If I'm inclined to bid NT with 15-17 points, but am weak in one suit, how weak can I be, and still bid 1NT, as opposed to bidding 1 club, to find out if my partner can show strength e.g. a stopper in my suit, by bidding it?
Your partner's response(s) ought to give you a good idea of whether a no trumps contract is the correct one to pursue, or if you might be better off looking elsewhere.
Perhaps your partner will bid Stayman over your NT bid. If you find a satisfactory fit in hearts or spades, then the question of whether you have a shortage somewhere else becomes irrelevant (in fact, it turns into a bonus).
Otherwise, your partner may well - indeed, is statistically quite likely to - try to bid the suit that you are weak in. If he does, then this reinforces your initial assumption that a no trumps contract may be a good place to be.
If your partner avoids the suit you are weak in - especially if he avoids it twice, then perhaps NT is not such a good idea. However, if this is the case then he has almost certainly bid in a suit that you hold 4 cards in, by now. If so, you have a pretty good option to shift to, outside of no trumps!
If you have a balanced hand, 15-17 HCP, but you don't open 1NT, you may encounter difficulties rebidding.
For example, you open 1m and your partner responses 1NT, and then you are in a dilemma. Your 2NT rebid promises 18-19 HCP (between 1NT opening and 2NT opening), which is unsuitable now. Sometimes you reverse with a 4-card major and your parter goes 4M with only 8 points. Other times you pass or bid a 3-card suit, but your partner has 9-10 HCP.
For 15-17 HCP, I open 1NT for all 4-3-3-3, 4-4-3-2, 5m-3-3-2, and 5m-4-2-2. Whether to open 1NT for 5M-3-3-2 or 6m-3-2-2 is another question to discuss. Don't forget 1NT opening preempts opponents' majors!
Something I wrote on Another Site, but it's still relevant, and contains some information not in the current answers:
"If it looks like a balanced 15-17, open 1NT". That's the modern guideline.
All of the caveats of the past:
- need stoppers in 3, preferably all 4 suits;
- need 2.5 QT;
- 4333, 4432 or 5m332 only;
- no small doubleton;
and the rest have all dropped by the wayside. People still discuss what to do with 5M332 and 6m322, but more and more pairs are moving to "put it in 1NT". Most will bid 1NT with 5m422, even 5m4M22.
People are pushing the boundaries of what regulators consider "balanced", as well. Something like AKTx KJ9x K QTxx has always been opened 1NT by many with "looks balanced to me", and regulators are bowing to the inevitable. So now, players are saying "well, of course AKTx KJ9x 7 KQTx is balanced." Others are saying "are you out of your mind?" and "if you describe that as balanced, that's clear misinforming of the opponents"... You can see from this, or from the 7m222s that people want to open 1NT as well, just how much those caveats/old rules have disappeared.
The problem isn't that any of those old caveats are bad - in fact, we'd prefer to avoid them even now. The problem is that if you don't open 1NT with a balanced hand in your range, it's almost impossible to show it later, or you have to devote so much of your system to "15-17 balanced, unsuitable for NT" that could be used to distinguish between all the rest of the hands in a "12-21, 3+" 1♣ or 1♦ call (which needs a lot of distinguishing as it is). Never mind when it goes 1♣-p-1♥-2♠; now you really want to be able to say "pass is minimum, no 4-card raise (if BAL, 12-14, much easier than 12-16), 2NT is a big hand (18-19 much easier to handle than 16-19),..."
It does cost sometimes, like all decisions. You will get 1NT-p-3NT off the first 5 heart tricks sometimes. But it pays back 4, 5, 6-1 on hands where partner can rely on you not having that hand when they try to figure out this crazy auction.
But the stopper requirement went out with Goren in the 1960s. You just can't bid standard sanely with it.
I frequently open a 15-17 1NT with a small doubleton minor, but guarantee at least Qx or xxx in each major to stand partner's possible weak transfer.
A hand that fails this standard, but does not have a 5-card major, has at least 7 minor suit cards and thus is opening a 4-card or longer minor suit.
This is very much a matter of partnership agreement. Some people hold to the definition of "No voids or singletons, no more than one doubleton" for a hand balanced enough to open 1NT. Some prefer "no suit weaker than Qx" instead or in addition. Some will open with a singleton A or K, or even a singleton Q.
The ACBL's Standard American Yellow Card" says that: "Notrump openings show a balanced hand and may be made with a five-card major suit or a five-card minor suit." This is likely what a pick-up pair who have not discussed the matter will play. An established pair should discuss.
The vital thing is that a partnership have a clear agreement on what hands will be opened with 1NT.
As Mycroft points out, if you don't open 1NT with some such hands, there can be a problem finding a good rebid, particularly after a 1NT response to 1 of a minor. On the other hand if you include more distributional hands in the range of a 1NT bid, there may be other bidding problems or missed fits. Personally I would not open a hand with a 6-card suit, or a singleton, with 1NT, but many good players do so.
If you are going to limit what hands can be opened with 1NT, discuss with your partner responses and rebids when opening a 15-17 HCP hand in a suit, esp a minor suit. If you don't both know the sequences you will use with such hands, you are setting yourselves up for a problem.
There are also rules limiting what the agreements here can be. These depend on the sponsoring organization. The ACBL now defines as "natural" any "NT opening bid or overcall that contains no voids, no more than one singleton, which must be an ace, king, or queen, and that does not contain 10 or more cards in two suits combined." and permits most such bids in most sponsored games. As some other answers point out, such rules have grown more permissive over time. But just because something is legal does not make it good bridge, or right for a particular pair.