If anyone has heard of Wolfram|Alpha, it has a win percentage chance calculator - just input the ELO ratings you'd like to compare. It estimates the likelihood of a 1300 winning a match up vs. a 2700 to be 0.0316% (roughly 1/3164). Bear in mind it's a theoretical calculator only! In reality I would personally expect the odds to be even lower than that, I just thought some of your folks minght find it interesting.
Link: http://goo.gl/NLrlCk
I dont believe it.1300´s have good and bad days, same with the GM.
Magnus Carlsen blundered against Anand in a WCgame, and Anand blundered back, he didnt see it. The GM´s are not overhuman supergods. They too make mistakes,
and a skyrocketing 1300 on the way up (maybe actual strenght closer to 1900) does play at his best some days, and that can be fantastic chess.
One day a 1300 can play as a 2000, and at a very bad day a GM can play as a 1800. A Gm can also test a line he doesnt know well yet, and be punished on that.
I had a game when I was at878N-Elo , fideunrated, when I with black outplayed a 1800fide, and mated him in 78 moves. I played fantastic, and he wasnt bad. His mistake was that he did not try to play for a draw when I opened absolutely smooth. That day I was better. I played like 2000. A GM could have done a similar mistake.
Most players are theirselves worst enemy. If they are playing their best, they can beat almost anybody. If not, they can loose to almost anybody.
"As we seem to agree, reality would probably give an even smaller win-likelihood to the poor 1300."
Well, it seems just as speculative to insist the prediction is false as it is to insist that the prediction is true.
It pretty much does just come down to the number of mistakes players make in the end. A 2700 doesn't make a lot of them; that's what got them there. A 1300 makes a lot of them; that's what got them there. The harder the opponent for the 1300, the more this gets punished. The task becomes harder and harder for the 1300, but I don't see why this can't be measured mathematically. So for a 1300 to beat a 1500, they would have the same difficulties as say a 1400, but even more so. I don't really get why this logic changes if we kept going further. It's not like the value of 100 points increases as time goes on. So the 2700 suddenly plays like a 3500 when playing a 1300? No, their skill is just obviously much higher than the 1300, which is why the prediction is as low as it is (1 in 3164 is extremely low).
It seems like people want to inflate the strength of the 2700 just because the encounter is lopsided. If the difference in strength was really that high then the rating system would stretch out more. You'd have people who really do have a 1 in 3164 chance of losing to a 1300; then those people would be the 2700s, and maybe the Carlsen's would be at 4000. In any case 1 in 3164 is virtually unbeatable anyway.