Not at all. What we are saying is that a random player can, and will, play the perfect game 1 in x times. The application of human knowledge applies filters to the way we think (hence why we even have "bad habits"), which limits the floor and ceiling of performance by applying set criteria over what moves are acceptable and what are not. The level of understanding affects how these levels move.

I'm arguing that a 20k player will have a range of equivalent performance, maybe between 12k and 28k, and a random bot will have a range of performance from 12p (whatever theoretically perfect play would be) to probably 150k, with an enormous skew towards the lower end. So a random bot will almost never achieve 50k performance, but has the potential to play perfectly, but 20k will play better than the random bot in almost every single game, but never reach such dizzy heights.

Seriously? You guys have too many pens in your shirt pockets.

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Patience, grasshopper.

The opinion that 20k's don't have the right moves in their inventory is backed up by nothing, it is just a gut feeling you have. Perhaps you feel that it is obviously true. I don't. I think it is obviously false. The only way to defend either point of view here would be with some data. Since there is none, and it is impossible to come by, the point is moot.

Really, at the probabilities we are talking about, it also becomes probable for the stones to randomly hop out of the bowl and into the right position, purely because quantum fluctuations caused all the molecules to move in the same direction at the same time, or some such thing.

There is none for Go, but as I alluded to, there is sparse data for chess that imply that, for example, an ELO 1600 rated player cannot beat an ELO 2800 rated player (at least in serious games from which the limited data are drawn). The difference between a 9p and 20k is hugely greater, and on top of that, the room for game-critical losing errors in a Go game is significantly lower.

I'm not sure if the burden of proof lies with either side here more than the other (although the fact you think it is "obviously" false implies some requirement of a burden of proof I think!), but there's still only any data provided for one side of the argument. Like I say, I'm interested in data you have supporting your side more than a simple refutation of the argument.

The sample size on that is nowhere near enough.

If every particle in the visible universe was a random go monkey (or a 20k), and all of them could simultaneously play against a player the strength of Lee Sedol, and each could finish a billion games every nano-second, and they had been at it since the big bang, the sample size would still be laughably insufficient.

Actually I do have a lot of evidence. I've taught a lot of players from beginner level, and played teaching games with 20k's, and reviewed games after playing 20k's. So I'm aware of the kinds of gaps they have in their thinking. We're not talking about a lot people, perhaps a few dozen. However, I've certainly never come across a 20k who could consistently demonstrate some capability of finding 1d level moves. No doubt your experience is similar. Do you reject this data?

I entirely agree with all this. My example player was merely to and understand what kind of 20k could beat a 1d, even theoretically.

Note also that a game is also long enough that 1d could see soon enough where a 20k was strong and weak, and focus on the weak aspects (if his mortgage was riding on it)

Yeah, I know. Which is why I proposed the thought experiment as a way of bypassing the overwhelming effect of the miniscule probabilities involved.

Then you're misinterpreting the point of the data. It's not to collect enough games between a 20k and a 9p to disprove the 10^x games required for a win theory, it's the fact that rating variation appears to have a reasonably close to linear relationship with winning probabilities, over a few tens of thousands of games of data. The data all point towards a trend line that hits 0 and 100%, even though there's no real data collected between players far enough apart to be on this line.

It's pointless claiming that "my theory is dubious until I've collected enough billions upon billions of games of data to prove beyond doubt that it is impossible for a 20k to beat a 9p", that's a very blinkered way of assessing or debunking the veracity of theories. Sure, it would be ideal if those games could be collected, but they can't be for obvious reasons, and there are other ways to support or refute the theory (such as trend modelling on existing data of win probabilities across disparate ranks).

Regarding the comparison of ideas, data with a non-compelling sample size is still better than no data at all. All your arguments are aimed towards poking holes in my theory (which is fine, and important), but you aren't allowing anyone to view the supporting evidence of your theory with a critical eye, by the very nature of not providing any supporting evidence. Even a data set that seems to indicate a true s-curve between rating difference and performance would be compelling, but you haven't shown one.

Have you ever come across a random monkey who could consistently demonstrate some capability of finding 1d level moves?

