The Probability of a Monkey Defeating Yi Chang-ho

[hyperpape]

Some of you might want to read this: http://lesswrong.com/lw/mp/0_and_1_are_ ... abilities/

It's not possible for a 20k to have a literally 0 chance of beating a 9p. We know 9p players occasionally keep the game close and occasionally self atari near the end. This is vastly more probable than random play producing a 1d game.

We must make some sorts of abstraction from actual play--either that or get Robert to write rules about what happens when a player suffers a heart attack during the game. If you don't do that, then what are the odds the 9p resigns in disgust against the random bot?

[HermanHiddema]

It's not possible for a 20k to have a literally 0 chance of beating a 9p.

Proof?

EDIT: Probabilities of 0 do exist aplenty. What's the probability of rolling a 7 on a standard 6-sided die?

That's not a probability, that is a certainty. If we can enumerate all the possible outcomes, then it is easy to say what is and isn't possible.

To make this apply in this case, you would have to enumerate all possible games that a 20k and a 9p can play, an show that none of them are a victory for the 20k.

[topazg]

That's not a probability, that is a certainty. If we can enumerate all the possible outcomes, then it is easy to say what is and isn't possible.

Apparently not according to Daniel's linked article

[pwaldron]

Some of you might want to read this: http://lesswrong.com/lw/mp/0_and_1_are_ ... abilities/

It's not possible for a 20k to have a literally 0 chance of beating a 9p. We know 9p players occasionally keep the game close and occasionally self atari near the end. This is vastly more probable than random play producing a 1d game.

The linked article isn't relevant to the discussion. The author was consider Bayesian inference, where one has a prior estimate of something (e.g., chess skill) and then updates the estimate based on new information. The author points out that it would take an infinite amount of data to conclude that someone will beat someone else with probability 1. We aren't doing Bayesian statistics here, although that is what underlies most of the rating systems that are out there.

In our case the question originally posed seems to be estimating whether a random monkey can beat a top pro. Clearly the answer is yes; in principle the monkey could find a sequence of moves that would.

Then the question shifts to estimating a probability, which then brings people to compare to non-random monkeys (us for example). At this point you have to have a model for the play, and even then you can't come up with a definitive conclusion.

For example, we might model a biased random monkey, which selects better moves more often than the random monkey. Such a monkey would be able to beat the random monkey more often than not, but also has a non-zero probability of beating a pro. On the other hand, we could consider another type of monkey (or human) that never selects the worst 10% moves, but crucially never selects the top 3% moves or strategies either. Such a player would show up somewhere in a rating system as being better than the random monkey, but lacking optimal moves might never be able to beat a 9p.

If we model a player as actually considering all available moves and selecting one using a biased method, then such a player could beat a pro. If we model a real player as selecting good moves, but having a blind spot that somehow prevents moves from being considered then the probability of beating a pro might well be zero, even if the player is better than a monkey.

[palapiku]

First, assume a spherical monkey in simple harmonic motion...

[hailthorn011]

Or to simplify things (which I like doing), you could simply blindfold the person that the monkey happens to be playing. That could dramatically improve the chances of the monkey winning. Then you have two players playing essentially random moves.

I suppose this isn't an honest method, but nobody said it had to be.

[tchan001]

Or to simplify things (which I like doing), you could simply blindfold the person that the monkey happens to be playing. That could dramatically improve the chances of the monkey winning. Then you have two players playing essentially random moves.

I suppose this isn't an honest method, but nobody said it had to be.

And how do you make sure that the blindfolded person would play legal moves rather than just random moves.

[daniel_the_smith]

OK, maybe I should avoid posting from my phone as it seems to make my posts terse and trollish sounding.

I do realize I'm being incredibly pedantic on the point of zero not being a probability, but I don't think I'm wrong. If you do bayesian updating, there's quite literally no amount of evidence that will cause you to ascribe 0 probability to a hypothesis. There's no amount of data that topazg can provide that will cause me to believe the true number is literally zero and not zero plus epsilon. (I'm prepared to accept that epsilon is arbitrarily tiny, though.)

Both of the cases we're talking about here have epsilon probability, we're just debating the relative sizes of the epsilons.

I accept the argument that the 20k can be better on the whole but still miss the top x% of moves required to beat a 9p. I have two reasons why it doesn't sway me: it's unclear whether 20ks actually function that way*, and it doesn't change the fact that the 9p can still have a brain fart; I believe there's a famous video of self-atari by one...

[*] I think it's something on the order of 90% likely that 20ks indeed cannot generate the top x% of moves. However, I can't believe that there's a 0.000000....00001 chance of a 20k beating a pro based on a proposition that I'm so relatively unsure about.

Anyway, I'm tired and have been working overtime so probably you should mostly ignore everything I'm saying.

[daniel_the_smith]

Another thought just occurred to me. To reliably reject the top 3% of moves, don't you have to have a pro-level move rejection module in your brain?

[hyperpape]

No, it doesn't require a pro-level move detection module, so long as the claim is that it isn't only the top 3% that get rejected. The 20k reliably rejects the top 3% of moves, the 12th-17th%, the 28-34th%.

Seriously, I think there are just going to be certain kinds of tenukis, certain kinds of tesuji moves that will never be seen by the 20k. There will occasionally be death-in-gote hallucinations that won't affect him, because he doesn't have the knowledge that I misapply in a game.

[daniel_the_smith]

No, it doesn't require a pro-level move detection module, so long as the claim is that it isn't only the top 3% that get rejected. The 20k reliably rejects the top 3% of moves, the 12th-17th%, the 28-34th%.

Hm, I have a hard time believing that the distribution is really a sawtooth thing like that. I could readily believe something like 20k's are 10 times less likely to find a move in a given percentile than the one below it. I can't tell without doing some math if that's enough to cause the effect people are arguing for or not.

[pwaldron]

Another thought just occurred to me. To reliably reject the top 3% of moves, don't you have to have a pro-level move rejection module in your brain?

Possibly, but not necessarily. Imagine playing someone who generally played very good moves, but had no concept of sente. It would be a hole in his game that would be absolutely devastating in the yose. He doesn't need a fancy rejection module, but a module that discounts entire strategies and concepts.

[jts]

Or similarly; for me to be reliably unable to produce any sentence of fluent Cantonese, must I be secretly fluent in Cantonese to know which sentences to avoid?

It's probably best not to treat the possibilities we draw out of the statistical analyses of data as being comparable either to the ideas of possibility and impossibility we get from a systematic study of the sciences, or to the practical confidence we have when we need to make decisions without calculations.

[Garuseimasahi]

This is hilarious. No chance of becoming 9dan proffessional, so sit here and debate the chance of becoming 9dan professional. XD

[tchan001]

I'd like to think of the comparison of a 9p to a 20k similar to a weapons race. With the highest level of strategic and tactical knowledge, the 9p is similar to being armed with a battery of target hunting missles while the 20k is armed with a wooden club. The 9p is in the control room inside a heavily guarded mountain fortress while the 20k is 50 miles away still trying to figure out how to cross the river to reach the mountain fortress. The probability that the 20k will beat the 9p is pretty slim if at all.