How do you play your 11 if the dealer has an Ace showing? We are going to say that you are playing Vegas Strip Blackjack and the dealer has checked for a natural blackjack and does not have it. Which 11 is stronger, yours or his? And how do you play an 11 versus an Ace?
If you look at your basic strategy chart because I know you have one, you will see that you do not double down on a hard 11 against Ace despite doubling down on against all other dealer up cards. And there is a very good reason for this.
As a player you would think that your 11 is stronger than the dealer