Monday, 21 May 2007

1M:2C Artificial: Slam Bidding

When responder has a balanced hand and is interested in slam, he can use a relay-like sequence to find out about opener's shape. Depending on the continuations being used, it may be possible to find out opener's complete shape below game level. But even if not, it should be possible to find out the most important aspects - that is, the suits where opener has length (by which I mean 4 cards or more) and where he has shortage. If you work it through, you should find that for most hands these things can all be described at or below 3NT, but for some hands with a 6-card suit or 5-5 shape, a complete description may involve bidding 4C or 4D.

We need to know how to continue after this. Relay systems have to use very different slam-bidding methods to natural systems. However, because the relay-like scheme only applies when the asker has a balanced hand, you do not need many of the very complex methods found in the most advanced relay systems. This is because when you have a balanced hand, you know that nearly all of parnter's high cards will be "working". And since you know partner's shape, you can tell which of your own cards are useful as well. So, if you are able to get a good description of the strength of partner's hand, you will be able to deduce very accurately how many important high cards your side is missing.

Standard high-card points are not a particularly good way of describing the strength of a hand for slam purposes (not for suit slams, at least); a better approach is to count points on the scale A=3, K=2, Q=1. These are called "queen points" or "slam points": I'll use SP for short. Playing standard opening bids, a minimum opener will usually have 6 or 7 SP. A hand with 9+ SP can be considered significantly better than minimum for slam purposes, and when dividing opener's strength into "minimum" and "maximum", it makes sense for the maximum range to start at 9 SP unless playing very limited opening bids.

An important question is how much to count for honours in short suits. A singleton king or queen should probably not be counted at all, though of course it could still turn out to be a useful card. A doubleton queen is more interesting. I think it is best to count a doubleton queen as worth 1 SP unless you have a 5-5 or longer two-suiter. The reason is that the main value of the queen in Qx is that it can set up an extra trick for a discard, but when you have 5-5 shape a discard is unlikely to be useful. It may make sense to compensate for this to some extent by requiring only 8 SP for a "maximum" when holding 5-5 shape. (There is no problem with having different requirements for different hand types, because responder always finds out at least this much about shape before asking for a detailed description of strength.)

The main slam-bidding tool, then, is a bid which asks opener to show his exact strength measured in SP. After responder has heard enough about shape, his 4C bid can ask about strength. Simplest is to have step replies, so that if opener has shown a minimum,

4D = 6 SP (or fewer, but this would be very rare)
4H = 7 SP
4S = 8 SP.

Whereas, if opener has shown a maximum,

4D = 9 SP
4H = 10 SP
4S = 11 SP

Sometimes 4C is not available because opener bid that to show a shapely hand, in which case 4D would be the strength asking bid. (And similarly, some agreement is needed as to what to do when opener's shape-showing bid was 4D or higher, if such a thing exists.)

Here's an example of a possible hand for responder:

S Q4
D A82

Suppose that after a 1S opening bid, opener shows a minimum hand with 5 spades, 4 hearts, 3 clubs and a singleton diamond. We can see that the missing cards are the ace and king of spades, the ace of hearts, and the ace and queen of clubs - a total of 12 SP. The king and queen of diamonds are not important because of partner's known singleton.

Say we bid 4C asking about opener's strength and he bids 4D showing a minimum 6 SP. Then we know that there are 6 important SP missing. This could be two aces, or an ace together with the SK and CQ. Either way, this will not be a slam we want to be in, and we can sign off in 4H.

If opener bids 4H then we are missing 5 SP, which can only be the SK and an ace. Since there is no way to dispose of four of partner's spades, a 6H contract would be at best on a spade finesse, and could have no play at all. So we know to stop in game.

If opener bids 4S then we are missing only 4 SP, which must be the CQ and an ace. This time we can see that the contract should be at worst on the club finesse (barring some very bad splits), and could be much better than that if the spades are solid enough. So, this time, even without any further investigation, it looks like 6H should be worth bidding.

Generally, if you are missing 5 or more SP you are very unlikely to want to be in slam; whereas missing only 3 SP slam is likely to be good. The hardest hands to judge are those where 4 SP are missing. There you would often like more information. The example above is made relatively easy by the fact that we have the minor honours in our long suits: take away the HJ, CJ or even the CT and it is more difficult to know what to do. This is fairly inevitable because our way of describing strength does not count these cards.

