The Probability of a Monkey Defeating Yi Chang-ho

[palapiku]

Specifically, "tesuji" are moves that a 20k would never play, as compared to a completely random monkey. The reason we distinguish tesuji from other moves is that they are strange moves that a human wouldn't play without being able to read why they work.

On the other hand, I'm sure that at least one of those 1000000 games will be perfectly "natural", without any need for tesuji, and the 20k will have his chance

[topazg]

Specifically, "tesuji" are moves that a 20k would never play, as compared to a completely random monkey. The reason we distinguish tesuji from other moves is that they are strange moves that a human wouldn't play without being able to read why they work.

On the other hand, I'm sure that at least one of those 1000000 games will be perfectly "natural", without any need for tesuji, and the 20k will have his chance

Except they are playing a human, who can make things messy to his heart's content. This is the problem with predictions based on probability curves, they don't apply very well to human reasoning at extreme differences differences in rank.

As an aside, there has been an interesting following in chess of the accuracy of the ELO rating model for predicting game outcomes, which effectively generates an s curve with 50% in the middle, disappearing to but never quite reaching 0 at the bottom, and to 100 at the top. From models done by statisticians, reality comes much closer to a linear gradient than an s curve, with very specific 0 and 100 points that aren't grossly far in ability from the reference player. I suspect in Go, because of its scale, this is even more the case, and I really don't think that 20k player's chance will come

[palapiku]

Except they are playing a human, who can make things messy to his heart's content.

We can solve that by telling the 1d that his opponent is 9p.

[HermanHiddema]

I'm not over-estimating it, as I said, I'd be very happy with either. I think the randombot chances are non-zero, but almost indistinguishable from 0. I think the 20k's chance is actually 0.

Yes, I understand. And I think you are over-estimating it. I do not think the 20k's chance is exactly 0.

[quantumf]

I do not think the 20k's chance is exactly 0.

As I see it, it's only non-zero if you allow for some external influence, e.g. topazg suffers a stroke during the game, or receives some shocking news.

Barring this, I fail to see how a 20k could possibly beat topazg. Are you imagining a scenario where they don't play as a 20k and instead play in a more random or reckless fashion?

[topazg]

I'm not over-estimating it, as I said, I'd be very happy with either. I think the randombot chances are non-zero, but almost indistinguishable from 0. I think the 20k's chance is actually 0.

Yes, I understand. And I think you are over-estimating it. I do not think the 20k's chance is exactly 0.

Isn't that a case of under-estimating the 20k, rather than over-estimating the bot

From Jeff Sonas (a chess ratings statistician), a chess rating difference of 400 (equivalent of ~4 stone in go) involving master level players equates to an effective 8% chance of winning, with it falling to about 0 by 700 (somewhat extrapolated as there's very little data, but the data spread from -400 to +400 is fairly close to linear). I think the spread is slightly broader in Go, although not drastically, and I would intuitively guess that it is at least as linear due to the length and depth of a typical Go game. However, I do believe 0 and 100 would be reached well before the 19 stone strength difference, particularly involving players above a certain strength. I strongly suspect that the stronger the player, the closer the 0% mark would be, and at my strength I suspect it will be before it reaches 20k. Conversely, I feel very confident that my chance of beating a 9p active title pro to be 0% too. I also consider it impossible for a 20k to beat Lee Sedol, even though a random player by its very nature will have a finite chance of winning, even if it is infinitessimally small.

Herman, do you really think that, given enough games between Lee Sedol and a 20k, both not under the undue influence of drugs or whatever, would ever result in a 20k win, even over 10^1000 games?

FWIW, I'd much rather play the random bot 10,000 games where I have to win them all rather than a 5k in a single game, but 20k is a completely different prospect.

EDIT

As I see it, it's only non-zero if you allow for some external influence, e.g. topazg suffers a stroke during the game, or receives some shocking news.

I agree, and if we should model the likelihood of such things as well as the difference in strength I would end up choosing the random bot, as the chance of an extreme external influence is many orders of magnitude higher than the chance of a loss to the random bot. However, I think this argument is to model strength alone as opposed to all the other confounding factors that could possibly apply to an actual instance of a game.

I suppose my point is that the whole exponentially formulaic predictive accuracy of a result based on rank (or actual playing strength if pedantic about it) is unsupported by any data. What little data there is for chess (I'm not aware of any data for Go) seems to argue against the exponential formulae being reliable.

[speedchase]

I agree with Topagz. the 20k has misconceptions in his mind that will prevent him from playing well. Te random bot will choose a good move every once and a while.

[HermanHiddema]

I'm not over-estimating it, as I said, I'd be very happy with either. I think the randombot chances are non-zero, but almost indistinguishable from 0. I think the 20k's chance is actually 0.

