[Greathale]

My partner and I have only been playing for 6 months but are keen to learn. We play weak 2's in hearts and spades, Stayman and Transfers. Last week my partner had a 28 HCP balanced hand (3343) and I had a 5 HCP balanced hand (4333). Partner opened 2 Diamonds (25+ balanced) and I responded a negative 2 hearts. Partner rebid 2NT, and I responded 3NT denying a major. Partner passed and we made 12 tricks. Where did we go wrong? We have had a lot of conflicting advice. We are wondering if partner should have bid 4NT, with me raising to 6NT with by 5 HCP hand?

[Cyberyeti]

There are several ways of accomplishing this, you just need to decide which is the one for you in agreement with partner.

You can bid as you did, then partner can bid 4N.
You can bid 4N over 2N.
You can agree ranges for 2♣-2♦-3N and 2♦-2♥-3N so that partner shows 27-28 or 28-29 immediately.

[Greathale]

 Cyberyeti, on 2013-December-29, 09:59, said:

There are several ways of accomplishing this, you just need to decide which is the one for you in agreement with partner.

You can bid as you did, then partner can bid 4N.
You can bid 4N over 2N.
You can agree ranges for 2♣-2♦-3N and 2♦-2♥-3N so that partner shows 27-28 or 28-29 immediately.

[Greathale]

Thanks. Makes sense. As I understand it, if I bid 4NT straight after partner's 2NT it's telling partner I am at the max end of my 2 hearts 0-5 range, which allows partner to pass with 25-27 HCP or bid 6NT with her 28 HCP. I can bypass the 3NT denial of a major as it is going to be superfluous given that I don't have a four card major.

[Cyberyeti]

 Greathale, on 2013-December-29, 11:20, said:

Thanks. Makes sense. As I understand it, if I bid 4NT straight after partner's 2NT it's telling partner I am at the max end of my 2 hearts 0-5 range, which allows partner to pass with 25-27 HCP or bid 6NT with her 28 HCP. I can bypass the 3NT denial of a major as it is going to be superfluous given that I don't have a four card major.

4N is an invite with no major, by the way you need to agree whether 2♦-2♥-2N-3♣(some form of stayman)-3major(puppet or not, but showing a major)-4N is blackwood or the same quantitative invite.

If your range for 2♥ is 0-5, 4N is probably best, if it's 0-7 it's a matter of choice who bids 4N.

[Cascade]

Like Cyberyeti said.

However you probably won't have to worry about 28 points opposite 5 again in the near future or indeed vary many times in your entire bridge career. The quantitative principles are however important in lots of auctions - although again relatively rare but more common than your example so that they are worth learning.

1NT 4NT - invitational to six
2NT 4NT - invitational to six

Also I usually play:

1. Stayman then immediate 4NT is a quantitative invite (without a fit) over both 1NT and 2NT

1NT 2♣
2♥ 4NT - denies heart fit and invitational to six, opener can pass, bid 6NT or introduce a second suit

This also applies after a 2♦ or 2♠ response to Stayman and over similar auctions with a 2NT opening or even after a strong two level opening and a 2NT rebid;

2. (Assuming you play transfes) Transfer then immediate 4NT is a quantitative invite over both 1NT and 2NT

1NT 2♦
2♥ 4NT - quantitative invite opener can choose to play 4NT, 5♥, 6♥ or 6NT or rarely even introduce a new suit

Again similar agreements apply over other transfers and after a 2NT opening etc.

There are agreements that you can have to show a slam interest hand with a fit after Stayman as there are for using an ace ask after a tranfer.

A quantitative raise of no trumps can also be used in almost any other auction in which one or other partner bids no trumps, for example after a 1NT rebid or a long and tortuous auction where you finally, at least you think, rest in 3NT.

1♣ 1♥
1NT 4NT - invitational to slam

1♣ ...
...
3NT 4NT quantitative invite to slam

[fromageGB]

 Greathale, on 2013-December-29, 11:20, said:

Thanks. Makes sense. As I understand it, if I bid 4NT straight after partner's 2NT it's telling partner I am at the max end of my 2 hearts 0-5 range, which allows partner to pass with 25-27 HCP or bid 6NT with her 28 HCP

Yes, if you play the 2NT rebid as unlimited.
However, as Cyberyeti has implied, it is more normal to have a restricted strength range. When opener has these huge hands, responder normally has next to nothing, so I am in favour of opener's rebid showing just a 2-point range. This makes it simpler for responder to decide whether to bid game.

When I played Benji many years ago, I also used 2♣ followed by a rebid of NT as a different range to starting with 2♦. From your statement that it is 25+, I assume you also do. My assumption is that you play
2NT = 20/21 (maybe 19-21)
2♣ then 2NT = 22-24
2♦ then 2NT = 25+
You could think about changing this to 2-point ranges and include rebidding in a greater number of NT. For example if you open 2NT on 20, it could be
2NT = 20/21
2♣ then 2NT = 22/23
2♦ then 2NT = 24/25
2♣ then 3NT = 26/27
2♦ then 3NT = 28/29
2♣ then 4NT = 30/31
2♦ then 4NT = 32/33

The top end bids never happen, of course, but you don't have to remember them because it is a simple 2-point ladder starting with 2NT that you work out when you need to. Calculators are probably out, but there is no rule against putting your hands under the table and using your fingers.

With a 2-point range you wouldn't usually bother with invitational 4NT/5NT bids, but look at the quality of your hand to bid the best slam. Your bidding using this ladder would have been 2♣ 2♦ 3NT 6NT.

If you open 2NT on 19, move the ladder down a point.

You can still keep transfers on over a 3NT rebid.

[fromageGB]

Incidentally, if you moved the ladder down a point the 3NT rebid would be 27/28, and then you may wonder with a possible 32 count that 2 aces were missing. Use 4♣ Gerber to find out, then if OK bid 6NT.

[Zelandakh]

My "vanilla Benji" solution to this is fromage's second solution with 2 card ranges. I first read it in a Master Series book back in the 80s.

I do diasgree over a minor point though - over the 3NT rebids, 4♣ should be Stayman and not Gerber. I would also encourage not opening 2NT with 19 points, which is potentially dangerous even with an expert deeclarer but can get really ugly in the hands of a beginner.

When I was younger I developed a version of reverse Benji based on this scheme but also including a sequence for strong 3-suited hands:

2NT = 20-21
2♣ - 2♦; 2NT = 22-23
2♦ - 2♥; 2NT = strong 3-suiter
2♣ - 2♦; 3NT = 24-25
2♦ - 2♥; 3NT = 26-27
2♣ - 2♦; 4NT = 28-29
2♦ - 2♥; 4NT = 30-31

Now a little older and wiser, I would extend the 3NT rebids to 3 point ranges (24-26 and 27-29) if I revisited this. Having written this, although I played it as a complete beginner, it is not something I generally recommend. There are some other solutions out there too that are more advanced.

The actual questions in the OP have pretty much been handled expertly between CY and Wayne. Quantitative invites are often overlooked by beginners in favour of the "sexier" Blackwood. They are however a very useful tool and solve many bidding problems based on having a slam try without a known fit.

One extension to this that I think is very much applicable to B players is to allow partner of the 4NT bidder to do something else other than pass or 6NT. The simplest is to say that partner passes with a minimum but bids a new suit naturally with extra length in that suit. Only with a max and no extra length do you bid 6NT. This allows you to get a little bit of extra functionality out of the quantitative invite without having to learn any new conventions or anything unnatural.