it means the probability or likelihood. For example, what are the odds getting either heads or tails when you flip a coin? the odds are 50% or 1 in 2 that the next flip will result in "heads"

It is neither common nor correct. It seems that the writers of the show were trying to be funny - so they had the character speak about himself in the third person. It can be done in this context - to be funny. It is still rare and a little strange. The use of the word don't (which is incorrect also) instead of "doesn't" is an intentional error which adds to the humor. I wouldn't try to copy it if I were you.