They're debating the merits of their respective societies. They argue about moral values and which country is doing better.
Obama: I've heard that all Russian are alcoholics.
Putin: That's a Russophobic myth. I bet there's not a single drunk out in Moscow tonight.
Obama: I don't believe you. I bet if we take your limo out for a spin I'll see some drunks staggering around.
Putin: Okay, let me prove you wrong. We'll drive around and if you see a single drunk you can shoot them with my own gun.
Putin let's the FSB know what they're doing, and tells them to do a sweep and round up every single drunk on their route. He says if Obama sees a single drunk everyone will get sent to Siberia.
Obama and Putin drive around for 10 minutes, and the streets are empty. Not a single person is out, let alone a drunk. Obama is about to accept defeat when a visibly drunk man staggers out of an apartment building, singing a Russian folk song. Obama leans out the window and shoots him.
Obama: See Vlad, I saw one person and he was drunk! All Russians are drunks!
Six months later Putin travels to Washington DC and he and Obama are having the same argument about morals and society. Putin suggests they do the same thing they did in Moscow, and he will shoot any drunks that he sees on Washington's streets. Obama let's the Secret Service know to go ahead and make sure there are no drunks anywhere on their route.
The two presidents drive around for 10 minutes, without seeing anyone. Just as they're turning around a huge group of drunks stumbles out of a bar. Putin gets excited, leans out the window and mows them all down. He teases Obama for the rest of the night.
Putin: Barack, you said Russians were worse drunks than Americans. I just killed 20 of them, looks like Russia wins again!
The next morning Vladimir Putin picks up the newspaper and sees the headline: 20 Russian Embassy Workers Slain In Drive-By Shooting.