Exologist wrote:Is it really a 0.0039% chance that an 8d would beat a 9d? Although perhaps if it is an 8d amateur vs a 9d pro I could see that, but if you are talking 8d pro vs 9d pro, I'm sure they win more likely than that.
Technically, if you won 45% of the time against a certain rank, you are lower rank (since it is not 50%), why the 25%?
Nothing to say for the monkey. I think it'd be very slim chances random moves of a monkey could even beat a 30k.
A 0.0039 probability is a 0.39% chance.
That aside I intuitively consider a KGS 1d has a greater chance of beating Lee Changho than the monkey does of beating the KGS 1d. However, I may be mistaken - for sure, I think that a 20k player has literally no chance of beating Lee Changho, whereas the monkey does have a non-zero chance. The reason for this is the very non-randomness of the human brain will predispose the 20k player to repeatedly make mistakes. The monkey has access to the entire tree of Go possibilities, whereas the human will attempt to apply what knowledge and reading is available to him to make superior moves, and therefore both increase his
overall performance compared to the monkey, but almost completely remove his ability to play a game devoid of mistakes.
All of it makes the theoretical rank argument rather moot - it's an abuse of mathematical probabilities. Probabilities like this are only going to be vaguely realistic without any external factors influencing the outcome. With humans in involved affecting the outcome by making decisions, this is not the case. Probabilities do not predict the future with any more accuracy than the complexity of the model on which they're generated.
I really thought Roger Federer was going to beat Andy Murray in the Olympics at Tennis. If I looked at history (both vs and generally against other top players), I could have created a fairly arbitrary (although mathematically pseudo-justified) % winning chance for Roger and Andy. However, what if Roger woke up that morning with a terrible migraine and was feeling under the weather the whole match. Probabilities based on historical data do nothing more than mathematicall model the past in the hope that they give some insight into future possibilities - assuming that a 4.2% chance of winning based entirely on historical data gives a 1/25 chance of winning the next game between two individuals with permanently fluctuating internal factors is ... foolish IMO.
There's the argument that over time these all even out to match the percentage is also equally flawed (and here I'll stick to Go for why I think so, I promise!): People get older, married, divorced, have kids, go senile, whatever ... all of these factors influence what's going to happen, and rank in itself is, again, based primarily on analysis of historical data, and a poor metric for evaluating likelihood of future results (this is even worse in the pro world where ranks are not correlated directly to recent or lifetime performances in the way that something like online server ranks are).
Who here can relate to being person A, who always beats person B and always loses to person C (all being the same rank), despite the frustration that person B always seems to beat person C? This often isn't a statistical blip that will work itself out over time with more games (assuming the players don't improve over this time), it's a simple fact that modelling overall historic results across the spectrum of each player's opponents doesn't act as a good proxy for the probability of the outcome of a single future game between two people.
Like a number of papers I have the semi-pleasure of reading these days, it looks like a theory borne out of people's delight for what appear to be stats and proofs of cool sounding phenomenon (or an attempt to create a proof for some wider point like what a deep game Go is), but build on a foundation of false premises and weak understanding of confounding factors.
If Go was a solved game (as a 0.5 point win for White with perfect play, but a loss with any deviation from perfect play, for example), then you could model the chances of perfect play as Black being beaten by a randomly legal playing bot as White, and even then it would be somewhat governed by the rules given to the random bot player.
Having arbitrary rules like "first moves not on the first or second line" is also not only arbitrary but distortive. What person is going to develop any basic opening theory whilst otherwise playing completely random moves? I learned to stop atari-ing anything before I learned anything about 2nd/3rd/4th line opening dynamics.
I would rather the author didn't make the attempt to appeal to the audience by involving a monkey at all (which inherently drags people in at the idea of a monkey beating one of the greatest players ever to play Go). It's a purely theoretical mathematical argument on probability trees, and can be left in the domain of mathematicians that find it interesting. It doesn't correlate at all to the chance of a monkey beating Lee Changho, nor does it actually model the probability of any individual player with rank X beating another player with rank Y, and shouldn't be construed as such a proof.
I still enjoyed reading what I could though!
EDIT: The are also other statements that make me twitch, such as "For an absolute beginner who is learning weiqi at a natural pace, the journey is probably just a casual walk to get from the weak level probability P0 to a higher level probability P1. However, from the perspective of mathematics, we can see just how vast such a gap actually is." This is not logical. From a mathematics point of view, an improvement in an exam score from 0% to 1% represents an "infinite" improvement, which based on any basic fomula of knowledge increasing over time (maybe N1 = N*1.03 per week or something) would represent an improvement that is literally unsurmountably vast. In reality, the flaws of the argument are pretty intuitively basic, as it disregards anything to do with how learning actually works, and also assumes that {total amount of knowledge} correlates exactly with {winning percentage} (which it doesn't).
I promise I'll stop ranting now 
