Hello MH (My initials are MH too),
My daughter was around 3 when we encouraged her to stop sucking her thumb. She would suck her thumb and rub her ear - so much so that she broke down the cartiledge and she can make it stick out now - a cute little trick she likes to show people.
My daughter really only sucked her thumb when she was tired and wanted a nap or about to sleep. Sometimes she'd suck it when she was scared, nervous or unsure about something too.
Our dentist was awesome with her and talked to her about how sucking her thumb was something that would effect her teeth and it was a really good idea to stop. I reinforced that talk when sucking was about to start. I was really matter a fact about the whole thing. I told her it was okay if she wanted to suck her thumb, but I thought it was a good idea if she stopped - and gave her the reasons why. Talked about her teeth sticking straight out.
I told her stories of ways that other people in our family stopped sucking their thumbs/fingers.
At night when she had the hardest time, I asked her if she would let me rub her hand while she fell asleep. I did that a few nights in a row and then a few nights later, she slept on her hands and that did the trick. The first night that she fell asleep without her fingers, we went to the store and picked out a special treat for her.
My sister was around 6 or 8 when she stopped sucking her fingers (2 of them) - my dad made a bet with her that if she stopped sucking her fingers he would stop smoking. We took an airplane ride from Wisconsin to California and she sat on her hands the whole way - never sucked them again - so the story goes.
Good luck with your daughter's sucking. It is a cursed blessing - my daughter fell asleep instantly sucking her thumb, but it makes for bad teeth in the end.
Positively,
M. H.
About me: Laughing for 15 years with the same husband, mommy to a darling 5 year old. Share our house and barn with 3 dogs, 1 cat, 2 rats, 1 snake, 1 fish and 9 chickens.