[jonath_laurent]

Yes. Go 19x19 would be completely intractable on a single machine (one comment is citing a $25 million cost estimate in computing power to train AlphaGo Zero). A more reasonable target would be Go 9x9 but even this would be an extreme challenge on a single machine.

There is an Oracle blog article series about training a close-to-perfect Connect Four player using AlphaZero. Even here, they had to rely on multiple GPUs.

You have to keep in mind that AlphaZero is an extremely sample-inefficient learning technique, even for simple problems. Rather, the strengths of this algorithm is that 1) it is pretty generic and 2) it can leverage huge amounts of computation.