Humans vs. Alpha Go Zero

[gennan]

@gennan
Let's suppose, in theory, that you are playing against 5 kyu, playing at full strength every game. do you agree that he will never win? but if you calculate the probability, it is not equal to 0. If you are not sure about 5 kyu, then 10 kyu

From my own Elo to EGF rank conversion estimate, I estimate the gap between me and a typical 5k to be about 600 Elo, which would imply a win% of about 5% for them (1 in 20 games).
And I would estimate the gap between me and a typical 10k to be about 900 Elo, which would imply a win% of about 0.5% for them (1 in 200 games).
I don't know if those estimates are realistic, but I don't intend to play very long matches against 5k and 10k players to accurately determine their winning probability.

I did lose an online game last December against a player with an OGS rating hovering around (2021) OGS 3k. And in the past 25 years I have lost several tournament games against 1k players. I just looked up my score against 1k in the EGD and it is 25-7, so 1k has about 20% winrate against me (suggesting a 250 Elo gap, though it might be a bit biased, because I usually only play against 1k in tournaments when they have a good day and I have a bad day).

I think there is always some probability that my opponent wins, no matter how weak they are. Yes, at some point the probability becomes less than 1%, but it's never going to be 0.
For example, I could get a stroke during the game. I don't know the exact odds for such a thing happening, but I think it's at least something like 1 in 1,000,000 games.
That probability is small, but clearly bigger than your example of throwing balls at the moon, because it's physically impossible for even the strongest humans to throw a ball with a velocity close to escape velocity (11.2 km/s) and then I'm even ignoring drag from the atmosphere.

[gowan]

We are familiar with the humerous idea that if a monkey were randomly typing on typewriter eventually the works of Shakespeare would come out with probability 1. By this reasoning even random play could eventually win a go game against alphago. Of course "eventually" would likely mean longer than the existence of the universe. In practice I would think that machines 10 time stronger would be developed every so often so that eventually Alphago will seem to be ridiculously weak

[jlt]

I know a 1d who self-ataried and lost a tournament game against a 20k.

[gennan]

I think the odds of a 10k beating me is many orders of magnitudes greater than the monkeys typing all of Shapespeare's works within a billion years. Occasionally, I make a blunder of 100+ points. I don't know how often, but once in a 100 games or so is not far off, I think. Such odds are not crazy small.

[gennan]

For my own curiosity, I looked up my tournament score against 6d. It's 10-31 over the past 25 years, so about 25% or 200 Elo difference.

[And]

I think the odds of a 10k beating me is many orders of magnitudes greater than the monkeys typing all of Shapespeare's works within a billion years. Occasionally, I make a blunder of 100+ points. I don't know how often, but once in a 100 games or so is not far off, I think. Such odds are not crazy small.

if you make mistakes, you are not playing at full strength. the computer makes no mistakes

[And]

@gennan
Let's suppose, in theory, that you are playing against 5 kyu, playing at full strength every game. do you agree that he will never win? but if you calculate the probability, it is not equal to 0. If you are not sure about 5 kyu, then 10 kyu

From my own Elo to EGF rank conversion estimate, I estimate the gap between me and a typical 5k to be about 600 Elo, which would imply a win% of about 5% for them (1 in 20 games).
And I would estimate the gap between me and a typical 10k to be about 900 Elo, which would imply a win% of about 0.5% for them (1 in 200 games).
I don't know if those estimates are realistic, but I don't intend to play very long matches against 5k and 10k players to accurately determine their winning probability.

I did lose an online game last December against a player with an OGS rating hovering around (2021) OGS 3k. And in the past 25 years I have lost several tournament games against 1k players. I just looked up my score against 1k in the EGD and it is 25-7, so 1k has about 20% winrate against me (suggesting a 250 Elo gap, though it might be a bit biased, because I usually only play against 1k in tournaments when they have a good day and I have a bad day).

I think there is always some probability that my opponent wins, no matter how weak they are. Yes, at some point the probability becomes less than 1%, but it's never going to be 0.
For example, I could get a stroke during the game. I don't know the exact odds for such a thing happening, but I think it's at least something like 1 in 1,000,000 games.
That probability is small, but clearly bigger than your example of throwing balls at the moon, because it's physically impossible for even the strongest humans to throw a ball with a velocity close to escape velocity (11.2 km/s) and then I'm even ignoring drag from the atmosphere.

the example with the moon is an allegory, I meant that it is just as unrealistic, and most understood me.
for fun: the probability of a ball hitting the moon is not zero, you did not take into account the possibility of a hurricane passing by a meteorite, which "took the ball with it to the moon", etc.

[And]

@gennan
I want to play a match of 1000 games AmiGo (~ 11 kyu) - KataGo b6c96-s48921344-d7092247, 1 playout (~ 2 kyu). can you calculate the probability of winning AmiGo?

[gennan]

How did you determine that Amigo is ~11k and that this KataGo instance is ~2k?

[And]

How did you determine that Amigo is ~11k and that this KataGo instance is ~2k?

viewtopic.php?p=261404#p261404
Amigo give a couple of minutes ...

[gennan]

@gennan
... but clearly bigger than your example of throwing balls at the moon, because it's physically impossible for even the strongest humans to throw a ball with a velocity close to escape velocity (11.2 km/s) and then I'm even ignoring drag from the atmosphere.

the example with the moon is an allegory, I meant that it is just as unrealistic, and most understood me.
for fun: the probability of a ball hitting the moon is not zero, you did not take into account the possibility of a hurricane passing by a meteorite, which "took the ball with it to the moon", etc.

Yes, and there is also quantum tunneling. So indeed that probability is not exactly 0, but it would be astronomically smaller than me losing an even game to a 10k.

[gennan]

How did you determine that Amigo is ~11k and that this KataGo instance is ~2k?

viewtopic.php?p=261404#p261404
Amigo give a couple of minutes ...

That links to a post where you say "network g170 6 block d7.09M probably plays on 2k.". That post doesn't explain how you determined it.

[And]

AmiGo 10k
https://github.com/breakwa11/GoAIRatings
and somewhere else it was 11k

[And]

I don't want to argue if it plays 2k. I think something like this. I'm more interested in the outcome of the match. can you calculate the probability?

[gennan]

I doubt if computer programs that score 50% against some level of human players are a good model for human-like play at that level. A nerfed KataGo that scores 50% against 2k players is more like a Formula 1 car with square wheels to make its lap time on a race track similar to a VW Beetle. That doesn't make it the same thing as a VW Beetle.

Also, I expect computer programs to be a lot more deterministic than humans. If one program plays in way that happens to exploit the other's weaknesses, the results will be more skewed than a match between humans of similar levels.

And I don't really know how accurate your estimates are for the level of these programs, so I'll include some uncertaincy for that in my estimate. I would also add some uncertaincy for short time settings (making blunders more likely for both players).

But anyway, for a non-blitz match between a human 11k(±2) and a human 2k(±1), I would guess that the weaker player will score around 1%-5% wins.