How many chess positions are there

How many combinations?

  • Is it actually mathematically possible to determine how many possible combinations there are in chess?
    And another question: who invented the game of chess? The devil? Don't laugh, I know some Persians who claim this?
    Greetings to you all, micha6
  • micha6 wrote:

    Is it actually mathematically possible to determine how many possible combinations there are in chess?


    Chess has clearly defined rules and thus the exact number of all possible moves can be determined. I made an estimate back then and came up with an incredibly high number. Nevertheless, this number is smaller and infinite - logical.

    Even more: if there are a finite number of train combinations, then a mainframe computer could determine or chain all predecessors and successors for every position. Exactly then you would have to everyone Position the exact result (because the perfect game is also a pull chain, and you know which chains are not perfect). Then a game with or against such a chess database would be pointless, because a result can also be assigned to the starting position. (So ​​it is no longer a chess engine in the classic sense)

    Consideration:
    If we connect all computers to the cluster and try all positions in reverse (i.e. always one move back from the end position), save / calculate in a DB, and include the doubling of the CPU's performance every 20 years / 30 years, that would still be over 10,000 Take years. (At least that was my rough calculation that I did years ago)

    All right?

    P.S. I don't know if I'm right there either ... I can't work it out for you either. I'm already too old ...
  • I only know that GM Helmut Pfleger once said that there should be more possible chess games than atoms in space ...
    An incredibly high number indeed.
    Hopefully the perfect game or a perfect opening will not be found so quickly, because then we wouldn't have to play anymore ...
  • micha6 wrote:

    Is it actually mathematically possible to determine how many possible combinations there are in chess?
    Theoretically yes. But I don't know of any solid and proven source / statement which names "the number". Apart from the fact that you have not defined what "possible combinations" should be exactly. #Positions? Consideration of train options? # Train combinations? Consideration of train changes? Belongs in the field of combinatorics and is certainly very difficult to solve.

    But in the end it doesn't matter, the number is so gigantic that it is practically impossible to calculate everything once. Never for humans anyway (noticing it yourself would not work), for computers in such a distant future that it is now irrelevant.

    In terms of game theory, chess is (theoretically) uninteresting, as it qualifies as a finite two-person zero-sum game. Something like Doko is more interesting because you don't know what the other side is up to (or not even who they are at the beginning). So there would be the bluff factor.

    @Webbi: the doubling of the CPU's performance used to be every 1.5 to 2 years and thus part of "Moore's Law". But it has not been the case for a long time. Not 20-30 years.

    In conclusion to "who invented it": the devil definitely not. He made the schnapps.
  • In chess, the maximum combination, including the "senseless" moves, is 10 to the power of 70. - Is then only exceeded by the go on the large board (19x19) with 10 to the power of 72.
    At least this (approx.) Approximate value was calculated with deep blue.
    Franz
  • I've already tried the combination, drinking beer and chess a few times. If I've tried longer, the beer always wins. cheers
    mfG Rico
  • Chess is one of the most complex board games. The number of possible positions is estimated at 2.28 · 10 ^ 46 .... The number of possible game courses is again many times larger

    Source: Wikipedia

    dmtom