Then you should ask your granddad about mathematical approaching techniques. I am curious, what his answer will be.

MNb wrote on 08/24/07 at 00:50:46:


No, in "real" mathematics, you find the solution to a problem and then write a proof of the solution with cleverly crafted layers of formalism until any element of human intuition that might have been used to solve the original problem is completely unrecognizable.  Now that is an exact science.  Remember:  the guesswork never happened.  

Smyslov_Fan wrote on 08/23/07 at 12:49:45:


Yes. Alas I don't know what "grondtal" is in English and it is not in my dictionary. I hope you still will follow my argument.
The simple approach is just to estimate. 20 moves per ply is probably too high; 15 may be too low. Then we also have to estimate the average length of the game until mate, say 60 moves (frankly I am not sure at all). Then you get 15^120. I suspect that this estimation is too low.
The uncertainty because of the different stages might not be that big. The rook and the queen get a lot of more freedom in the endgame and this may compensate for the lower number of pieces. Moreover we can correct with a random effect survey. The formula gets a little more complicated, but will not change essentially. Let us say, that the three stages all last 20 moves. Then you get a^40 * b^40 * c^40, simplified to (a*b*c)^40. A, b and c are the average amount of options in each stage per ply.
The effect of transpositions is far more difficult to incorporate in my opinion.

@Willempie: the mass of the earth is 6*10^24 kg. The mass of a watermolecule (consisting of 3 atoms) is about 30*10^-27. Dividing gives about 10^50 atoms. It may be three times more, but that does not really matter; such is the nature of exponential numbers.
This is probably too high, as the earth also consists of heavier atoms like iron.

A better approach though is to start with the model of the expanding/contracting universe mentioned by Udav and Markovich. This depends on the total mass (which causes gravity according to Newton). Alas there is a big uncertainty here (see the subject of dark mass). Also we must assume, that 80% (might be somewhat more or less) of the mass consists of Hydrogenatoms and 20% (idem) of Helium. With the same calculation as described above we can estimate the number of atoms in the universe.

Note: don't call physics and mathematics "exact" sciences ever again! It is so often just clever guesswork.

I did a quick search of Alexander's games.  He played two games that today would be considered a Benoni, but in his day one would have been considered a King's Indian (because of his move order) and one was probably more accurately a Blumenfeld.  I am don't know for sure because I sometimes can't tell the difference between openings that are very similar.

Alexander made the Dutch famous in the West, and played it against world champions.  He also might have shown an interest in this thread.  He was one of the Codebreakers working for the British during WWII!

BTW:  adding on to my previous note,  By the third ply (white's second move) I think the number of possible moves jumps to about 8000! (400 x20, give or take).

Smyslov_Fan wrote on 08/23/07 at 00:12:56:


I thought he said that (or something like it) about the Benoni.  No?

A question to MNb: I am not a good mathematican so i am not sure,whether it is possible to calculate all the possibilities by calculating the possibilities pertaining to the moves.E.g. 1st move :400 possibilities 2nd move.... 3...4...
After lets say the 5th move we have to draw the graph into a graticule with x = N (number of moves) and y= P (number of possibilities)
Is it possible that this graph will have some proportion and so we will be able to find out the possibilities after the 1500 move?
(Maybe it would be benefecial to use a logarithm-paper)

MNb wrote on 08/22/07 at 21:38:50:

I am very bad with big numbers, but just for me, how many atoms are for example in earth? I honestly have no idea, so it would be interesting to compare with the number of positions in chess.

Lastly there is one implicit assumptions which is not necessarily true:
-Data is stored in the same way as now. However it is quite possible to store data in another way. Already DNA-computing allows for much more possibilities as you use 4 iso 2 "freedoms". Furthermore data doesnt have to be stored in atoms at all.