Infinite possibilities in a game of chess?

And think of the moves that lead up to them!

The Koch snowflake isn't made up of finitely many parts, it's an infinite construction, and it's made up of infinitely many points. Finitely many finite parts implies finite.

"Getting back to the original topic.... yes, the number of possible moves is infinite.  The 50 move rule is not automatic: one player must claim the draw (the same applies to the rule about repeating the same position three times)."

The 50 move rule is not automatic? This surprises me. Apparently, the same thing is true for threefold repitition. What you said is true then. Still, current position is more important in some sense (since current position determines what the best move is, independant of game history). There are finitely many positions, and therefore, there are finitely many games where the position does not repeat. Also, there are fintiely many game where there is no threefold repitition. In this sense there are only finitely many games: you need to assume repititions will be declared draws. But, if none of this is automatically declared, there could be infinitely many games, though there wouldn't be any interesting ones.

Alternatively, it is a single line generated by a single algorithm. That would appear to be finite to my mind.

Indeed!!

"Alternatively, it is a single line generated by a single algorithm. That would appear to be finite to my mind."

Huh? 

there are 2 schools of thought,

those that see infinity as a quantity that is constantly ongoing,

and those that view infinity as a single discreet entity.

the first school of thought argues that infinity minus one is still infinity

or for that matter, infinity minus 'infinity minus one' is still infinity. :@

as for how this relates to chess, i dont think the possible number of moves is infinite, but it is definitely beyond calculation.  or i guess it could be infinite, as someone pointed out earlier that perpetual check could very well go on till the end of time if allowed to.

I believe it's been mathematically proven that there are some infinities larger than others:

If you imagine a circle with an infinite number of radii coming from the centre to the infinite amount of points on the circumference, then for a larger circle, one could fit more radii to more points on the larger circumference....

I think I understand, and somewhat agree. I forget the name of the mathematician who came up with this theory, but I know he spent the final years of his life in an asylum.

Careful staring into infinity, folks, it's probably just too big for our comprehension.

 No there aren't two schools of thought. Not within mathematics at least. Infinity minus one or minus a million for that matter is still infinity. Infinity minus infinity is undefined just like a rational number divided by zero or infinity multiplied by zero.

 Actually you couldn't fit more radii because the circles are similar. However, there are more irrational numbers than rational, although there is an infinite number of both.

shut up. we're talking about chess.

 You're probably talking about Cantor. His diagonal argument was the first proof that there are more real numbers than integers. (This might seem trivial, since the integers are inside of the reals, but it's not. For example, the integers and the rationals are the same size.)

There are infinitely many sizes infinity, and there is no largest infinity.

No one will live so long to learn if chess is infinite or not.The fact that there are 400 combinations only for the first move is quite discouraging to think how far a game can go,if we consider every possibility and not only the logical ones.Think of all the different players(of all levels!!!),what is logical for each of them?

Thank you

According to "Men of War", a 6-part booklet series on chess, published by the times newspaper in 1993:

"A Grandmaster game is classed as "miniature" if it lasts 25 moves per player, or less. If one undertook to print out every possible game, even of this restricted kind, in books printed with the same page and type-size as the London telephone directory, then the result would be, first, to cover the entire surface of the earth, and then to work outwards, filling all available space to a distance in every direction equal to that from Earth to the farthest known galaxy - not once, but 100,000,000,000,000,000,000,000 times."

It's just far too big to comprehend. About as close to infinite as finite gets.

That big number, 10^120, is called the Shannon number after the mathematician who first calculated it.  Do a websearch for "shannon number" to find out more about it.

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A man with one clock knows what time it is.  A man with two clocks is playing chess.

Yes, it was probably Cantor. Thanks for filling in the gaps in my memory.

There are an infinite number of moves if neither player claims a draw by 3-move repetition or the 50-move rule. A draw is only automatic with insufficient material and stalemate. As for checkmates, I think there are a finite amount of checkmating positions, but the sequence of moves to obtain that checkmate is infinite. For example:

1. f3 e5 2. g4 Qh4#

1. Nf3 Nc6 2. Ng1 Nb8 3. f3 e5 4. g4 Qh4#

1. Nc3 Nf6 2. Nb1 Ng8 3. f3 e5 4. g4 Qh4#

Of course, if either side would claim a draw when possible, then the possibilities are finite. 

Agreed. My mind doesn't have the capacity to hold infinity, but my stomach can certainly hold beer.