From a woman's point of view....
1. Guy comes up to you, pulls a gun from his pants, and says "Give me your wallet or I'll kill you."
2. Same deal, but he only lifts his shirt and shows you the grip of his gun...but doesn't draw it.
3. Same deal, but he puts his hand under his shirt in what looks like a gun-gripping, getting-ready-to-draw move...but you never see a gun, just his hand disappearing under his shirt.
4. Same deal, but he only says "I have a gun...give me your wallet or I'll kill you."
So he would probably refer to my purse instead of my wallet. I also presume this might be in a desolate and maybe even dimly lit place where he would not be seen or attract attention. And I would probably be alone because it's doubtful he would try to rob me if my husband was along. So....first off I would be terrified. Not so much that he was going to rob me as I might be terrified that he was going to also rape me and torture me and and then kill me anyway. It's a bit different when you're a woman.
Still, even if he had his gun drawn and pointed at me I would not attempt to outdraw him. But I would assume at that point that it was my life or his and that I must be smart about it. I would be glad I had a concealed weapon and wasn't completely helpless. I would stay as far away from him as possible and gently toss my purse to the ground. I would not be worrying about identity theft or credit cards or whatever cash I had in my purse. I would be thinking about surviving. And still, my concealed weapon would be my ace in the hole in my mind, all the time wanting him to just take my purse and leave.
However, once he picked up my purse I would be ready to do whatever it took to defend myself from any further advances I perceived to be threatening to my existence or safety. I would consider myself to be in extreme danger and that my life completely depended on whatever actions I took at that moment.
He wouldn't be thinking I was armed. He would be thinking I was compliant. This might be my last chance to do something to save my life. Even though I had already given him my purse.
I would wait for him to turn and leave, but if he took one step toward me I would grab my gun from my waist holster and then if he shot me at least I would know I didn't choose to be the victim, rather I tried to fight back.
The same goes for #1, #2, #3, #4. I would feel just as threatened under any of those circumstances.
Otherwise...what would be the point of my concealed carry?