Some books serve horseplayers free drinks while requiring sports bettors to get drink tickets when placing wagers. So just pick up a Daily Racing Form and waitresses generally don't need to see more than that.
Disclosure statement: I'm employed by the Form, but that doesn't lessen the validity of the advice.
Meyer Lanksy brings up a good point, too. Having tickets garners more respect. Above and beyond that, something I learned long ago (and applies to many other situations) is that if you look like you know what you're doing or that you're in the right place, people won't question you. If it looks like you're just begging for free drinks, that's not a good sign. If you act like you belong there (without being an a--hole about it), you'll usually be treated accordingly.