As with all tipping, how much you want to leave is entirely up to you — whether that’s a penny or 25 percent on the bottom line. So when it comes to leaving a gratuity on a happy hour bill, you should ultimately follow your own personal tipping philosophy, and maybe that means finding the regular menu price and tipping on that. But I think it’s fair to tip on whatever the total is that’s dropped in front of you.
Bars and restaurants make the decision to have happy hours with discounted drinks with careful consideration for the financial implications (a well-designed happy hour program and other drink promotions can often be very profitable for a bar). So I think it’s safe to assume that operators expect guests to leave a tip based on whatever they’ve deemed a reasonable price for a drink to cost, so it’s both an appealing deal to customers and not a loss for the bar. (I think it’s also safe to assume that people who go to happy hours are often looking to spend less or just get more for their money.) Whether or not you want to leave more based on the deal you’re getting is up to you, and certainly a nice gesture. But if you’re going to do that regardless of the discount, then you might as well skip the happy hour in the first place.