It all depends upon which advantage you want to rely upon the most.
Link Removed
Deterrence is a strategy for peace, not war, designed primarily to persuade opponents that aggression of any kind is the least attractive of all alternatives.
Fear of punishment, not promise of reward, is most likely to keep foreign armed forces from riding roughshod. Military power is especially persuasive when coupled with clear intent to inflict frightful wounds if attackers leave no alternative.
Six Elements of Special Operations
The element of surprise in any military encounter cannot be underestimated. If the enemy are not expecting you then they will not be prepared. If you can catch them eating, sleeping or otherwise away from their weapons, you have them cold.
By carrying openly I am seeking the advantage of allowing the criminal to decide that it just isn't worth it to attack me for whatever they hope to gain through the attack. It is a strategy for peace - peace for myself and my family.
The element of surprise is a tactic that is designed to enhance the effectiveness of an attack or counter-attack - not a means to prevent the attack in the first place.
So, are you seeking the advantage of increasing your chances of not being attacked at all, or are you seeking an advantage to improve the effectives of your own counter attack after the aggressor has initiated the initial attack?
Now certainly you can point to this:
Six Elements of Special Operations
If they have an inkling of what you might do, whether by intelligence or simple analysis of possibilities, then they may place booby traps, set an ambush or just be on a higher state of readiness.
But one must ask - how often is the common street criminal we are likely to encounter going to go to such lengths to attack a person they know to be armed when they can just wait for the armed person to leave or go down the street two blocks and attack the next person who is not visibly armed when the potential gains from the attack are no less?
And if the criminal is seeking to obtain a gun - there are a helluva lot easier and less dangerous ways to do so then attempt to take it from the person carrying it.