So, after having found out about SP, what else might be useful to know? This is a difficult question because often there are various different combinations of cards which would make slam good. But notice that it is certainly not necessary to play any form of Blackwood. If the partnership was missing two aces, then you would find out that you were missing at least 6 SP, and this is too much for slam. Similarly, if you are missing one ace together with the king of your potential trump suit, responder will discover that at least 5 SP are missing, and this is nearly always an indication that slam is not playable. Thus, if you have enough strength to warrant bidding slam, you can't be missing two key-cards.

Sometimes it's impossible to bid slam with confidence (or avoid a bad slam) without finding out the precise location of opener's high cards. Unfortunately there is nowhere near enough space to be able to do this. We need to decide which things responder is most likely to want to know. There are two things in particular which seem to come up relatively often:
  1. Minor honours in opener's long suits. If your prospective trump suit is Axxxx opposite xxx, you have no chance of making slam whatsoever. Whereas, if you have AJT9x opposite xxx, there's an excellent chance of avoiding two losers. More generally, the jack and ten of opener's long suits can make a big difference to the slam chances. It is often very useful to be able to ask about these cards.
  2. Kings and queens in doubleton suits. When either responder or opener has a doubleton, honours in that suit are often much less valuable than if they were elsewhere. It is useful for responder to be able to pinpoint a particular suit and ask whether that is where some of opener's SP are. Opener should make a discouraging bid if holding the king or queen, and encourage with nothing in the suit or just the ace (which is always a useful card). This is generally more effective than asking about suits where responder wants to find honours, becuase there are usually two or three suits where honours would be useful.
So it is worth finding ways to ask about these things. Bids in suits where opener has shown two cards or fewer cannot be to play, and so they can be defined as specific asking bids. However this does not usually result in many bids being available. One way to free up more bids is to define some of responder's bids as setting trumps. For example, in situations where 4C is the normal strength ask, 4D can be used to set a particular suit as trumps (maybe opener's second-longest suit). The replies to 4D still show SP, but afterwards any bid below slam level except in the named trump suit can be an asking bid.

Another issue is the meaning of a 4NT bid. If opener has shown a 6-card suit then this should not be natural and can be used as an asking bid (but remember that Blackwood is useless). If opener only has five cards in his longest suit then 4NT should be natural - to play if the bidding is already at the 4-level, and quantitative otherwise. A quantitative 4NT is often useful when there is no big fit and responder isn't particularly interested in SP because jacks and maybe tens would be helpful as well.

Tuesday, 15 May 2007

1M:2C Artificial: Continuations

Since I wrote about an artificial 2C response to 1-of-a-major, some people have asked me about continuations. There are certainly plenty of options. There are a few complete schemes available on the web, but I'd imagine that for most people who want to play this sort of thing, part of the fun of the method is in designing their own structure - and doing it yourself also makes it easier to remember (though perhaps not for partner!) Still, there are a few things that can be said about how best to go about it.

First of all, natural bidding works adequately well and is a good place to start. The important thing, in my opinion, is to distinguish responder's balanced hands from hands with clubs as soon as possible, and if you play natural continuations this means responder always bidding 2NT at his next turn if this is available. It follows that you can have a problem if opener's reply to the 2C bid is 2NT or higher - these rebids do not allow an easy, natural way to continue. So ideally these replies should not be too frequent, and the natural meaning probably is a little too frequent.

At the same time, opener's 2D rebid is rather underused if played as natural. So a big improvement on strictly natural methods is to bundle some more hand types into 2D. Glen Ashton has written up a convention he calls "2Dlay" (see here) where the 2D bid shows a hand which would have rebid 2D or 2NT or 3C playing natural methods. After the 2D bid, responder can rebid 2H to ask which hand type is held (with 2S showing most hands with diamonds). If you are looking for a simple approach, this is a very good idea, since it makes the system much more efficient while still quickly leading to natural bidding later in the auction.

However, natural-based continuations have their faults. My main concern is that there is often no easy way for either partner to show the strength of their hand. This is a common problem in 2/1-based systems: hands with extra values can be difficult to bid. I feel it is much better to show something about strength explicitly as soon as possible, and this can only be done using artificial methods. Now, you can arrange things so that opener describes his strength, or so that responder describes his strength. I prefer it to be opener, because responder has some catching up to do in terms of describing his shape, and having to have two ways of showing a balanced hand would make life difficult in various ways.

But since showing shape is also very important, the description of strength cannot be too detailed, and so nearly all the methods I have seen divide opener's strength into just two ranges. For simplicity we can call the ranges "minimum" and "maximum", though if the opening bid is wide-ranging this is a bit misleading - the upper range would typically start at about 14 HCP, and the very strongest hands would have to make a further move later.

