Alternative way to estimate the number of possible chess positions:

Using permutation math and 32 pieces and 64 squares, it may sound simple to estimate the number of possible chess positions. But not only are most not legal, many are impossible to arrive at. The math problem may then sound more difficult. But I have a plan:

Over 2 million or so games have been played and recorded, electronically I think. I don't know the important details of that statistic (please respond with the details), but here is my idea:

1. We collect all these games from people as a list of moves and the names of the players.

2. We have a computer create each position from the list of moves and compare positions after move 15 or so.

3. We have it create a distribution analysis showing what percentage of the positions are singlets, doublets, triplets, etc. For example: if a particular chess position has only occurred twice in electronic recorded history, it is a doublet.

4. The distribution could be a table, so that it has the number of repetitions as one dimension, the move number as another dimension, and the percentage as the value at each intersection.

5. With the names of the players known, we can rule out anonylies if some players are more likely to do repeats than others. You can even make a distribution for that if the psychologists are interested.

6. Finally: If you see a ton of repeats, that means the probability is high that total possible positions is not much bigger than the number currently attained. If there are few repeats compared to the singlets, that means the odds are that there are far more positions.

7. And one other point: We need to secregate the games based on the skill levels of the players. Class E vs Class E, master vs master, and Class E vs master, and see how those combinations affect the percentages. It would also be good to see if lower rated players produced a wider range of positions than higher rated players. It would also be important to account for the number of players in each category.

My brain hurts...>_<

i still don't understand what's the point of this

did any1 read the whole thing?? plz brief me!! thank you. 

echecs, lets go fishing!!

I understood up to part 2, then my brain started to become a mush.

I think people got scared by the phrase "distribution analysis". If a particular chess postion only occurred twice in the history of electronically recorded chess games in data bases, then that position is a doublet. If it only occurred once, it is singlet. If 8 timies, it is an octuplet.

The goal is to estimate how many possible legal/aquireable/logical chess positions there are (and much more with the later ideas). If almost every position is a singlet, then the odds are that there are many many more possible positions not yet played. If most positions occured 50 times, there are other explanations, but a very likely one would be that there are not many more positions possible.

If we can get some kind of estimate on how many logical chess positions there are, we can have an idea of whether it is within our reach to solve chess with computers. Other people have used other methods to estimate the number, but my method is a statistical approach.

One problem though is that most of the recorded games are tournament games, and as such most follow book for the first 15 moves. Because of the copy catting, and the unknown true strength of book moves, the data base probably is not a good enough source from which to draw these statistics. But that is why I said we should only count positions after move 18, and also compare the distributions as the game progresses.

I do not think you realize the scale of the positions you have to maintain.

An average game lasts around 40 moves or so.  If your approach is to be followed, you have to use the number of plies as those represent the number of positions.

40*2 = 80 plies

Now you have to include millions of games that have been played all-time.  For all intensive purposes, lets say 10 million.

80 plies average*10 million games=800 million positions available at a conservative estimate.  This of course does not even cover the vast number of positions still available.

This would require a huge database in the terrabytes range.  Then, you have to spend days pruning through the duplicates and separating it into categories and their statistics.

Not a small task.  You would still have to get all of these games. 

As for the number of games, I would have agreed: 20x20x20x20 or so every half move does climb fast. But you have to remember that many pieces are blocked and can't go more than 2-4 spaces. When a king is in check, the number of possible moves drops fast or the game ends with king capture. Many games can be considered the same if the same position re-occurs in it, which would be expected if beginners were just hopping knights around forever. Pawns can only move so far before they are blocked. It is hard to have many queens on the board without the king being checkmated. And I read in an article that while the possible number of games starts out as 20x20, it reaches steady state fast as many of the games end in checkmates or draws by repetition.

They might have done the math wrong, but I think it is worth looking into. If there truly are just a few hundred million positions total from beginning to end, then chess can be solved.

As for 5 pieces, two kings, a pawn, and a rook each have been solved by GM Nunn and are explained in 352 pages, though I still question whether he could have accounted for every possible starting position.

I agree though, that there are many possible positions even there. I wonder how many endgames can be played without ever having any positions in common.

who cares-got better things to do

A few points here.

While positions may be repeated in a database, you would also have to include whether it is black's or white's turn in the same position when trying to solve chess.  The idea of triangulation for example.  So that effectively would double my estimate.

It took 12 years to solve a seven piece endgame with all the possible moves AND  positions.  That is a long ways away from a 32 piece endgame to give you a scope of what you are talking about.

A game compilation is simply too dense and would require many lines of programming to be of any use.

A compilation of the number of chess positions is far easier to obtain than a move list of every position.  Even so, it is a tremendous amount of work and I think using a game database is not an effective means of carrying that out.

I'd rather spend my time learning how to be a better player than piling through all that data.  You could literally make yourself go crazy thinking about all the different possible combinations of moves all day long.

It's kind of like calculating all the possible combinations of X's & O's on the board of a tic-tac-toe game.  Sure, it could be done,it would be easier to calculate than chess, and once you're done you'd have a number, but what's the point?

I actually read the whole but still dont quite get it but I really want to could you dumb things down for me ? I think it has potential.

Just one question. Will all this help me win more? If not... What's the point?

There are thought to be about 10^120 possible chess positions. The fastest supercomputer right now can manage 8.16 petaFLOPS (Floating-point Operations) per second. Assuming a very, VERY conservative rate of 1 position per FLOP, that computer would require ~10^104 seconds (slightly more) to go through all the positions.

It is estimated that 10^17 seconds have passed since the Big Bang.

I think it's funny, all the people who wasted their time posting that they think this is a waste of their time.

The point is the fun of designing a program to find the stuff. There has to be a way to simplify things. I bet I could do it. As for the seven piece example, the number of possible positions (not all legal or possible to get to) is 64*63*63*61*60*59*58*2 and can be simplified by discounting mirror reflections about both dimensions, whose turn it is, and illegal/impossible positions such as two kings checking each other. That number is huge, but I think even a PC could crunch it out, in far less than 12 years. Or maybe not, since it actually has to then solve each position, not just have it in the database. But once a few positions are solved, it would know exactly what to do once that position is reached.

That is working from the back end, though. I'd prefer instead of making up every possible position, to start from the beginning and just create every possible move combo. The huge problem is the amount of search time needed to know if a position is a repeat or not. The search has to be done for every position in the database. Yeah, sounds pretty huge.

One nice thing is you don't need a super computer to do this. It can be done just as easily with 1,000,000 PC's. Chess can very nicely be divided up into variations.

it's about two thousand. My brother allready did this.

And then if you made it try to figure out all the positions in a 4 player chess game, the CPU would melt down!

http://en.wikipedia.org/wiki/Four-handed_chess

 That looks really fun. Wish I could play it.