Yes, it's normal for the stronger player to benefit from blitz. For example at BIBA in Korea I played the professional teachers on 3 stones in slow games and 6 in blitz. Another pupil who was a bit stronger than me and 8d wbaduk got beaten down to 8 stones in blitz by On Sojin 7p! A lot of that is psychology and keeping calm under pressure which stronger players are usually better at.

Is there a convergence? With enough time to think, the differences between the pros and the amas disappear?

It's funny that you should ask Uberdude of all people. He beat Alex Dinerstein (1p) in a turn-based game on OGS. Dinerstein is probably not the strongest pro out there, but he's still several stones stronger than Uberdude in live games. It probably depends on the person, too. A child who has the same live-game rank as Uberdude probably wouldn't benefit as much from the extra time.

That said, there are plenty of strong Asian amateurs that can beat the weaker pros, even in live games. The gap is really between the strongest pros (the ones who regularly get past the preliminaries of big tournaments) and the rest.

...
In the context of what you say about top pros, let me ask the question in a different way.
Given enough time, would a low-level pro and a high-level pro, when analyzing the same position or game, come to the same conclusions? If not, why not?

They had, and frequently used, nearly unlimited time.

Think about it. If this were the case, we would not be able to observe the dominance of the historical greats like Dosaku, Jowa, et. al. They had, and frequently used, nearly unlimited time. Also, in modern tournaments we would expect that those with longer time limits would see more people competing on relatively equal terms. We do not. Why not? Ask me when I reach 9p! I may know by then.

I think the fact that blitz games favour the stronger player in high handicap situations has less to do with the relative strength of the players and more to do with the board position. Allowing players less time to read things out means that the board position becomes less stable (e.g. "live" groups die) and this is bad for the person who's ahead because that means their lead is less stable. In other words: It's not that the stronger player copes better with the time constraints, but rather that handicap stones become worth less when players are forced to play quickly.

Just an idea.

My guess is that the is a difference between top-level and low-level, so it is not meant to be a leading question. I am really just curious. What *is* the difference, when we take away the time and the pressure? I have no clue and thus the question.

PS>
By the way - what does mean? That you posted a lot of words without really answering my question but still somehow beat me up?

This sort of thing is often said but it's just plain wrong. Most games were meant to be finished in a day but could go into the wee hours. Some games would spread over several days but this was relatively rare, and the full days were not always used - some of these days were just PR exercises for a sponsor, etc, or days out a temple). In general, players could not expect sponsors to sit for days watching paint dry, and lower ranked players could not try the patience of senior players very often.

Indeed, there were many cases of two or three games on the same day.

There were occasional exceptions, of course, but the famous marathons belong mainly to Shusai's time and were usually seen as abuses of the system.

The real difference between then and now was lack of time pressure. You did not have to press your candle, or worry about your clepsydra running dry.

Well, as John said - there is never really unlimited time. And there is never really lack of pressure. So all the games and matches you are talking about are in the sporting context. My question was more in the analysis context, where the time is really unlimited and the pressure is none.

My guess is that the is a difference between top-level and low-level, so it is not meant to be a leading question. I am really just curious. What *is* the difference, when we take away the time and the pressure? I have no clue and thus the question.

Or, coming back to the amas - what is the difference between, say, the knowledge of 1d and 3d players? I know 1d players who know more joseki and generally read deeper than some 3ds, but still lose games to those 3ds. I have some better understanding of that, of course, but still find it interesting.

PS>
By the way - what does mean? That you posted a lot of words without really answering my question but still somehow beat me up?

If go were a game that could be won by brute force, there would be no difference between top and not-quite top players given unlimited time - but it isn't. My assumption is that there are some things that stronger players know that weaker players don't, so the difference is a matter of knowledge. What exactly that knowledge is is probably impossible to say, but I imagine that if "complete knowledge" of go existed, there would simply be larger gaps in the knowledge list of the weaker player. This doesn't mean that the weaker player couldn't ever win - a single game might by luck develop towards one of the stronger player's gaps. In the long run, I doubt that this would happen often, and were Überdude and Breakfast to play a 10 game series without time pressure, I would be willing to bet the bank on Breakfast.

I think it means that one is enjoying the slugfest - like in go.