I know how weak 20 kyu players are. But random players are staggeringly much weaker.

Sure - the Monte Carlo bots



Only in a statistical sense. They are not constrained by faulty logic and flawed reasoning and hence could play a perfect game, or at least perfect enough to beat topazg.

I'm sorry, but I don't understand the argument. I think there is a clear relationship between rating difference and performance. The larger the difference, the worse the performance of the weaker player. And since the random player is weaker than the 20k, therefore his performance is worse than the 20k, when playing the same opponent. In your first paragraph, you seem to be arguing the same thing, proposing to extrapolate from the linear relation between rating and performance. But then later you claim that data that shows a relationship between rating and performance would be compelling, but I haven't shown it. So now I'm a bit lost here. It seems to me that you are arguing that the data that you yourself provided supports my position. But that can hardly be what you mean, can it?

I'm arguing that the support data collected argues towards a relationship between rating and performance where, with a large enough rating gap, the chance of the weaker playing is 0%. There is limited by existant data supporting this by demonstrating that, for chess at least, the relationship is closer to linear than logistic.

You are arguing that the relationship between rating and performance exists, but the lower and upper bounds of winning chance never reach 100% or 0% - a true logistic function. I'm asking for some data that supports the view that a true logistic function is more reliable model than a function that is linear with logistic elements.

Oh, I see.

Well, the basis of the Elo rating system and similar systems is logistical. There is no rating difference for which the formula returns 0 or 1. The data fits that curve reasonably well, AFAIK. The fact that a certain result, which according to the formula should have a very small but non-zero chance, has not in fact happened, does not in any way constitute proof that it cannot happen.

Anyway, I really don't know how I got dragged into this argument.

It is my opinion that neither side has any chance of proving that they are right. All I have is an opinion. I also think that that is all you have, an opinion. I'm not claiming that the burden of proof is on either side. I'm not claiming that there is any support for my position at all. In fact, I think there is no meaningful support for my position. And that there is also none for yours. I do not think that thought experiments have value in a discussion like this. I do not think there is any meaningful way to extrapolate from the data we have.

My original reference to the chess world revolved around an appeal from mathematicians (led, IIRC, by Jeff Sonas) that FIDE change their rating formula, precisely because the Elo rating system does not, in fact, fit the data very well, the data being closer to a linear model. Elo's model, whilst a really nice way of having a decently designed rating system at the time, is a very crude model, and was never originally based on supporting data (and with k values and rating difference / sd type values arbitrarily assigned so the model could be refitted to be as closely predictive as possible).

I fully understand that I have a rather sad life to find this so interesting, but I do (and have spent quite a lot of time trawling through data surrounding it)

Because everyone loves graphs, and because some people probably don't have the faintest idea what we're talking about, I've made some very crappily drawn graphical examples:

Herman's theory (standard logistical function):



My theory (somewhat logistical function, but with upper and lower floors), please ignore the fact I can't draw freehand curves very well:



EDIT: p = the probability of the player beating the reference player, 1 being 100%, and r being the amount the player's rating in question differs from the reference player.

The Monte Carlo bots, which effectively play random moves and random games in order to pick the best move, are surely a proof of some form that random playing monkeys can play at least 5d moves.

It is not equivalent to the claim that 20k players are worse than random. What people are claiming is that random play is vastly worse than the 20k, but that the range of play that the random player has is wider. Thus, the chances of a 20k player to beat a 20k player are 50-50, decreasing as you go up to 10k and onwards. For all these ranks, the random player is vastly worse, but at some point there is a crossover, where both the 20k and random player have absurdly small chances. Then the claim is that at some point, the 20k player reaches zero, while the random player continues to have an extremely small chance.

This is impossible according to our ratings math, but so what? You're confusing the model imposed by our rankings with reality.

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Occupy Babel!

Exactly this ^^

Ranking models are exactly that, models, and it's not valid to assume that they are accurate across ranks. Models improve over time, because we all want better models. Why should we assume that a logistical model is definitive?

I think it's also fairly crucial for daniel's specific point not to assume that a random playing bot is just an absurdly weak human player.

That random play can produce 5d moves is rather obvious. Random play can play any move on the board.