The following is an experimental argument. I have no way of proving that (1) is true or even probable, but it seems reasonable at any rate.
1. All things being equal, intuition is a generally reliable guide to truth. (Premise)
2. My intuition is that I have libertarian free will. (Premise)
3. Therefore, all things being equal, my intuition that I have libertarian free will is most likely true. (From 1 and 2)
Libertarian free will entails that even though I chose X, I could have chosen ~X under the exact same conditions. Again, this isn't really intended to be a proof, so please take this argument with a grain of salt. It seems to me that I could have chosen to refrain from a second helping of macaroni and cheese under the exact same conditions in which I chose to eat that second helping.
Part of the issue hinges on this question: are all things equal? That's a key portion of premise (1). If there is overwhelming evidence to reject my intuition that I have libertarian free will, then "All things being equal . . ." is a moot point.