Slam tries

The Granovetters' column in the Dec 2009 issue of the Bridge bulletin affords a perfect illustration of the way I like to play control-showing slam try sequences – i.e. not the way Pam's partner did it.

Here's the hand:

	♠ J62 ♥ AKT4 ♦ J3 ♣ KT86
♠ T98 ♥ Q973 ♦ T976 ♣ J2		♠ K7 ♥ J65 ♦ Q852 ♣ 9754
	♠ AQ543 ♥ 82 ♦ AK4 ♣ AQ3

The auction went as follows:

West	North	East	South
	1♣	p	1♠
p	1NT	p	2♦ 1
p	2♥	p	2NT
p	3♠	p	4♣ 2
p	?

1) game-forcing checkback
2) control-showing slam try

What would you bid with the North hand?  Pam, who was playing South, was bemoaning the fact that her partner did not bid 4♥ in response to her own 4♣ call – and she is totally right to complain!

There are two rational methods of searching for a good slam.  One method, generally favored by experts, is the so-called "serious 3NT".  After a three-level bid, and when a major suit has been agreed, a bid of 3NT says "I'm seriously interested in slam, please show a control".  Making a different control-showing slam try says "I'm somewhat interested in slam, please show a control, but only if you are now seriously interested".

The other method, which doesn't require so much memory work and uses less of a distinction between major and minor suits, is as follows:

When the first control-showing slam try (cuebid) is made, the response depends on whether responder has already narrowly limited his hand.  If he has so limited it, then he is required to show a control (the cuebidder already knows responder's hand strength and still wants to know about controls).  If he has not narrowly limited his hand, then showing a control implies enthusiasm for slam while signing off in the trump suit denies a suitable slam for hand, but doesn't deny a showable control.  A second cuebid by asker now demands responder to show a control.

Unfortunately for Pam, they were apparently playing neither of these schemes.  North thought that he had a "bad" hand and therefore should not show any enthusiasm for slam.  But he'd already said he had a balanced 12-14 and South knew that.  Within the context of a 12-14 point hand and the auction so far, North has a terrific hand.  The ♥AK are golden (South hasn't shown shortness in hearts) as is the ♠J. Only the ♦J is of dubious value. We assume that the ♣K is useful because partner has cuebid the A and since it's in the suit we opened and partner has shown interested in slam, it's extremely unlikely that he is showing shortness.

So, somewhat unusually, I'm totally in agreement with Pam this time.  I don't buy the argument that the strong hand (South) should make another effort beyond the safe haven of the spade game.

Some thoughts on prepared bids

Bridge seems to be full of strange names for concepts, like restricted choice.  The prepared bid is another.  It seems to me that it is the rebid that is prepared by the first bid. But in any case this topic is about non-forcing opening bids that don't truly reflect the kind of hand that is held.

First, why would anyone want to make a prepared bid?  The Hideous Hog likes to make them because  a) they prepare the way for he himself to be declarer in his favorite 3NT and b) they tend to dissuade an opening lead in the bid suit.

But what is it about our systems that require the use of a prepared bid?  Well, generally speaking if we only promise four cards in a suit when we bid it, it obviates the need for most prepared bids (not all).  Playing a system that expects 5-card majors and a narrow range of notrump openers, however, definitely requires prepared bids, 1♣ in the case of standard american or 2/1 system or 1♦ in the case of precision.  We could relax the range of notrump openers (12-17) for instance and open just about all balanced hands with 1NT, but it's an unwieldy big range and, at least in the ACBL, disallows the use of system responses like transfers.  So we remain with the problem that the 1NT range cannot cover all balanced hands.  Those that don't fall within the range for 1NT must be opened with the prepared bid if no other bid is appropriate.

