LEARNING CENTER

Quantitative (invitational to slam). We don't have a suit, so we can't ask about keycards. Generally, this is the best way to invite slam with no interest in a major. A typical hand for this auction: 

 A2  
 K43  
 KQ1032  
 KJ8
 

16 or 17 HCP and interest in slam if partner likes his hand. Note that we don't care about aces. Partner is unlikely to like his hand with only one ace anyways. Partner could have,

A) 

 J543  
 AQJ  
 J87  
 AQ4 

which has two aces but not enough tricks (even without a spade lead there are only 11 tricks). You want partner to have something more like

B)

 K876  
 AQJ2  
 J76  
 AQ
 

17 HCP, and so slam is laydown. 

Quantitative (invitational to slam; no heart fit). With a heart fit, the way to set trumps is to bid 3. 3 can't be natural (we would transfer) and so we can use this odd looking bid as a forcing raise. Over a 2 response to Stayman, 3 is the way to make a forcing raise. 

Blackwood (Spades). Sure, the last bid was notrump, but it was an artificial call. Jacoby 2NT set spades as trump. We might use Blackwood now if we opened 1 with, say: 

 KQJ932  
 KQ2  
 AK2  
 2
 

or a number of other hands where you have controls in the other suits. 

Other. This 4NT shows two places to play. It might be both minors, or it might be hearts and a minor. South could have something like: 

 43  
 K9842  
 6  
 AJ984
 

Quantitative. One thing to consider: is there a way to set trump? Here, the way to set trump would be a cuebid of 4. A hand South could have: 

 K2  
 AQ2  
 KQ872  
 Q98