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.

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