Playing artificial relay-like continuations, there is actually enough space available for opener to describe his complete shape, as well as whether he is minimum or maximum, below game level. This is what responder would want to happen whenever he has a very strong balanced hand. However, being able to do this is not the only important consideration when devising continuations. There are two reasons why responder may not want opener to describe his hand completely: firstly, it may be possible to name the final contract without having had a complete description (and further information would only be helpful to the opponents), and secondly, when responder holds an unbalanced hand he might want to make a descriptive bid himself.

Trying to take these things into account, let's look at a method which is based around the following rebids for opener:

2D = any minimum
2H = maximum, balanced or 4+ cards in a minor
2S = maximum, 4+ cards in the other major
2NT = maximum, 6+ cards in the suit opened, not 4+ in the other major

After 2H or 2S, 2NT will be a further asking bid (implying a balanced hand), whereas after 2NT, balanced hands will have to continue by bidding 3C. More interesting is the scheme after 2D: using 2H as responder's next relay, opener will reply:

2S = balanced or 4+ cards in a minor
2NT = 6+ cards in the suit opened, not 4+ in the other major
3C+ = 4+ cards in the other major: bids show the same shapes as after 1M : 2C , 2S : 2NT.

Notice the symmetry here: once opener has begun to show shape, any further bids are the same for minimum hands as for maximums.

This scheme works particularly well when it comes to responder breaking the chain of relays. As said above, the first reason responder might want to do this is if he already has enough information to be able to name the final contract. In order to achieve this, the replies to 2C are arranged so that we get the most important information first. In particular, it is very useful to know immediately if opener is minimum, since responder is unlikely to be able to sign off confidently if he does not have that information. A common auction is 1M : 2C , 2D : 2H , 2S, where opener has shown a minimum and denied four cards in the other major. This may well be enough for responder to place the contract in 3NT or 4M. [Actually, making one more relay is more common, since opener could still have an extreme shape such as 6-5 with a 5-card minor. One useful idea is to use 3D as a "weak relay" in this auction, asking opener whether he has a 5-5 shape, promising that responder will be able to set the contract otherwise. This gives away the minimum amount of information.]

It is also important for opener to make a good start at describing his hand in case responder is unbalanced. If this happens then relays will stop, and the partnership will revert to natural-based bidding. So we want to ensure that opener's first reply to 2C does not make subsequent natural bidding too difficult. Most importantly, opener's more space-consuming replies must be very well defined. This is why, in the scheme above, 2S shows a more specific hand type than 2H. Over 2H, responder can bid 2S with an unbalanced hand (artificial showing 5+ clubs), which leaves room for opener's hand type to be revealed. This would not be possible if 2H and 2S were reversed.

Some aspects of opener's hand are particularly difficult to describe using natural bidding, and so we need to use the reply to 2C to help with this, in case responder declines to relay afterwards. This is the main reason why the very first thing we do is distinguish between minimum and maximum hands: showing strength is very difficult in natural bidding, particularly if you are unable to identify a trump suit quickly. Another thing which is difficult to show naturally is a hand of 5-5 shape. In order to describe these fully in natural methods, you would have to bid and rebid the second suit. So ideally, when you hold a 5-5 hand you would want your reply to 2C to show the second suit. However, in the scheme above, we only do this on maximum hands with both majors. Other two-suiters can cause a problem if responder needs to know about the fifth card in the second suit. This is particularly likely to be problematic if the second suit is the other major. For this reason, it seems to be a good idea to use opener's currently undefined 3C response to show a minimum hand with at least 5-5 in the majors (5-6 after a 1H opening).

When working out the replies to responder's 2NT or 3C relays, I feel that showing shortage is most useful. So for example, after 1M : 2C , 2H : 2NT (and 1M : 2C , 2D : 2H , 2S : 2NT) we could use

3C = no shortage (i.e. 5-3-3-2, or 5-4-2-2 with a 4-card minor)
3D = 5+ diamonds
3H = shortage in the other major
3S = shortage in diamonds
3NT = shortage in clubs

[This assumes that 5-5 hands with clubs are put somewhere else: this is possible if you use 1M : 2C , 3D for maximums and 1M : 2C , 2D : 2H , 3D for minimums. The latter sequence is not needed for a major two-suiter if that hand would bid 3C directly over 2C.]

Further asking bids are possible over 3C, 3D and 3H, but usually once opener has shown shortage it should be possible for responder to work out what the best game should be, and in particular whether 3NT will be a good contract.

After that you would need some slam-bidding methods. The sort of slam-bidding conventions you find in natural systems aren't really appropriate here. You can go a long way just using 4C as asking about general strength. I'll write a post about this at some point.