Thumb Sucking...

So my three year old still sucks her thumb. I don't really know if she is too big to do this or not. My six year old was a pacifier baby, which was much easier to deal with. Just after her first birthday I threw out all of the pacifiers and that was that. But, there is no way to throw my little ones thumb away! Truth be told I sucked my thumb as a child, so did my brother. I remember stopping on my own at age five when I started kindergarten. My brother not so much. She doesn't do it all the time, only when she is upset or tired, but I fear the longer she does it, the harder it will be to stop. She does look pretty darn cute doing it though! It makes me wonder, what is this little bird gonna be like? Will he like a pacifier, or passey as they are referred to in my home, or will he be a thumb sucker? Maybe he will like neither. So my lovlies, any opinions on what age is to old to be sucking their thumb?