After partner's NT bid, a raise to 4NT is invitational, asking partner to bid 6NT or pass. It works in the same way that 1NT 2NT invites partner to 3NT only this time you're interested in bidding slam rather than bidding game.
Use the quantitative 4NT bid when you have a strong balanced hand and you're not sure if your combined strength is enough for 6NT.
Points needed for 6NT
Typically you need 33 HCP to bid 6NT when you don't have long suits to give you extra tricks. If you know you have 33 points between the two hands you can just bid 6NT, but if you are close to 33, you can use the quantitative 4NT. Partner will either pass with a minimum opener or bid 6NT with a good opener.
North opens 2NT to show 20-22 points and a balanced hand. South invites to slam with 4NT but North has a minimum 20 points and so passes.
South's hand is the same but this time North has 22 points and is maximum for the 2NT opening. 6NT makes 6.
Quantitative 4NT or Blackwood
The Quantitative 4NT bid is used when partner's last bid was NT. To ask for Aces when you are planning on playing in a suit contract use Blackwood.
If you are wanting to ask for Aces after a NT bid you can use Gerber.
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