He did...but...like, you can’t really trust that. He’d have said that (or similar) no matter what. It isn’t game commentary, its signalling.
There’s a sort of humblebrag attitude that permeates all of Go. Every press conference is the same. Your opponent was very strong, you were fortunate, you have deep respect for your opponent and thank him for the opportunity.
In the game commentary you get the real dish. They stop using names and use “White/Black” to talk about either side. There things are much more honest.
And looking at how he used up his time much sooner, he was more cautious today. He still lost and probably also took a psychological hit, so now my estimate of chances of Lee Sedol winning the whole match went down to ~5%.
Ignoring psychology and just looking at the results:
Delta-function prior at p=1/2 -- i.e., completely ignore the first two games and assume they’re equally matched. Lee Sedol wins 12.5% of the time.
Laplace’s law of succession gives a point estimate of 1⁄4 for Lee Sedol’s win probability now. That means Lee Sedol wins about 1.6% of the time. [EDITED to add:] Er, no, actually if you’re using the rule of succession you should apply it afresh after each game, and then the result is the same as with a uniform prior on [0,1] as in #3 below. Thanks to Unnamed for catching my error.
Uniform-on-[0,1] prior for Lee Sedol’s win probability means posterior density is f(p)=3(1-p)^2, which means he wins the match exactly 5% of the time.
I think most people expected it to be pretty close. Take a prior density f(p)=4p(1-p), which favours middling probabilities but not too outrageously; then he wins the match about 7.1% of the time.
So ~5% seems reasonable without bringing psychological factors into it.
Laplace’s law of succession gives Lee Sedol a 5% chance of winning the match (and AlphaGo a 50% chance of a 5-0 sweep). It gives him a 1⁄4 chance of winning game 3, a 2⁄5 chance of winning game 4 conditional on winning game 3, and a 1⁄2 chance of winning game 5 conditional on winning games 3&4. It’s important to keep updating the probability after each game, because 1⁄4 is just a point estimate for a distribution of true win probabilities and the cases where he wins game 3 tend to come from the part of the distribution where his true win probability is larger than 1⁄4. It is not a coincidence that Laplace’s law (with updating) gives the same result as #3 - Laplace’s law can be derived from assuming a uniform prior.
Hmm, I explicitly considered whether using LLS we should update after each new game and decided it was a mistake, but on reflection you’re right. (Of course what’s really right is to have an actual prior and do Bayesian updates, which is one reason why I didn’t consider at greater length and maybe get the right answer :-).)
Lee Sedol has just resigned the second game.
I thought he was ahead for a lot of game two. I wonder if that was true, or if AlphaGo was in control all along.
According to this, Lee Sedol said in the post-game press conference that he didn’t think he was ahead at any point in the game.
He did...but...like, you can’t really trust that. He’d have said that (or similar) no matter what. It isn’t game commentary, its signalling.
There’s a sort of humblebrag attitude that permeates all of Go. Every press conference is the same. Your opponent was very strong, you were fortunate, you have deep respect for your opponent and thank him for the opportunity.
In the game commentary you get the real dish. They stop using names and use “White/Black” to talk about either side. There things are much more honest.
I thought it was an very likely AlphaGo victory about an hour in, and nearly certain about two hours in.
And looking at how he used up his time much sooner, he was more cautious today. He still lost and probably also took a psychological hit, so now my estimate of chances of Lee Sedol winning the whole match went down to ~5%.
Ignoring psychology and just looking at the results:
Delta-function prior at p=1/2 -- i.e., completely ignore the first two games and assume they’re equally matched. Lee Sedol wins 12.5% of the time.
Laplace’s law of succession gives a point estimate of 1⁄4 for Lee Sedol’s win probability now. That means Lee Sedol wins about 1.6% of the time. [EDITED to add:] Er, no, actually if you’re using the rule of succession you should apply it afresh after each game, and then the result is the same as with a uniform prior on [0,1] as in #3 below. Thanks to Unnamed for catching my error.
Uniform-on-[0,1] prior for Lee Sedol’s win probability means posterior density is f(p)=3(1-p)^2, which means he wins the match exactly 5% of the time.
I think most people expected it to be pretty close. Take a prior density f(p)=4p(1-p), which favours middling probabilities but not too outrageously; then he wins the match about 7.1% of the time.
So ~5% seems reasonable without bringing psychological factors into it.
Laplace’s law of succession gives Lee Sedol a 5% chance of winning the match (and AlphaGo a 50% chance of a 5-0 sweep). It gives him a 1⁄4 chance of winning game 3, a 2⁄5 chance of winning game 4 conditional on winning game 3, and a 1⁄2 chance of winning game 5 conditional on winning games 3&4. It’s important to keep updating the probability after each game, because 1⁄4 is just a point estimate for a distribution of true win probabilities and the cases where he wins game 3 tend to come from the part of the distribution where his true win probability is larger than 1⁄4. It is not a coincidence that Laplace’s law (with updating) gives the same result as #3 - Laplace’s law can be derived from assuming a uniform prior.
Hmm, I explicitly considered whether using LLS we should update after each new game and decided it was a mistake, but on reflection you’re right. (Of course what’s really right is to have an actual prior and do Bayesian updates, which is one reason why I didn’t consider at greater length and maybe get the right answer :-).)
Sorry about that.