The risk of opening a prepared bid is not small. As described in a previous blog, opening 1♣ with ♠KQJ7 ♥K75 ♦A42 ♣T96 resulted in a penalty of 1700.  See A small slam on defense.  Obviously, there are other ways to go for 1700, but opening a suit you don't really have has its definite dangers.  Some of the risk may be ameliorated by opening weak balanced hands with 1NT and therefore only opening a prepared minor when holding at least, say, 15 high card points.   Such a hand is certainly no guarantee against going for 1700, but the probability is lessened. 

In the form of precision that I play with one of my partners, when we are not-vulnerable in 1st or 2nd seat where our 1NT range is 10-12, we can open a prepared 1♦ with relative equanimity because if don't we really have diamonds (we promise only 2) we should have at least 13 hcp.  The bigger problem arises when we are vulnerable or in 3rd/4th seat.  In such cases (75% of all balanced hand openers) we have a range of 11-13 for our 1NT rebid after opening 1♦.  The combination of bidding a suit we don't have, and being vulnerable with only 11 points is a very dangerous one indeed!  So much so that I am recommending that minimum opening hands, such as 11hcp, if opened at all, should have at least four diamonds.  That means that if partner makes a limit raise (we use criss-cross) and we end up at the 3-level with only 21 hcp, we will at least have nine trumps and thus some hope of making.  Nevertheless, we rarely run into trouble with our 1♦ openers.

Incremental Raises of Preempts

In my previous blog, I alluded, without proof or justification, to the generally held principle that if you take more than one call to reach a contract that you could have reached in just one call, you must have a more defensive hand.  Let's examine why this should be so in the case of raising of partner's preempt (although similar arguments would apply to all situations).

For the sake of an example, let's assume that partner has opened with a disciplined weak two (spades) in second seat at all white.  You have a relatively balanced hand with some values and some spades.  If he makes his contract, you will be +110 or +140.  You don't really expect him to make game based on your hand (but you can never be sure).  On the basis of just your hand and partner's, there is no point in raising or bidding anything else.  A pass will do just fine.

But now let's suppose that you have exactly three spades and some moderate shape, say a doubleton.  Opponents, being what they are, are quite likely to get into the auction.  They have only four spades between them so that leaves them 22 other cards.  There's no guarantee they have a nine-card fit of their own, but if not they must have at least one eight-card fit (and two seven-card fits).  So, let's take a look at the total trick possibilities (No, I am not going to assert that total tricks equals total trumps!). We assume for now that each side knows when to double, although in practice this is usually not the case.  In the following table of absolute par scores for our side, the left-hand column shows the total number of tricks available (may or may not equal the total number of trumps) and the other columns show the par score when we can take the indicated number of tricks with spades as trumps.  For simplicity, we assume that their best suit is ♥.

Total Tricks	Par (7)	Par (8)	Par (9)	Par (10)
15	-100 (2♠X-1)	+110 (2♠=)	+140 (2♠+1)	+420 (4♠=)
16	-140 (3♥=)	+100 (3♥X-1)	+140 (2♠+1)	+420 (4♠=)
17	-420 (4♥=)	-100 (3♠X-1)	+140 (3♠=)	+420 (4♠=)
18	-450 (4♥+1)	-300 (4♠X-2)	+100 (4♥X-1)	+420 (4♠=)
19	-980 (6♥=)	-450 (5♥=)	-100 (4♠X-1)	+300 (5♥X-2)

Essentially, the upper-right of the matrix half shows where it is our hand (we can make a plus score) while the lower-left half shows the situations where it is their hand.  The right-most column is there for completeness – as mentioned above, we don't think we have game.  It's also possible that we can take even fewer than 7 tricks, but that would be unusual and even then, such hands are "their hands" and despite having the lower-ranking suit, they will generally be able to control how the auction goes.

As I recall, the most common number of total tricks in practice is 17, with 18 being a bit more likely than 16.  It's also possible of course to have fewer or more total tricks.  Fewer total tricks than 15 would be fairly rare, especially given that partner has a six-card suit.  Having more total tricks would not be so very rare, but such case would require great shape and purity of suits.

