[Ethel]

Bidding by South: 2C (22+points)
North: 2D (waiting)
South: 3NT (25-27Pts)
North: 4NT

East and West passed in between.

[eagles123]

quantitative (bid 6 with top end pass with bottom end)

[mikeh]

eagles is basically correct.

As one advances in the game, the question becomes a little more nuanced.

Put another way: when 3N shows 25-27, with 27 the answer is obvious...bid slam.

With 25, the answer will usually be just as obvious: pass.

But what if you hold an 'average hand'. What do you do?

You may say: why bother worrying, I don't get very many of these. However, the same idea appears frequently both with 4N and on lesser hands.

Thus 1N 4N bears the same meaning, but with responder holding a much better hand this time around. The same question is being asked....do you bid slam or not?

And say you play that 1N 2N invites game (many play that this is an artificial sequence but even if it is, they have another way of asking the same question...opener....do you want to bid game? And the same general principles apply in this and many other 'quantitative' invitational sequences.

Maximums and minimums are easy, but the in-between hands are important and not as clear cut.

As one advances, especially as one develops a steady partnership, it becomes useful to have an agreement as to what the invitational bid means.

In my partnerships, and I think this is the majority view amongst experts, the invitational call asks partner to 'accept the invitation' (whether to game or slam) unless partner has a reason not to accept. This basically means accept UNLESS one has a minimum.

The converse approach, which is (I think) a minority school) treats the invite as saying: accept ONLY with a maximum.

Playing in the style I recommend, responder will have to have a slightly stronger hand to invite than playing the other way around. Playing in the style I don't like, responder can be a tiny bit lighter, because opener won't accept without a true maximum.

Both approaches will reach or miss about the same number of contracts. The difference comes on those hands where even the invitational contract fails. Thus 4N is down 1. This happens rarely because after all we were considering 12 tricks, so it must be a bad day when we make only 9. It happens far more frequently when we play in 2N, after a rejected try for 3N. My view is that it is best to play a consistent philosophy on invitational sequences, in the absence of a reason not to do so.

[Mbodell]

The other advantage on this auction of playing the style mikeh recommends and is probably most common is that the 3nt isn't 1/3 of the time 25, 1/3 of the time 26, 1/3 of the time 27. When you are on the extreme tails of the distribution you will get many more 25 point hands than 26 point hands and many more 27 point hands than 26 point hands. So the bulk of your hands will be 25. If your invite was about separating the 27 from the 26 and less, it wouldn't add as much value as if it were separating the 26 from the 25. In fact, if you up grade very good 24 point hands in to the range, even if 80% of 24 point hands don't get upgraded, it wouldn't be surprising to find out that on a frequency basis you will have 24 points for 2♣...3nt more often than 27, possibly more often than 26. You can see this here where the likelihood of 24 hcp is about 6 in 10,000 hands; 25 hcp is about 3 in 10,000 hands; 26 hcp is about 1 in 10,000 hands; 27 hcp is closest to 0 in 10,000 hands. So if you upgrade the top 20% of 24 hcp hands that will be about 1.2 in 10,000 hands which is more likely than 27 hcp for sure and quite possibly more likely than 26 hcp too. If you play 2 sessions a day, every day, you'll have a 26 hcp hand roughly once every 8 months - enjoy!

Note even at much less extreme levels there is a similar, though not as extreme, asymmetry in the points. 15 points is nearly twice as likely as 17 points. A 15-17 NT is about 50% 15 and 50% 16-17 - especially if you ever upgrade 14 counts into the hand (if you never ever upgrade it is more like 43/57 or something). A 20-22 NT is more likely to be 20 than 21+22 combined - even without any 19 point upgrades. Everyone is already somewhat used to this feature in a "normal" 1 opening bid. If the range is about 11-21 for such a bid you already know than 11, 12, 13, and 14 are all much more common than 18, 19, 20, and 21. In fact all hands 17 hcp and higher (all hands 17-37 hcp combined) are less likely than all hands with exactly 13 hcp!

[relknes]

When debating whether or not to accept a NT invite with the middle value, I have a rule that I often use: count your honors, and if you have at least half as many honors as points, accept the invite.
For instance, after 1N-2N, playing a 15-17 NT, I would pass with AKxx, Ax, JTxx, ATx (7 honors), but I would bid 3N with KQxx, Ax, QJTx, KJx (8 honors).
This is somewhat related to "Suit texture". Suit contracts mostly rely on aces and kings, but NT is often about developing your lower honors so having a bunch of them to develop is a bonus. Your expected number of honors is half your high card points, so you will upgrade about half your middle hands and downgrade about half of them.

[Stephen Tu]

Quote

When debating whether or not to accept a NT invite with the middle value, I have a rule that I often use: count your honors, and if you have at least half as many honors as points, accept the invite.

