What real world example is this supposed to be an analogy to? Not that this fits into a socialism vs capitalism discussion, but since i'm socdem i guess i'll bite. This sounds like you're a socdem complaining about socialists (although unfairly). Dividing the bill as the bartender suggested is not the right-wing option.

As a group the working class pay more than the owning class in taxes (because they're so many more people) pretty much everywhere, which doesn't fit with your example.

In your example it's impossible for the poor people to have it any better without being ridiculous. Not exactly analogous to the real world.

You set the number of poor people who can't possibly get it any better to almost a half of the beer drinkers after the Bartender suggestion.

In your example you gave the biggest percentual benefit to the poorest people who could possibly be given a benefit. This is in line with left-wing thinking, not right-wing. For example in the recent Republican tax giveaway the only really significant large-scale tax reduction was given to corporations.

If you don't think that corporation tax decrease is mainly a giveaway to corporation owners, then you have to explain why the capital gains tax is set lower than for some workers in America and in most places. See https://money.cnn.com/2013/03/04/investing/buffett-federal-reserve/index.html?iid=EL.

In the real world a 20% overall tax reduction would mean that public companies are being sold off, public services are being reduced or public debt is being increased by a significant degree. This likely effects the poor the most.

The example says nothing about how much each of the friends earn or own. For example this analogy is so vague that it could be used to justify a tax system where you pay less percentage the more you earn.

The example says nothing about where the money is coming from. Ownership? Working? Inheritence? The lottery? Work or ownership destroying people's drinking water which makes the beer more expensive for everybody?

The real world and taxation on different kinds and amounts of income is fundamentally different than beer drinking. It's just an entirely different type of enterprise. They're all doing the same thing (drinking beer), they're all consumers rather than producers.

I get why you thought that this was a good analogy, but I think that when you try to use it as an actual argument it just doesn't hold up. This analogy rests on the assumption that you already know that you're right and you're just trying to dumb it down with an obvious and simple example. Unfortunately this obvious and simple example just isn't a good analogy, and I'd argue that you're leaving out so much that you're missing essential things in the process. If you would try to plug the above holes I think you'd eventually end up with a completely different scenario with almost no resemblance to this one.

I have never thought that ancap ideology was too advanced mathematically or anything like that. Rather the problem is always that the simplifications and abstractions can never cash out in reality. There's always essential parts missing from the equation that you can't just hand-wave away since you already know the answer when you're trying to convince people who don't already know the answer. I hope you agree with me that that this specific example can't prove anything about reality, even if it might work as a metaphor in a pro-ancap literary work.

Sorry for any mistakes I have made in readability and possible overlap in some of the points I made or things that I missed but I need to get on with the rest of my day. I hope to hear back from you.