Let's see which conditions are favorable for a direct raise to 4♠ over either a pass, double or 3-level bid by RHO:

• whenever we can take 10 tricks (in all such situations we will double if they bid on);
• whenever there are 19 total tricks;
  
• when there are exactly 18 total tricks and we can take exactly 8 of them.

This is a total of 8 cases out of 20.  The specific case of 18/8 is not easy to diagnose of course.  Now, let's look at the remaining situations where we should want to raise to 3♠:

• whenever we can take exactly 9 tricks (but see below);
• when there are exactly 17 total tricks (the most likely number) and we can take 8 of them.

Note that there are only half as many cases (four) where it is right to raise to 3♠ as opposed to 4♠.  Taking the cases where we can take 9 tricks, there are some dangers.  In two situations (15 and 16 total tricks) we are unnecessarily risking a minus score.  The other 9 trick situation is discussed below.  There remain seven situations in which it is appropriate to pass throughout.

There is exactly one case where we may do well to bid 3♠ and later take the push to 4♠:

• when there are 18 total tricks and we can take exactly 9 tricks (giving us a chance of 300 at the risk of -100).

Can it ever be correct to bid 3♠ and then take the push to 4♠?  Yes, if by doing so we increase our chance of beating the absolute par.  It is reasonable in just this one situation.  We can make 3♠ and they can make 3♥.  As shown in the table, par on this board is 100 for pushing them to 4♥ and then doubling.  Assuming we're in a good field, this will give us more or less an average score.  Can we do better?  We might do a bit better if they don't take the push and we get to make 140.  But we hit the jackpot if we push them to 5♥ and double them for down 2 (300)!  Of course, if they don't take the push, we will be minus 50 (best) or 100 (worst).  So, how does the "slow play" strategy compare with the "fast play"?  Let's say that the opponents have a 50% chance of getting it right (more or less) at each level.

Let's assign the following match-points (on a 51 top like you might find on the second day of an NABC event):

• 500  (1) 51
  
• 420  (2) 49-
  
• 300  (3) 47
  
• 170  (3) 44
  
• 150  (1) 42
  
• 140  (3) 40
  
• 110  (1) 38
  
• 100  (12) 31
  
• 50 (5) 23
  
• 0 (1) 20
  
• -50 (6) 16-
  
• -100 (8) 9-
• -140 (3) 4
• -300 (1) 2
  
• -420 (1) 1
  
• -500 (1) 0
  

Our expectations with the slow play strategy are:

• they pass us in 3♠ and we beat par with 140 (40 mps) 50%: 20
  
• they bid on to 4♥ and we bid on to 4♠ (50%)
• they let us go down quietly (16- mps) (25%): 2.06
  
• they double us (9- mps) (25%): 1.19
• they bid on to 5 and we double for 300 (47 mps) (50%): 11.75

The total expectation this way is 35.

With the fast-play strategy, we give up being able to bid and make 3♠.  Our net expectation this time is 30, slightly lower than with the slow-play but still a little above average.

So, what kind of hand do we need for the slow-play strategy to work?  It's a hand we're reasonably confident of making 140 if allowed to play it.  But, at the same time, it has defensive strength too because, combined with partner, we expect to take four tricks on defense.

Granted, I have only examined the white/white situation above.  Naturally, things get even more exciting when one of both sides is vulnerable!

A hand such as ♠J84 ♥Q6 ♦743 ♣KQT92 (the one I discussed in the previous post) is a defense-oriented hand but, combined with partner's hand, is likely to be significantly outgunned.  I would expect us to be able to take 5 spades, perhaps a heart ruff, and maybe two other tricks, in other words we can just about make 2♠.  We probably have around 16-17 hcp between us, which means that our opponents have 23-24.  I would expect them to be able to take 9 or perhaps 10 tricks if they have a decent fit in hearts.  Note that the presence of the ♥Q in our hand tends to reduce our estimate of the total tricks.  As it happened, we were already three tricks too high at the two-level! Opener's hand was a not-very-powerful ♠KQT762 ♥9543 ♦85 ♣7.  And the opponents can actually make 7♥ (although nobody bid it).  So the number of total tricks was about as expected (18) but the tricks were distributed 13-5!
A hand such as ♠J874 ♥– ♦7643 ♣AKT92, however, needs to bid to 4♠ immediately!  It might even make (you have no idea if it will), but it might keep the opponents our of a making slam even.  Given the void in RHO's suit (he did bid 3♥) and the purity of the layout, the total tricks on this deal could easily be 20 or 21.

