So, Epicureanism isn't about having a three-martini lunch. It's a complex moral and physical theory about the nature of the world. The best surviving exposition of Epicureanism is Lucretius' de Rerum Natura, a poem written in epic meter that Lucretius used to advertise and praise Epicurus' ideas.

The core of the Epicurean philosophy is that the world, including humans, is matter, and the gods (though they exist) don't care about us. At all. Why would a god give two fucks about humans? This is based in the atomic theory of matter - everything is made of up atoms (an indivisible physical thing) that are falling through space, and combine in different ways by chance, and those combinations are what we experience as the world. When someone dies, their atoms become disassociated and make other combinations by chance. That's our world. Lucretius tries to prove the human consciousness is physical through, for example, considering the effects of wine on the mind. Wine is a material substance, and when you drink enough of it, it messes up not just your physical motions, but the activity of your mind. Hence your mind must also be a physical thing.

If both your body and mind are physical, and are going to dissolve and be recombined with other things, and the gods don't give two fucks about you, you don't have an afterlife to worry about.

So the question then becomes what is a good life to live while you have it? Epicurus' answer is to avoid suffering. The cause of suffering is frustrated desire. You can't always control the fulfillment of your desires, but you can control the desires themselves. So just stop wanting stuff that cause you pain when you can't get them.

That includes things like staying out of political life (you can't control how people vote in an election, so don't ask them to vote for you).

That retirement from public life is something Romans associated with luxury. It's literally engaging in what Romans called otium - leisure - as opposed to negotium - business.

That's where the three-martini lunch image of Epicureanism popped up.