Natalie and her thumb!

Natalie loves to suck her thumb. She didn't discover her thumb until she was a few months old, but ever since she did, she has loved it. She really has no interest in stopping anytime soon. She sucks her thumb when she's sad, sick or bored. She sucks her thumb when she sleeps, when she's awake or whenever. There is even a permanent indentation that is discolored on the top of her thumb from her teeth but she doesn't mind. What's a girl to do without her thumb? The doctor and dentist both want her to stop sucking her thumb, but she doesn't care for any of the incentives that they offer. So... what I have done lately is hold her, but only if she doesn't suck her thumb. She looks at me to see if I'm being serious. When she decides that I am, she puts the thumb away and decieds that she can leave it alone for a few minutes. HOWEVER, as soon as she needs to suck her thumb, she slides off of my lap and sucks it- sometimes for just a few seconds- and then she returns. I told her that I am going to get a marker and paint it black, but she doesn't like that idea. What do you do when bribery doesn't work?!