A 30 year old asian pro will have perhaps 40,000 hours of playing experience (20 years * 50 * 40 hrs/week). The average game duration is perhaps an hour and consists of 200 moves. In addition, pros (and even fans) study published games. Reading a game takes less time, perhaps as little as 5 minutes or so.

So we can estimate very roughly that a top pro will have absorbed between 100,000 games to 1 million games, and between 20 to 200 million individual positions (around 200 moves per game) .

I asked a pro player I know whether these numbers sounded reasonable. He replied:

At least the order of magnitude should be more or less right. Hours of playing weekly is probably somewhat lower on average (say 20-30 hours), and I'd also use 10-15 minutes to read a game instead of five. Just 300 seconds to place 200 stones sounds pretty tough. Still, I'd imagine that a 30-year-old professional has seen at least 50 000 games, and possibly many more.