LEARNING CENTER

21-22, balanced with a diamond stopper. If South overcalled 1NT, it would show 15-18 with a stopper. After the double, South could bid 1NT to now show 19-20. Doubling and jumping to 2NT should be 21-22 or so. With four hearts, the doubler would raise. 

19-20, balanced, with a heart stopper. Again, we need to think about the logic of the auction. A direct notrump overcall shows 16-18 (or a good 15), and so doubling first before bidding notrump shows 19-20 (or a bad 21). The preempt can have the effect of squeezing our ranges, so occasionally we have to make our best guess at evaluation. 

19-20, balanced, with a spade stopper. This time, South didn't have the room to jump to show 18-19, but still doubled before bidding notrump at the lowest level. That must promise a bigger hand than a direct 1NT overcall which would be 18-19. 

Both minors. The strength of your hand depends on the vulnerability, but you should care more about how good your suits are than high card points. I'd rather bid 2NT with: 

 43  
 2  
 QJ1098  
 KJ1098
 

than:

 KQ  
 Q  
 A5432  
 J8532
 

even though the second hand has more points. 

18-19, balanced, heart stopper. North gets a chance to bid again, so with 12-14 (which North knows about from South's opening bid), South should just pass. 

11-12 HCP, balanced, heart stopper. The way to make a raise would be to cuebid hearts. This is invitational, and responder needs roughly 11 or 12 points to invite. This denies four spades (South would have made a negative double). 

12-14, balanced, spade stopper. The reason our range is a little higher is that partner is simply an overcaller and could have only 8 or 9 points. Some experts are using this as a conventional raise, but that requires partnership agreement.