11-7-4-2-1 in action

I was just commenting on the Seniors Camrose on BBO and watched Paul Hackett open 1D (2nd seat, vul vs not) on the hand below:

♠	K Q J 6
♥	7 5 2
♦	K 9 5 4
♣	Q 3

That's 11 HCP on the 4-3-2-1 scale and only 9.6 on the 11-7-4-2-1 scale (7+7+4+4+2=24 * 4/10 = 9.6). That's before adjusting for the doubleton queen. The spades are worth a bit extra due to the honours working together, but still the hand is clearly weaker than an average 10 HCP when evaluated correctly. The Kaplan/Rubens hand evaluator calls it 9.75.

Most players wouldn't open the hand anyway, but I think most would wrongly invite game opposite a weak notrump.

The full deal is below, though it doesn't really prove much as South has a good hand and North's gets better when South bids clubs so the values for game are there. Only the misfit in diamonds and hearts makes it poor.

		♠	K Q J 6
		♥	7 5 2
		♦	K 9 5 4
		♣	Q 3
♠	8 4			♠	10 5 2
♥	K Q J 9			♥	A 6 3
♦	10 8 2			♦	A Q J 7 6
♣	9 5 4 2			♣	10 6
		♠	A 9 7 3
		♥	10 8 4
		♦	3
		♣	A K J 8 7

Weak Notrump vs Strong Notrump

Below are some arguments that might be made ('weak' is 12-14 and 'strong' is 15-17):

Weak NT

1. When the weak NT is not used, there is an inference that opener is either stronger or more distributional that a minimum balanced hand, so for example, major suit raises by opener don't cover such a wide range.

2. The strong NT leads to more awkward situations where it is necessary to open 1NT offshape, because the hand is too good to rebid 1NT or repeat the suit opened, but is not strong enough to reverse. The weak NT also has some offshape 1NT rebids but they are less frequent.

3. Any 1NT bid leaves your side well placed in competitive auctions because it is limited in both strength and shape, compared to opening 1 of a suit. This favours the weak NT because it occurs more often.

4. Typical methods over 1NT are not well suited to constructive auctions so a weak NT will cause opponents to miss games and/or overbid. Alternatively, they can play overcalls as always sound but risk losing the partscore battle.

Strong NT

1. The weak NT is more likely to go for a large penalty.

2. Playing weak NT, the strong NT hands can be awkward when interference prevents a 1NT rebid. The hand is better than minimum but further action may still be too much.

3. You may lose your own 4-4 major fit after opening 1NT. This is less frequent with a strong NT and also less dangerous because 1NT will often make anyway.

I also think investigating slam or the best game in an uncontested auction is more difficult after 1NT than after 1 of a suit. Traditional methods over 1NT make poor use of the available bidding space. It's not clear which side this favours as the weak NT is more common but the strong NT makes it more likely your side has a game.

I'm not attaching weights to these factors at this stage - just trying to identify the issues.

Four card majors and weak notrump?

Twenty years ago, four card majors and a 12-14 notrump dominated bridge in the British Commonwealth. If a serious partnership in New Zealand played five card majors and a strong notrump, you'd look at their card and say "Oh yeah, my grandmother used to play that. Do you play Fishbein as well?".

That's not the case any more. In New Zealand and the UK, top pairs are switching to Standard American or 2/1. The Australians have always been a bit closer to the American style, but the weak notrump is losing ground there too. What has changed people's minds?

The obvious reason is that the most successful pairs in World Championships use these methods. But there are some equally obvious objections to this:

1. If copying World Championship winners is so clearly right, why aren't we all playing Blue Club?
2. The USA was winning for a long time before we started copying them.
3. The Americans have markedly superior card play. If Bridge had no bidding and was scored on play alone, I expect the USA would have won even more World Championships.
4. I'm not entirely sure that the weak notrump has done badly in World Championships, when considered in proportion to the number of players using it.

If we just consider four vs five card majors and 12-14 vs 15-17 NT, I think it's nearly impossible to establish objectively which is best. My gut feeling is about a 60-40 preference for five rather than four card majors and a 75-25 preference for weak rather than strong notrump.

Switching to five card majors may be explained by a desire to use the Law of Total Tricks and Bergen Raises. I think this is an error, for reasons which are spelt out clearly here. However, there's no reason that five card majors and strong notrump need to necessarily go together. If people are switching to a strong notrump for that reason, I'm fairly sure they are just mistaken.

I'll post a detailed explanation of my preference for the weak notrump later.

How much are high cards worth?

A few weeks ago I built a double dummy solver and have been using it to analyze the relative value of honours. I'm not sure I have the methodology exactly right and will post more on that later, but for now I'll just report the results. This is based on computer simulation of about 130,000 hands.

Card	Average tricks
A	1.2660
K	0.8145
Q	0.4618
J	0.2275
T	0.1133

The trick value is the average extra tricks taken in your side's best fit (or notrump). In order to use this, we really need to convert to a scale with 40 total points in the pack, so that values will be comparable. The following table compares the above simulated results with various point counting methods, all adjusted to the same scale.

Card	Simulated Value	4-3-2-1 Value	6-4-2-1 Value	11-7-4-2-1 Value
A	4.391	4	4.615	4.4
K	2.825	3	3.077	2.8
Q	1.602	2	1.538	1.6
J	0.789	1	0.769	0.8
T	0.393	0	0	0.4

As you can see, the 11-7-4-2-1 count is extremely close to the actual trick taking ability of honours. Probably someone has discovered this before, but I haven't heard about it. Now of course there is a lot more to life than counting points, but I think this can improve bridge decision making. Conveniently, the total of 11+7+4+2+1 is 25 so you can add up your points, double the total twice then divide by ten to get a value corresponding to the 4-3-2-1 scale.

Introduction

Hi, my name is Nigel Kearney and I live in Wellington, New Zealand. I played international bridge back in the early nineties at Open and Junior level including winning a silver medal in the 1995 World Junior Championships. I've been out of bridge for the last 13 years and am just getting back into it now.

I'm interested in bidding theory and hand valuation so will be posting quite a bit about that.

Welcome to Bridge Thoughts.