I've never heard this theory, and think it's pretty wack. Aces are good for NT also. If you have to knock out more of them to get your tricks, that's more entries for the opps to run their suit, and that ace might be their 5th trick before you can run your 9. Also, 2nt is a stupid contract, particularly at IMPs you don't want to be finding weird reasons to play more of them.

I did a quick double dummy sim of 200 hands balanced 9 count (4432/4333) or 8 count with 5 cd minor for partner opposite both of your example hands; they are both easy accepts of an invite to 3nt. And the first hand took quite a few MORE tricks on average than your second hand. It was like 76+% making vs. 65+% making.

Accept with 16+, decline with 15. Upgrade hands with lots of tens. Not this "count your honors" nonsense. If you have more of the high value aces and kings, on balance your partner will have more Qs/Js to justify his invite and this will basically balance out. Traditional point count has been shown to work fairly well for NT contracts with balanced hands facing each other.

[relknes]

Hmm... well, maybe I am crazy then. The theory came from the 5-4-3-2-1 count, which I thought was supposed to be better for marginal NT contracts.
So what do the sims say about Axxx, Ax, Axxx, Axx? As a 16 point hand, I take it that it is an accept, but what are the percentages?
By the way, in deciding to invite or not, the hands that you mentioned would just jump to 3N with decent intermediates the way my partner and I play. We count an extra point for a 5 card suit, and invite on 8 with decent intermediates or 9 with lots of spaces.

[Stephen Tu]

Aces and spaces fare somewhat worse, but still a 60% game opposite balanced 9. Balanced 8 would drop it below par. I didn't try to quantify "decent intermediates" since you didn't really specify what the dividing line for that is.

If you are looking for point count improvement look at http://bridge.thomas...luesfor3nt.html
After a bunch of simulations he settled on 4/2.8/1.8/1/0.4, with a slightly lower target for 3nt (24.4 instead of 25). Simply counting a half point for tens and using 25.5 for game instead of 25 worked fairly well also.

I personally "invite with 9 and accept with 16", and treat having multiple tens as basically +1, no tens as a partial minus, 5 cd suit as maybe +0.5

[mgoetze]

For the reasons that Mbodell gave, 4NT should mean "please bid slam with 26-27 and pass with 25". Noone has yet told you how many points that means North should have. The answer, interestingly enough, is 6 HCP. With 7 HCP, North should just bid slam.

http://www.rpbridge.net/8j25.htm

[ArtK78]

I have a suggestion, which I have posted elsewhere.

First, I assume that transfers are on in this sequence. This is something you will have to agree upon.

Presumably, a 4♠ call on this auction does not have a meaning. This is true in many notrump auctions when the partnership plays transfers.

In a notrump auction where 4♠ has no meaning, you can use 4♠ and 4NT as invites. My personal preference is that 4♠ says bid slam only with a maximum, and 4NT says bid slam unless you have a minimum.

[NickRW]

Stephen Tu, on 2015-January-25, 14:48, said:

Aces and spaces fare somewhat worse, but still a 60% game opposite balanced 9. Balanced 8 would drop it below par. I didn't try to quantify "decent intermediates" since you didn't really specify what the dividing line for that is.

If you are looking for point count improvement look at http://bridge.thomas...luesfor3nt.html
After a bunch of simulations he settled on 4/2.8/1.8/1/0.4, with a slightly lower target for 3nt (24.4 instead of 25). Simply counting a half point for tens and using 25.5 for game instead of 25 worked fairly well also.

I personally "invite with 9 and accept with 16", and treat having multiple tens as basically +1, no tens as a partial minus, 5 cd suit as maybe +0.5

Yeah. 5-4-3-2-1 scores (when it does) because it takes 10s into account, but it messes with the relative value of the other honours too much. Andrews' adjustment is best, but if I was incapable of either counting in fractions or even using the principle it embodies, I'd be happier sticking to regular 4-3-2-1 for low level NT contracts

Nick

[Zelandakh]

ArtK78, on 2015-January-26, 07:17, said:

In a notrump auction where 4♠ has no meaning, you can use 4♠ and 4NT as invites. My personal preference is that 4♠ says bid slam only with a maximum, and 4NT says bid slam unless you have a minimum.

An alternative that I am rather fond of is to extend the transfers upwards, so 4♠ becomes the invite (allowing something extra such as Baron to be bundled in) and 4NT/5♣ become minor suit transfers. You could probably also use 4♠ as something along the lines of PK's sand wedge Blackwood if you have recruited 4♣ for a purpose other than Gerber.

[TylerE]

Another option I like over 4N...

Pass = Min
5x = Feature, usually a quality suit, asks responder to reevaluate in context of that feature + middling values (could be min HCP but with a robust 5 bagger, say). Responder's 5NT over 5x is to play. Responder can also counter-slam try by bidding a suit where he wants to be in slam if opener has a good/useful holding. The overall concept is similar to 3 level game trys after 1M-2M.
6NT = Max