I’ve circulated the hand below around my club and can get no one to agree with me. I must be wrong. My intuition says otherwise so I have resorted to brute force hand analysis, as I didn’t know how to do this analytically, to see what I can find out. I’m telling you what the results show so that you can add these to your intuition to see if they persuade you to agree with me later, if you don’t now. Here’s the problem from a Silver Points in-person matchpoints duplicate. [I quit playing around 1970 long before the ACBL invented Silver Points and created new hurdles for us old timers. Even with the grandfathering awards of some token points, the change in requirements irks.]
The auction assumes you play a relay over a 15-17 1NT opening bid commanding a 3♣ response, which the responder will deal with according to the shape and quality of his hand, presumably loaded with some minor suit cards.
The diagram shows the North hand who commanded the relay with his seven-card club suit and now must decide whether to pass 3♣ or to invite game.
What do you do?
Me? I’m from the old school who learned about revaluing for length and adding, approximately, one point for the 5th card and two points each for the 6th and 7th cards, so I revalue this hand upwards from its nominal high card points of 5 to about 10: King + Queen + five for length. And working points, too. I figure there is about a 2/3 chance the spade King will carry its weight and produce a trick (or otherwise help partner with his suit). Moreover, the club Queen is no quack in this context. I think this hand warrants an invitation to game. Partner will not accept if his club holding is a worthless doubleton and if his outside-club holdings are quack-like, more-or-less worthless in a minor suit game contract. For me, this is an easy raise to four Clubs.
Many I’ve shown this hand to disagree with me. Some think the risk of encountering the doubleton club and going down in four clubs is too great to take the chance of finding the fit needed to grope for five.
The most helpful comment came from modern guy BBOer Miamijd, who said,
The first thing you need to do is get a better system. You need a system where 2♠ reveals interest in clubs and 2NT in diamonds, so that there are two possible responses. The first one becomes negative; the second one is positive. So if opener hears 2♠ and rebids 2NT, you just sign off in 3♣. If opener rebids 3♣ (accepting the invitation) I would try 5♣. That way you don’t end up in 5♣ down when partner has a hand that doesn’t accept an invitation.
Time for me to adopt the modern convention that lowers the level of the bidding for making the key decisions. Note that with the modern convention, one gets to decide at a lower level whether the hand is worth pushing towards game. Still the holder of that 7-card club suit with the outside king needs a good way to think about it.
Miamijd often uses the losing trick count — he’s about persuaded me to start using it — and continues his evaluation of this hand as follows: This seven-loser hand in clubs has a good chance to make 11 tricks if partner has a good 1NT opener with six losers. [Those who use the losing trick count for hand evaluation add the counts for the two hands, once a trump suit has been established, and subtract that sum from 24 to estimate the trick-taking potential of the two hands. Here 6 + 7 = 13; 24 – 13 = 11. Here’s a good, thorough introduction, which tells you how to do it. Wikipedia gives a good history, but is weak on how to do it.]
Before I started this column, I had no firm idea of the likelihood that partner has only a doubleton club. Now, I do. I decided to find out by brute force and give you a link to the results, which I’ll tell you about in a moment, after I discuss the results.
If you start with the notion that your partner has no worse than a doubleton in any suit when he opens 1NT and you hold seven cards in a suit, you can be confident that partner holds a doubleton only 20% of the time (tripleton 40% of the time; four or more 40% of the time). Further brute force analysis, of the sort in the link, shows that the expected trick loss is just one trick if all we know are the deal probabilities. If we know that partner accepts our club invite, meaning he has three cards to a top honor, then the expected loss drops to under one trick. You didn’t need any detailed computations to tell you that: If you hold ten cards in a suit Q-seventh opposite A-third or K-third, but you’re not sure which it is yet, you expect to lose no more than one trick.
Here’s the link to the computations where I show you how I derive the probabilities described in the preceding paragraph.
|South/Declarer has Club Length||With Probability||Then Expects to Lose This Many Club Tricks|
How about that spade King? Could be wasted. Could be worth a trick in the play. As I said earlier, a partner revaluing his hand to accept a minor suit game invitation will likely disregard quack [non-]values and focus on top honors. If he follows such a process, then a King is more likely valuable than usual. That’s my case for thinking the invitation is a good idea.
What about the risk averse thoughts — those who worry about the possibility of the rotten club fit? The expected loss with the worst of all possible fits is a trick and one-half. We write off the heart and devalue the spade King. Three and one-half down-graded tricks. How big a risk is a raise to four?
Show me a hand that makes four a bad bet and has the property that if I swap the non-club holdings in the hand, then a four-level contract remains a bad bet. I just want to be sure you are not cherry picking.
I end with the actual hand I held as South, which proves nothing except that when I held it, I thought about super-accepting. I decided that partnership discipline demanded that I stay in lane. I had scolded this very partner for bidding my values for me in an earlier session, so super-accepting seemed unwise for morale, even if sound bridge.
If you are inclined to comment, tell me what you think of the old advice I still carry with me about adding length points: one for the 5th card and two for each card after that. I think the main lesson here is to use a system in responding to opening NT bids that enables exploration of minor suit fits without going beyond the 3 level. A secondary lesson is that a seven-card suit headed by the Queen facing a known doubleton, or better, expects to lose no more than one trick.