Contemporary atheists often assert that there is no need for them to provide arguments showing that religious claims are false. Rather, they say, the very lack of good arguments for religious claims provides a solid basis for rejecting them. The case against God is, as they frequently put it, the same as the case against Santa Claus, the Easter Bunny or the Tooth Fairy. This is what we might call the “no-arguments” argument for atheism.I take the side of atheists; I think theists have the burden of proof. This is not about giving atheists an unfair advantage in the debate, nor is it about making a "no-arguments" argument. In fact, I do not believe it is an advantage, fair or otherwise, at all. It's simply about who takes which role.
I'm somewhat influenced by the role of burden of proof in law, though law does not necessarily provide a paragon of debate format. In a court of law, attorneys set out to prove certain facts. But producing the arguments and evidence costs money, so the law must specify whose role it is to prove the facts, and to what extent they must be proven. In most criminal cases, the plaintiff must prove "beyond reasonable doubt", and in most civil cases, the burden of proof is a "preponderance of the evidence". If you're wondering how to interpret that, it depends whether you ask the defendant's or plaintiff's attorney.
(Please correct me if I made any error with regard to law.)
In the case of proving God, it is only sensible that the theist has the burden of proof. The atheist doesn't know beforehand what particular god or gods the theist believes in, and doesn't know what arguments to use. Theists keep on telling us that not all religious people believe the same things, and I wholeheartedly agree. That's why it's the theist's role to explain what they believe and why.
But this does not confer an advantage to atheists, any more than it confers an advantage to the defendant in a court of law. It just means that the theist makes the first argument. If the argument, taken at face value, meets the burden of proof, then it is up to the atheist to counter it. In other words, the burden of proof shifts to the atheists. The burden of proof shifts back and forth indefinitely, and does not give an advantage to either side.
By saying theists have the burden of proof, I only mean that they have the initial burden of proof. It is not meant as a "get out of an argument free" card.