Blackjack Strategy When Playing a Soft 15 and 16

Double Down: When the dealer upcard is 4, 5 or 6.
Hit: When the dealer has anything else showing.

Why to double down on soft 15 and soft 16

The basic strategy here is to get the dealer to go bust. If he or she is holding a 4, 5 or 6 upcard, there is likelihood that a ten will be hit and then another ten because of the higher density of ten cards being played in blackjack. In this case, the dealer has a higher probability to bust, but that probability gets smaller as the showing card gets lower because there are more available cards that would prevent a bust. You are safer having a soft 15 or 16 anyways so it doesn't hurt to double down and hope for a better hand.

Why to hit on soft 15 and soft 16

Now it becomes tougher if the dealer doesn't have those ideal cards showing and it's not as likely that he'll bust. Therefore the strategy is to try getting something better. It doesn't hurt to hit since the soft hand will prevent you from ever busting and you really have nothing to lose here. This is mathematically the correct blackjack move to make as well over the long term.