Yes, I understand. And I think you are over-estimating it. I do not think the 20k's chance is exactly 0.

Herman, do you really think that, given enough games between Lee Sedol and a 20k, both not under the undue influence of drugs or whatever, would ever result in a 20k win, even over 10^1000 games?

No, but I think the chances are much much much bigger than if the random bot were to play the same number of games (BTW, the number of games I mentioned earlier is infinitely larger than a mere 10¹⁰⁰⁰)

[topazg]

No, but I think the chances are much much much bigger than if the random bot were to play the same number of games (BTW, the number of games I mentioned earlier is infinitely larger than a mere 10¹⁰⁰⁰)

Ok, my point wasn't clear I guess. The question I was really asking was "do you really think that, given enough games between Lee Sedol and a 20k, both not under the undue influence of drugs or whatever, would ever result in a 20k win, even over infinite games?"

[HermanHiddema]

No, but I think the chances are much much much bigger than if the random bot were to play the same number of games (BTW, the number of games I mentioned earlier is infinitely larger than a mere 10¹⁰⁰⁰)

Ok, my point wasn't clear I guess. The question I was really asking was "do you really think that, given enough games between Lee Sedol and a 20k, both not under the undue influence of drugs or whatever, would ever result in a 20k win, even over infinite games?"

Yes. I think the chance that a random bot has of doing so is infinitessimal, but not zero. I think a 20k has a better chance. Therefore: Yes.

I understand the argument you (and others) are making, I just don't think it is true.

[quantumf]

I think a 20k has a better chance.

Why do you think this? What is the basis for this belief?

We've suggested that we believe its impossible for a 20k to win, because the right moves are not in their vocabulary. How then can this 20k have a non-zero chance?

[HermanHiddema]

I think a 20k has a better chance.

Why do you think this? What is the basis for this belief?

We've suggested that we believe its impossible for a 20k to win, because the right moves are not in their vocabulary. How then can this 20k have a non-zero chance?

I don't think it is true that the right moves are not in their vocabulary. So I don't agree with the conclusion, because I don't agree with the premise.

As I already said: I understand the argument, I just don't agree.

[quantumf]

As I already said: I understand the argument, I just don't agree.

Well, sure, but the point of a discussion is to state a point of view and then defend it

We're getting somewhere now, tho, since you've indicated that you disagree with the statement that 20k's don't have the right moves in their list of candidates. I'm racking my brains to think how this could be possible.

How about this - Herman's 20k is someone who has a sound grasp of the correct strategy, and is able to evaluate the right place to play and the correct direction to play in, but is 20k due to a particularly poor tactical ability. In this game against topazg, he is somehow able to fluke his way thru the tactical situations, and his superior stategic ability proves to be a match for topazg?

[daniel_the_smith]

What you all are saying amounts to a claim that 20k players are *worse than random*. I can't understand this. The random player is going to have to play like 10¹⁰⁰ games just to get one as good as an average 20k game...

Numbers scientifically pulled out of a donkey.

[topazg]

As I already said: I understand the argument, I just don't agree.

Well, sure, but the point of a discussion is to state a point of view and then defend it

We're getting somewhere now, tho, since you've indicated that you disagree with the statement that 20k's don't have the right moves in their list of candidates. I'm racking my brains to think how this could be possible.

How about this - Herman's 20k is someone who has a sound grasp of the correct strategy, and is able to evaluate the right place to play and the correct direction to play in, but is 20k due to a particularly poor tactical ability. In this game against topazg, he is somehow able to fluke his way thru the tactical situations, and his superior stategic ability proves to be a match for topazg?

My experience with Go is that your rank is close to the weakest part of your game. If you're 5d at fuseki and direction, 5d at understanding joseki and hamete, 4d at common tactical tesuji, but 1k at reading complicated issues around a fight, you'll be 1d, or 2d at best - I think this is true even if you change around the skills at will. As a result, a 1d player and a 20k player will have such a wide disparity in skills and knowledge that it would be extraodinarily rare case that 20k was even up to the 1d standard in any aspect of the game. You talk about "correct stategy", but tactical knowledge and understanding determine the correct strategy - it's particularly clear that knowing what aji and what sequences are available in a given position play a huge part in deciding what the correct strategy should be at my level, let alone the level of a Go title holder.

Even though it may be theoretically possible for a 20k to have some elements of their game at professional 9-dan level, I'd probably need convincing, and to have enough of their game at that level that chance probability will increase the remainder of their game up far enough to score the occasional win, whilst still being overall a 20k in strength, I really struggle to believe.

I'm not trying to say "I'm right, you're wrong" here, I promise I'm just really genuinely wanting to know what evidence supports your belief that a 20k beating a 9d pro is a theoretical possibility.