I'd like to add some more scenarios and calculate their expectations, too.  I haven't lost sight of the fact that when at the table, you don't know the total tricks, and you don't know how many tricks your side can actually take.  But experience gives you some good indications.  Watch this space.

Fixed – by partner

If there's one thing a dislike in bridge it's when I get fixed by the opponents.  But there's something even worse – being fixed by partner!

I've mentioned the principle of "one bid" here before (see Fall Foliage Sectional).  If you take two bids to get to the same place you could have bid in one turn, you are showing a better hand, particularly with more defensive strength.  Here's a prime example of not heeding the rule that came up online.

You hold: ♠J84 ♥Q6 ♦743 ♣KQT92.  Nobody is vulnerable and partner deals and opens 2♠.  Your RHO bids 3♥ and it's up to you.  What do you fancy?  Pass?  3♠ or a rather cheeky 4♠?  Personally, I think pass is about right but let's say that your bidding box has no pass cards and you have to come up with something.  Let's say you bid 3♠.  It now goes 4♥ on your left and there are two passes back to you.  Is there any amount of money I could pay you to get you to bid 4♠ now?  No, of course not.  Because when they compete to 5♥, partner will be within his rights to double for penalties, assuming a suitable hand.  Having four small trumps, partner did double and the opponents made the unusual non-vulnerable score of 850, i.e. they made all 13 tricks!

Aceless wonders

Here's a tip that I have found to be worthy. When you open an aceless hand, don't take any strong action later in the auction – your hand is going to be a disappointment to partner. Here's an example of the kind of thing I mean from BBO. I was playing with my favorite Canadian, E/W at favorable vulnerability. My hand (E) was ♠T8653 ♥A82 ♦AK ♣K65. Partner opened 1♥ (limited to 15 hcp) and the auction continued as follows:

West	North	East	South
1♥ 1	p	1♠	p
4♦ 2	p	4NT	p
5♦ 3	p	5♠	all pass

1) 11-15 hcp
2) splinter
3) 1 or 4 keycards

Probably, I was over-optimistic and didn't devalue my AK of diamonds sufficiently, but I've learned that it's easy to devalue such holdings too much, especially opposite the more typical singleton (admittedly, opposite a void, AK should be devalued somewhat).

There was nothing I could do to avoid the loss of two black aces and a heart ruff. This was expensive, in that most pairs were in only 4♠. This was the complete layout:

	♠ 94 ♥ T653 ♦ QT75 ♣ A82
♠ KQ72 ♥ KQ974 ♦ – ♣ QJ97		♠ T8653 ♥ A82 ♦ AK ♣ K65
	♠ AJ ♥ J ♦ J986432 ♣ T43

The point is that however good the West hand appears to be in support of spades, it is aceless and should probably not jump rebid, splinter or make any other strong rebid. Trade South's ♠A for partner's ♠K, on the other hand, and even slam rolls home. Equally clearly, if North has the guarded ♠K, only 5♠ can be made (but that still would be a game score).

As another example, I recall from several years ago a hand where my partner opened 1♥ and after my 1♠ response, rebid 3♥. Later, a key-card enquiry showed that we had two or five key cards (I had two myself). Not being able to imagine how partner could make a jump rebid with an aceless hand, I bid 7♥ with a fair degree of confidence (I had a good hand myself). Unfortunately, we were off three tricks, doubled. We had every honor card in the deck, save for two aces and the trump K!