of boards in play and the number of boards played per round are minimized.

Some clubs prefer to play sessions with boards totaling in the low twenties, while others prefer the high twenties. The Bridge Club of Chiang Mai is of the latter variety.

With all this taken into account, the following Mitchell movements are played (half tables are always rounded up, e.g., 61⁄2 tables is played as 7):

7-8 tables: 7 rounds of 4 boards
9-12 tables: 9 rounds of 3 boards
13-14 tables (rare, only 4 occurrences last year): 13 rounds of 2 boards
*15-16 tables (very rare, happened once last year): 14 rounds of 2 boards.

*We had 14-1⁄2 tables the day after the Pattaya Bridge Club bust. The turnout could be interpreted as either an act of solidarity or one of defiance—or both. In any case, it appears that we folks in Chiang Mai don’t easily get intimidated.

Of all these different configurations, 3 movements stand out as “perfect:” 7 tables with 7 rounds of 4, 9 tables with 9 rounds of 3, and 13 tables with 13 rounds of 2. What makes them perfect is that in each case all N/S pairs play against all E/W pairs, and all of the boards are played by everybody.

The Committee decided to drop the rare two section games for 13-1⁄2 tables and up. Multiple section games are played traditionally when there is an overall winner and section winners (relevant for awarding Masterpoints). However, whenever we played 2 section games, the results in both sections were conflated, i.e., there was only one N/S and E/W winner. Thus there is no need for 2 sections. Multiple section games are more difficult to run, require multiple sets of pre-dealt hands and are prone to unbalanced competition between them. However, Stewart aptly points out that the layout of The Pub, our previous venue, was such that the primary room could not accommodate large games, thereby necessitating an inside/outside arrangement which made a 2 section game far easier to handle for players and directors alike. Our present venue can accommodate up to 16 tables in one space.

The most important problem with two section events where there is only one N/S and one E/W winner is that they are inherently unfair. One section may be weaker than the other, allowing the winning pair in the weaker section to get a higher percentage and to win the overall event, just by virtue of playing against weaker opponents. This outcome is not hypothetical. In fact, it actually occurred with Club Day 2015. Please note that this observation is not a matter of sour grapes, as this author was a beneficiary, not a victim, of the imbalance. The fairest way to play with a large number of tables (13‒16) is to have everyone play everyone else (or almost everyone else). With this number of tables, this means 2 board rounds.

Has anyone noticed the little tweak on our website? To do so, from the home page click “results” and then “all results” from the menu on the left. Next, click “Friday Pairs Winter” to the right of “9 Fri.” Then, click on any pair. It doesn’t matter which one. Boards are displayed to the right with tabs for 1-33 above. Finally, click on 33. The board is displayed just like all the rest, so what’s the big deal? This marks the first occasion we’ve had the capability to display boards 33-36.

From November through February the Club traditionally enjoys its highest attendance, with about75% of Friday’s games exceeding 10 tables. Boards come in sets of 32, but 11 and 12 table sessions with 9 rounds of 3 require 33 and 36 boards respectively. Previously, we pre-dealt only 32 board so that anyone interested in checking out the hands for boards 33-36 was out of luck. John B. kindly reprogrammed the deals to include 36 boards for the four month high season, so now boards 33-36 have also been pre-dealt and can be displayed.

  Squeezes by Steve Ault

Squeezes, squeezes everywhere, but which is the right one to take?

7   9
Vul: All
Dealer: East
♠ A 8 6 5 2
 K 3 2
♣ A Q 9 7 2
♠ 4
 K Q 7 3 2
 J 8 7
♣ J 10 8 3
  ♠ Q J 9 7 3
 A 10 5
 Q 6 4
♣ 6 4
  ♠ K 10
 J 9 8 6 4
 A 10 9 5
♣ K 5


Optimum NS 620
  ♣      ♠  N
N 4 4 1 4 2
S 4 4 1 4 2
E - - - - -
W - - - - -


[Ed. note: This is a placeholder. The original version of this document (see PDF version) had several examples that did not match up with the text, so for now, they have not been reproduced.]