A bit late to the party, but since I wrote in answer to that question:
This auction ended at 3NT (why, I won't go into, but there's a bonus for making it that you don't get with any lower bid).
You're now asking a question that needs the answer to "why". Now, all the answers given are accurate and good - for someone who plays bridge. But since I know you don't, here's the information that answers "why".
This will be a story in sections and footnotes(0). Footnotes aren't necessary to understand...
Bridge deals are scored (provided declarer makes the contract) like this:
Trick score ("odd tricks" are defined as "tricks more than 6 of the 13"):
- 20/odd trick with clubs or diamonds trump
- 30/odd trick with hearts or spades trump
- 40 for the first odd trick, 30/further at notrump
Which isn't much. But there are big bonuses for bidding and making contracts at certain levels(1):
- 2000 for grand slam (7 level, make all the tricks)
- 1250 for small slam (6 level, all the tricks but one)
- 500 for game (100+ trick score)(2)
- 50 for partscore (<100 trick score).
Emphasis on bidding. If you take 10 tricks in spades, you get 120 trick score, but if you don't contract for at least 10 tricks (bid 4 or 5 Spades)(3), you only get the partscore bonus.
So, what are the "game" contracts? 100/20 is 5 Clubs or 5 Diamonds; 120/30 is 4 Spades or 4 Hearts; (100-40)/30 is 3 Notrump.
Now, remember that the goal of the (uncontested) auction is to answer the questions "where" and "how high". Once a player knows the answer to both of those questions, they set the contract and partner passes(4).
But since you get the same "trick score plus game bonus" for 3NT, 4NT and 5NT, there's no reason to want to play those last two(5). So, unless 6NT or 7NT is in the picture, if "where" is notrump, and you have the strength for game, "how high" is 3.
With that knowledge, read the other answers. As an example:
1NT is a very well-defined bid - no long suit, no short suit, and usually a 3 HCP range (15-17 is common). So when partner bids that, it is easy to see that with responder's hand:
- we have enough for game;
- we don't have enough for slam; and
- we don't have an 8-card major fit.
If that's the case, responder knows "where"(6) - notrump - and "how high" - 3NT. So they bid it, and partner passes.
Similarly, if responder knows that "we don't have enough for game" and "we don't have a good fit", they just pass 1NT.
If responder isn't sure, then other bids between 1NT and 3NT come out:
- if responder has a 4-card major and wants to know if opener has 4 to match, they can bid 2♣ systemically asking partner to bid one if they have one(7).
- if responder has enough for game if opener is at the top of their range, they can bid 2NT, which partner will pass with a minimum or bid 3 with more.
- if responder wants to play a partscore or game in their long suit, they have bids that allow that.
- ...
But "you bid 3NT over 1NT" when you know that's where you want to play. It's very common.
0: GNU Douglas Adams.
1: Yes, I know, NV bonuses are different, and I've combined "game+slam bonus" for simplicity. This is Wrong, but not incorrect.
2: okay, at duplicate. Rubber bridge is fascinating, but again, "simplicity".
3: This is the difference between Contract Bridge (what everybody plays today) and its predecessor, Auction Bridge (where you got the bonuses for game or slam whether you contracted for them or not). Contract and Vulnerability (1) are what made the game what it is today.
4: Handwaving like mad here. Please let me? We're talking a 1NT "responder is captain" auction.
5: In fact, that's why 4NT is almost always reserved for asking for Aces, and 5NT for some other conventional ask (except over 1NT openers, yes, I know. Again, simplicity). Nobody wants to play 4NT or 5NT when they could have played 3NT.
6: Rule of thumb is that you can take one more trick in an 8-card fit than at notrump. So 4 hearts is better than 3NT with a heart fit. But it is almost always easier to make 3NT than 5 of a minor.
7: which is why I said later in my response to the previous question:
There's little to go on with 1NT-3NT, but there is a strong implication that a major suit (hearts or spades) will work better than a minor suit (clubs or diamonds). Because of the way the scoring system works, finding a major suit fit is a big thing, and LHO hasn't even looked for one - so they don't have one.