Mm, no, I think your tutorial right now is already plenty thorough. Too much more and it's going to delay getting to the meat of the game too much, especially since there's already an intro sequence before that. Maybe have references to the kinds of hands or what beats what? Highlight potential hands you might have the opportunity to build with the cards you can see. That sorta thing. That might take the fun out of playing poker though, not sure.
Whatever you implement make sure it's integrated in to the gameplay well and not like... a button you click that brings up a popup window with some text and images you'll have to memorize. And maybe have an option to turn that stuff off for people who don't really need it? I'm outside of my area of expertise with this because I'm so unfamiliar with the subject matter.