I know they don't allow gambling advertisements, but would they allow advertisements for a poker strategy guide?
Are you sure? I just entered "poker book" and "poker strategy" into Google a few times and some listings popped up. Not many though. The reason I asked to begin with is because it didn't seem like anyone was doing this (hence why I thought it wasn't allowed). But I guess it just isn't very saturated.
I wouldn't risk trying it. Basically, there are ads for many niches on Google, that are not allowed by Adwords, and I don't understand why do they appear. Some of them get disapproved after few days, but some has been there for long. So, the best would be to ask Google directly. In my opinion, they will say no.
"Do you have an email address I could send my question to?" I guess, you wanted to say "do THEY have an e-mail address". Yes they have, but you can speak to them directly right now. Click on "Contact Us" in the right top corner of your account, choose the category and then "Live Chat" should be available. If not, their e-mail is: