LEARNING CENTER

3NT. Partner didn't ask "Do you have 17 points or 15 points?" Partner asked "Do you like your hand based on what you've shown?" Yes! This is a nice notrump hand. Mostly aces and kings. A good five-card suit. All the tens. These make it worth more than the 15 HCP. While we usually count using "Goren Points" (an ace is four, king three, etc), there are other hand evaluation methods including something called Kaplan-Rubens Points. Using K&R points, this hand is worth 18.05!

Pass. You have 16 HCP, but nothing about your hand that you like. You have no aces, no long suit, and no tens. 

4. You have aces, decent spots, and you have the QJ10 of hearts. Queens and jacks don't tend to be good cards, but they are very useful in partner's long suit. You also have a ruffing value with only two clubs. 

Pass. This is a fairly lousy 15-count. Lots of queens and jacks. Only one ace and one king. You do have a little bit of shape (4-3-3-3 is the worst). 

4 (or 3NT). Partner has six spades and 8 or 9 points. I would want to be in game. Sometimes it helps to re-imagine the situation. If partner has a weak two-bid in spades, do we want to be in game? Yes! Aces play really well opposite that type of hand. Additionally, the opponents have to lead something. All of our jacks are supported by 10s (and a 9). We can probably set up some extra tricks in one of those side suits. Game will be a good contract. 

You could also try 3NT. Partner can correct back to 4 with a hand that really hates the idea of notrump, but 3NT would be a good spot if partner has something like AQJxxx of spades. 

5NT or 6NT. 5NT here is "pick-a-slam" and you might have interest in, say, 6 or 6 if partner has some hand with shape. Or you could just bid 6NT, which is more practical. Either way, with four aces and a king (plus a jack), you should accept a slam invite. Partner must have something that they like in order to invite with no aces, so this one is clearly worth accepting. With either 20 or 21 points, you really need to use evaluation more than point count to decide whether to accept an invitational bid.