The Probability of a Monkey Defeating Yi Chang-ho

[Bill Spight]

Some go books, often the kind that come as inserts in go magazines, rate your play by multiple choice questions. I just rummaged around and found one. It has 15 questions with 5 choices each. Your score per question ranges from 2 (for the worst choice) to 10 (for the best choice). Random bot will have an average total score of 90, which would make it 2 kyu. Now, the test makers were not completely out to lunch. Any score below 62 indicated 6 kyu or below.

But really, wouldn't a 6 kyu do better than random?

Well, maybe not. There are certain bad plays to which low kyu players are drawn. It may be that the testers made the 2 point choices attractive for weak players. (BTW, I did a little studying of testing some years ago. You can rate questions on how well they differentiate test takers at different levels. I doubt if the questions in these books are the result of extensive research, though. )

I hardly ever review DDK games, because I do not understand them. They are not totally random, of course, but I don't know what the players are thinking. (Boidhre is an exception. His games make sense to me. You might say that he plays like a 5 kyu on a bad day. ) At around 10 kyu I start to see predictable errors. Bad play attractors, if you will. Much of advancement is unlearning bad habits. But players also have blind spots, where there are good plays that they do not even consider. Players stick to familiar patterns, and fail to consider the possibilities of the position. One advantage of studying pro games is that you see plays that you never would have thought of.

For me, one such blind spot was leaning attacks. But once I got the idea, the leaning attack was my secret weapon. For years. Here in the U. S., few players knew about it. Then "Attack and Defense" was published, and the secret was out.

It is the existence, for humans, of blind spots and bad attractors that make the possibility that, given a sufficient skill difference, the lower ranked player will never beat the more skilled player. (Maybe a 15 stone difference?)

OC, there is no practical test for that. However, I expect that it is possible to devise multiple choice tests where low kyu players will reliably score worse than random. (As long as they do not adopt a random strategy, OC. )

[Laman]

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.

were they in a movie, the 20k's chances would jump up drastically

but then again, movies are not usually shot to reliably model reality

[flOvermind]

Million-to-one chances crop up nine times out of ten.
-- Terry Pratchett

(sorry, couldn't resist )

[Bill Spight]

Million-to-one chances crop up nine times out of ten.
-- Terry Pratchett

(sorry, couldn't resist )

"Given a 50-50 choice, the weak player will make the wrong choice 75% of the time."

-- Victor Mollo

Victor Mollo was a very entertaining bridge author. IIRC, that quote was from his character, the Hideous Hog.

[tchan001]

It has 15 questions with 5 choices each. Your score per question ranges from 2 (for the worst choice) to 10 (for the best choice). Random bot will have an average total score of 90, which would make it 2 kyu.

A truely random legal bot would rarely be picking from just 5 choices per position.

[phrax]

It has 15 questions with 5 choices each. Your score per question ranges from 2 (for the worst choice) to 10 (for the best choice). Random bot will have an average total score of 90, which would make it 2 kyu.

A truely random legal bot would rarely be picking from just 5 choices per position.

I remember a time taking tests like and thinking "I wouldn't have played any of these choices." Suggesting my earlier play was closer to random than I'd care to admit. (Although I swear I [almost] always had a reason for my bad choices.)

[Bill Spight]

It has 15 questions with 5 choices each. Your score per question ranges from 2 (for the worst choice) to 10 (for the best choice). Random bot will have an average total score of 90, which would make it 2 kyu.

A truely random legal bot would rarely be picking from just 5 choices per position.

That's the conditions of the quiz. What would the bot score?

[Bill Spight]

It has 15 questions with 5 choices each. Your score per question ranges from 2 (for the worst choice) to 10 (for the best choice). Random bot will have an average total score of 90, which would make it 2 kyu.

A truely random legal bot would rarely be picking from just 5 choices per position.

I remember a time taking tests like and thinking "I wouldn't have played any of these choices." Suggesting my earlier play was closer to random than I'd care to admit. (Although I swear I [almost] always had a reason for my bad choices.)

Actually, some who train people to take tests advocate that, if you are unsure about your answer, do not give the one that seems right at first glance. That's probably the trap answer set by the test makers.

[luigi]

Sorry to derail the thread by commenting on an old post on this thread. I just want to point out something related to quantumf's suggested tought experiment:

Here's an interesting thought experiment. I'm aiming it at topazg specifically, because he nailed the problem of working with probabilities in the human sphere, but it can easily be rephrased for others.

Take your entire mortgage, or some other large sum of money, whose loss you would feel very keenly. You now have a choice - you can play this random move monkey, or you can play a 20k player. If you lose the game, you lose all your money. Which one would you rather play?

If a) the 20k player is a human, b) I were rich and c) my losing means he gets all my money, I'd choose the random bot, even if my Go skills were as good as topazg's.

A 20k human may not be good at Go, but there's a good chance that he's a clever guy. If he's presented with the chance of winning a huge amount of money he will be likely to give the issue a thought or two and determine that playing randomly would give him a better chance of winning than playing at his usual level.

This human opponent could easily find an algorithm on the Internet to generate pseudo-random numbers* and spend his thinking time using it instead of his Go skills. He would only make a non-random move when the best move is obvious. Since there are quite a few obvious moves in every Go game, this would be enough to give him a much better chance of winning than a random monkey would have.

* I'm not sure whether pseudo-random is enough here. If it isn't (which is my suspect), maybe he could try splitting the list of available moves in two and choose one half or the other depending on whether the seconds in his watch (or even half-seconds: some watches have flickering colons) are odd or even at the moment he looks at them. He would repeat this division process until only one move remains and then make that move on the board. But maybe I should start a different thread named "How can you mentally generate random numbers?" to discuss this...

[Joaz Banbeck]

...He would only make a non-random move when the best move is obvious. ...

But what is obviously the best move to a 20K is often not really the best move.

“It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so.”

I believe that the difference between kyu players and dan players is that to make progress a dan player has to learn more, whereas a kyu player has to forget the things he knows that aren't true. ( This is why many kyu players report being stronger after taking a long break from the game )

[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.

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

The same way you make a monkey play legal moves rather than just random moves.

[tchan001]

monkey sees, blindfolded person doesn't.

[topazg]

monkey sees, blindfolded person doesn't.

If we're going to be totally honest, there's no guarantee a blindfolded person isn't going to be putting his hand in his coffee and the stone in his opponent's eye. Of course, it's quite possible the well seeing monkey might resort to that too.

[hailthorn011]

monkey sees, blindfolded person doesn't.

While that's true, I have a hard time believing a monkey will play all legal moves. It might just decide to start flinging stones. Who knows?

[luigi]

monkey sees, blindfolded person doesn't.

If we're going to be totally honest, there's no guarantee a blindfolded person isn't going to be putting his hand in his coffee and the stone in his opponent's eye.

The latter is perfectly legal if the opponent is one-eyed and in atari.