The Mysterious Math of Chess: Probabilities and Possibilities

[cepheid]

Today my little cousin (age 10) showed me a line from his book (The Usborne Guide to Playing Chess, or something like that) that claimed that the total number of possible chess moves is greater than the total number of atoms in the known universe! I don't remember the exact wording, so I guess we'll never know exactly what they meant by "total number of possible chess moves". Still, it seems crazy to me! It's a question of probability right? How many permuations are possible for x number of chess pieces on a board with y number of squares, given that each piece is governed by a certain set of rules. Can anyone shed some light on this?

 

[Janitor]

I wonder if it was saying that the number of different chess games is greater than the number of atoms in the universe? The number of games is finite because of things like the 3-move repetition rule and the 50-move rule that comes into play when no pawns are advanced and no material is captured. I don't see any obvious link to probablity theory.

 

[cepheid]

That sounds possible, and it makes more sense.

 

[Chronos]

A set theorem thing. Take the same number of atoms that are not restricted in degrees of freedom and you get many more possible outcomes.

 

[somy]

Well as I know as a chess player, we have a lot of technics of playing, each with lots of possible ending that are always growing by the play of "the experts" of this game.
It means that we just accept a moving as a part of game, if there are reasons of "being a good possibility". If not, you will be checkmated very soon! and it is not an acceptable "game".
As you know, we have 10 princibles of starting in chess, that reasons in about 50(or more) technics of playing.
Also in every day of chess life, we see a lot of new "games" by the experts. So it seems that we haven't arrived to the limits of this game yet!
But I haven't seen any any estimations about the number of "acceptable games".
It should be a hard work!
Have any idea?!

 

[Fredrik]

The Wikipedia article about chess mentions some of the things that are discussed in this thread. This is a part of that article:

The number of legal positions in chess is estimated to be between 10^43 and 10^50, with a game-tree complexity of approximately 10^123. The game-tree complexity of chess was first calculated by Claude Shannon (father of information theory) as 10^120, a number now known as the "Shannon number". Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218.

 

[expscv]

yes the acceptable game that would ingnore a lot of moves, but ! but if say the possible of ways play chess could be infinite since checkmate or not is not include.d

alternative atom have they basic principle rules, and can limit to a n possible of ways

 

[Zurtex]

Of course you are comparing the number of combinations to the number of physical things. If you take every atom in the universe as individual and distinct and you can swap any two atoms around as a single move then given you can make as many moves as you want how many possible set ups of the universe do you think would be possible?

Answer, a lot more than the number of anything physical we know about.

 

[somy]

Another question!:
Can anyone introduse a neat way to estimate the number of acceptable games?
S
uppose that we can just accept the games with more than 50 moves (for each player) that has enough logistic reasons.
We can do it by a "genetic algorithm"!
Anyone expert in it?!