I don't think you can assume that winning percentage in go increases by the same factor for each rank once you go past 2 or 3 stones difference.

Agreed, I doubt I'd lose a game in a thousand against KGS 6k.

You also need to play thousand games to lose one in a thousand.

We are talking about ptobability here - even if my winning chance is 99.999% I could still lose the first game.

Actually, if you play 693 games at those odds, the probability is 0.500 that you will lose one.

Edit: Corrected, as lightvector pointed out.

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Do you mean 690? (Actually, 692 or 693):
(999/1000)^692 ~= 0.50040
(999/1000)^693 ~= 0.49990



An interesting source of statistics about winning chances between mismatched players in even games can be found here:
http://gemma.ujf.cas.cz/~cieply/GO/statev.html

The most basic versions of the Elo model assume that if we have players A, B, C and the odds of player A beating B are 1:x (that is, a probability of 1/(x+1)), and the odds of player B beating C are 1:y, then the odds of player A beating C are 1:xy.

If we assume that this is true, then roughly eyeballing the stats on the G+4 column and multiplying up the odds for a 6k beating a 2k, and a 2k beating a 3d, and a 3d beating someone around 6d or 7d, it does actually look like you need to go up to about 6d or 7d before you reach an odds ratio of 1:999. Indeed, 0.001 is a mighty difference.

However, it's common wisdom that the chance of a weaker player beating someone much stronger falls off much faster than this sort of model would suggest. The stats on that site seem to bear this out. In almost every case, if you multiply up the appropriate odds ratios for the stats in the G+1 column and/or G+2 columns to get a prediction for the G+4 column, you obtain an odds ratio that's smaller than the actual one. For example, multiplying up the ratios for 6k beating 5k, 5k beating 4k, 4k beating 3k, 3k beating 2k, you get a odds ratio of 1:2.69, but the empirical ratio for 6k beating 2k is 1:3.67.

Whereas this effect is clear in the G+4 column, if you do the same thing for the G+3 column, you only barely see this effect. If you do it for the G+2 column, you basically don't see it at all and the simplistic model matches up pretty well relative to the noise in the stats.

Based on this trend and some intuition, it seems likely that the effect will continue to increase as the strength difference between the players increases, although there's no data to pin down how fast it will increase. But playing with these stats in a spreadsheet with various extrapolations for how fast, it looks like anywhere from about 2d to 5d would be a plausible guess for how strong you need to be to have only a 0.1% chance of losing against a 6k.

Thanks.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

OK. After winning 693 ganes with this porbability you have to star fearing.

Sorry, still wrong XD

You have to be very afraid - that your opponent has gained seven or eight stones while you've been training him...

Yes, and there is of course the danger of you losing stones by playing so many games against a weaker player. However, for the purpose of the question I assumed you can ignore these two factors as it's only the probability of losing a single game (at least no more than 200 :p).

A fear of losing is unfortunately one of the few things that can prevent a player from progressing past the stage of being a beginner. I'd recommend reading David Mechner's advice. I particular, this part, which is one my favorite pieces of advice ever:

If you are winning more than half of your games you are not giving the correct handicap!