What are the chances of winning any game of chess by chance alone?

They say that if you put enough monkeys in front of enough typewriters they will eventually type out the entire bibliography of Shakespeare. Assuming that there are 26 letters in the alphabet (case insensitive) and maybe 6 punctuation marks the odds are not too hard to work out.

Could the same thing happen in chess? Could a chimpanzee crush Magnus Carlsen by chance? Would the odds be higher or lower than a team of banana-munchers successfully recreating Hamlet?

arkledale

There is practically 100% chance that game would be ended by the FIDE Article 6.9 because Carlsen's opponent would not comply to 6.7.

If by some miracle 6.9. would not be applied, then for sure a 7.4.a and b would kick in.

Of course, Carlsen's opponent would hardly comply to Article 8 as well.

Fell free to continue.

I can say categorically that the odds of a chimp defeating Carlsen by chance are higher than for him/her to write the works of Shakespeare. The reason is simply one of combinatorics. To play a perfect chess game requires selecting the right move (or one of a very small number of playable ones) from a set of about 40 alternatives (on average) for around 100 moves. To write the complete works of Shakespeare requires selecting the right letter from a set of 26 (+spaces and punctuation) around 5 million times. Since 26^5,000,000 >> 40^100, it is clear which task is the more difficult for the persistent primate to achieve.

You neglected several extremelly important things.

Chimp does not know how the move the pieces(Article 3 FIDE laws of chess), therefore he would eventually lose a game based on 7.4.a +b.

Nor does the chimp know when to press the clock(or how), therefore he would lose on 6.9.

You can continue ...

I disagree, Elroch.

I presume the chimps do not know the rules of chess. So they would not chose only legal moves...

That changes everything. That would be really difficult to the monkey even achieve a sequence of moves with Carlsen. It would make a lot of useless moves that a TD would have to cancel and let it try again.

By the way, if we are considering the monkey will allways move only one piece per time, would it ever castle?

Dragec said same things a minute before me.

And before someone cames with the weird idea that the chimp should already know the rules, than it will be the same of saying it already knows English vocabulary, making Shakspeare book much easier.

Actually I said it half an hour earlier (post #2), but I left for the readers to consult FIDE to find out what I meant.

Since obviously no one got my drift, I had to put it more clearly.

Are there any chimpanzees who actually know how to type?  Would they even try or go off looking for bananas instead?  Are there even any chimpanzees who actually own a typewriter?  And what if the 'e' key got stuck?  Who would fix it?  What if they typed out the complete works of William Steinitz by mistake?  Would you ask them to start over?  The whole enterprise strikes me as problematic at best.

Chimpanzees are not the point. Why are you discussing chimpanzees? Change the question to "what are the chances of a computer winning by chance against a computer that has "solved" chess and never makes a mistake?" The question is somewhat related to whether or not computers can ever solve chess. If you want the exact number you need to know the number of total possible chess games.

My basic intuition tells me that the answer is absolutely zero chance and that any thought of there being the one time in infinity that blind luck defeats intelligence is nonsense. Is there a way to mathematically prove that the chances not even 1 in a gajillion to the billionth power? Perhaps we should be asking how many moves such a game would be likely to last. Suppose on average a game would last 12 moves. If it can be proven that 4 mistakes leads to definite defeat, and that a game will always last more than 4 moves does this prove that defeat is a mathematical certainty? 

Another question is whether the intelligent player knows his opponent is playing randomly. Does the intelligent player only have to play "good" moves? Or can he play horrendous moves which set up mate in the fewest possible moves because he knows there is only a one in 25 chance of a simple mate in one being countered.

Sorry if it doesnt make sense. Its about 3 am here right now and im tired.

Because the OP asked it in post #1.

"Could a chimpanzee crush Magnus Carlsen by chance?"

Oh sorry.  The original poster was talking about monkeys typing out the complete works of Shakespeare, not chimpanzees.  My mistake.  Perhaps monkeys would have a better chance, but then again their fingers are smaller than chimpanzees, so it might be harder for them to press down the keys especially if it was one of those old-style manual typewriters.  Do monkeys even use typewriters any more?  I thought most primates had switched to using wordprocessing programs for their desktop publishing needs.  Or if all you want is a copy of the complete works of William Shakespeare, it might be cheaper to just buy them online.  You could probably get a Kindle edition for a dollar or two, and save the whole hassle of checking over the monkeys' handiwork for typos and spelling errors.

A back of the envelope calculation gives me an odds of 1:10^19 or so. One in ten times a billion, times a billion. The rough calculation follows:

Average number of possible moves at a given time = 32  (Fairly constant throughout all stages of the game. Read this in a book somewhere.)

The total number of moves in an average chess game = 60  (a guess of mine)

Now we need the number of moves available, on average, good enough to beat a Magnus Carlsen. How about assigning a number like 2. Might be a bit big, but I like whole numbers, feel free to correct me. Magus beating moves = 2.

Ok, one has to pick one of the "Magnus beating moves" out of the total number of moves possible at one time. Choosing at random the probability is 2/32. Doing that again and again throughout the game, 60 times, the odds are (2/32)^60.

Simplifying (2/32)^60 = 1/(2^64) or 1:2^64 or 1: (1.8 * 10^19).

I am curious if anyone else has another estimate, or finds a problem with or improvement to my calculation.

Yes. Chimp would be busted by failing to comply with laws of chess.

And while we're on this topic, what are the odds of Magnus Carlsen agreeing to play a game against a chimpanzee?  Somehow, I don't think his father would go for it.  Heck, he isn't even playing in the world championship cycle!  I think you'd have to see if you could get the chimpanzee a spot at Linares, maybe a local Spanish chimp.  Even then it strikes me as a long shot.

The idea of a chimp typing the works of Shakespere is the infinite monkey theorem. It states that given an infinite amount of time an infinite amount of monkeys randomly hitting the keyboard would eventually type the complete works of Shakesphere. 

That being said given the same condititions (an Infinite amount of time and an infinite amount of people) a human, who knows the rules of chess, would eventually defeat a computer that never makes mistakes.

Lets say the chances of playing the perfect game against the computer that never makes mistakes is a ridicolusly low number, as long as it's possible (regardless of how slim the chances are) eventually with an infinite amount of time it will happen.

I disagree. I think it's fairly likely that the monkey would win. I think Magnus would resign in protest at the prospect of having to play a monkey.

*raises hand*

Those who claim that monkeys could not play a legal game of chess are ignoring the fact that the game could be played using a computer interface, which could ensure that only legal moves could be played (like on chess.com).

It would not be a large stretch of the truth to say the chess.com interface is easy enough for a monkey to play but, even if that is not so, it would be easy to write a program to display all the legal moves on a touch screen for the chimp. Brief training with a few bunches of bananas would be adequate to ensure that the chimp bothered to play a move each time it was his turn.

Of course it is rather unimpressive turning a chimp into a random number generator, but more impressive is a fascinating experiment from a couple of years back.  This showed that trained chimps were better at certain types of short term memory games on a touch screen computer than humans. A video of this is well worth watching.

Maybe the game could be like Magnus Carlsen vs. the monkeys of the world.  When it was their turn, all the monkeys and chimpanzees in the world who have access to a computer could sign in, and cast a vote for the move they prefer.  We could choose a panel of elite monkey players to provide commentary, and help give the voting a focus.  It could help spread chess far beyond its usual audience.  Maybe that would get Magnus interested.