Infinite amount of monkeys playing chess

monkeys are stupid until the 8 sleeping in their heads. but infinity exist when we know the degrees of our ignorance the day where we can see, not through mist but to see in absolute reality.

They don't need to be motivated. The fact of the matter is that the vast, vast, vast majority of them will throw the pieces around, but 1 in 100 trillion (much higher than the true likelihood, I'm sure - this is 1 in 10^14) will end up actually moving a piece instead. That means that there will be 1 in 10^28 places where two moves have been made. Now, let's say that the making of the moves was completely random; even monkeys that made the first move originally still only have a 1 in 10^14 chance of making another move. And, let's say that Chess can go on for 20,000 moves (surely, far too much) at longest. This means that the number of boards required to provide an equal chance of this game being played would be 10^(40,000*14)=10^560,000 monkeys. Add another 10^1,000 for good measure, and you have a 99.9999999.... (with a total of 1,000 9's) % chance of the longest and perfect game being created. With infinite monkeys, 10^561,000 would be nothing.

An infinite number of monkeys playing an infinite amount of chess games would create every position an infinite amount of times.  That goes with anything.  It's really pointless to ponder infinity.

http://www.youtube.com/watch?v=zJAH4ZJBiN8

Or to play chess...

 what are you doing here troll. this place is called chess.com. if you think chess is pointless you are wrong, first of all, and even if you were right (i doubt you have ever been in your life), you should go troll somewhere else

I think ivandh had a point though

 Infinity is mostly a craft of imagination. It cannot be defined, it's used in place of "the highest number possible". Concerning the original argument, an infinite amount of monkeys would require that the whole world be filled with monkey, ie nothing but monkeys in the world, not even earth and sun. In this case a chessboard wouldn't be able to fit in or at least there wouldn't be space above the chessboard so that the pieces could be accessed and moved. So an infinite amount of monkeys couldn't play chess at all.

 Can anyone find the fallacy in this argument?

You are all being silly.

You need a single eternal monkey OR an infinite number of monkeys for half an hour. You could probably make do with filling a few thousand solar systems with monkeys, bananas, and chess equipment. The problem is noticing when they have done something interesting. So you would need an awful lot of researchers. Who would not be having a lot of fun.

So the question I am left with is whether it is worth it, just to see how long it takes them to recreate for example The Immortal Game, which I could recreate for you now, in about 5 minutes, if you like.

My two cents.

They could play on DGT boards or on the computer.
And then a chess computer analyses how much the balance of the game shifts and checks wether or not the amount of material changes. The games that shift the least and have a normal chance in material are interesting games :D

Guys, guys, it says "infinite amount of monkeys playing chess" not "an infinite amount of monkeys" first and then they start playing chess. What that means is that we get a set of monkeys playing chess (which also requires a chessboard, a table, space, breathing air etc) and then we start adding more and more of such situation. No congetion possible because having an extra set of monkeys requires that all previous set of monkeys and the new one are possible. "Infinite amount of monkeys playing chess" provides that, hence the argument stands.

(lol)

ah rrriight!!

well, the Iron Man has a 12 hour time limit , so of course they wouldn't finish the competition. BUT if you take away the time limit of the Iron Man, then yes, one of them could actually finish.  If the time isn't a factor, like in the monkey problem, then they could float instead of swim, bike slower, and walk instead of run.  And I have seen "fat" people make it across the finish line, just not in the tops.

Good point. But then, do we say that the monkeys are always playing legal moves? Or simply that they are moving the pieces around, one at a time? It seems that the latter is a better representation of the question.

There is still the interesting but more debatable question, given an infinite number of monkeys, would an infinite subgroup move the chess pieces on the board one at a time, creating the conditions we specified (that they are all "playing" chess)?

 In infinity, everythink is infinite, even though one infinite might be smaller than another. Remember, infinite is just the equivalent of "the largest possible number", in a given situation of course...

Functions of infinity are not always infinite. The most famous example of this is Gabriel's Horn, which is a geometric shape that has infinite surface area, but finite volume.

If we could express the number of monkeys who play chess as a function of the total number of monkeys, the limit of this function at infinity may or may not diverge (that is, approach infinity).

The question is whether this supposed function is one that has diminishing marginal gains, which would suggest, though it wouldn't prove, that the number of monkeys who will play chess is a finite number.

It's turtles, all the way down...

 I'd say that if out of x monkeys y play legal chess, out of oo*x monkeys oo*y monkeys would play legal chess, hence oo (an infinite number). I think we can safely assume that the probability of monkeys playing legal chess is a deterministic one, the probability being y/x.

 Maybe monkeys could play bullet?