I realize this thread is some months old, but there were some things said in this thread that I couldn't let pass without comment.
First off, I don't think the following point has been made even once in the thread (correct me if I'm wrong): the difficulty of the game can be measured by the probability with which a given player will play a good move (either mathematically sound, or judged good by consensus when its soundness cannot be proven) -- in other words, a move that will win, or salvage a draw if winning is not possible. My suspicion is that top checkers players play good moves more often than top chess players, but average checkers players bungle things just as much as average chess players. I don't have any data to back up this assertion; it's merely a gut feeling. But it can probably be tested by analyzing games with checkers and chess engines.
There's also the matter that, if my above hunch is true, then an expert checkers player can punish a beginner's mistakes more severely. That makes checkers easier for the expert, but harder for the beginner -- so it's not just a matter of checkers being "easier" or "harder", but also for whom!
Second, there seems to be a lot of confusion as to what "solving checkers" means.
Chexhero wrote:Computers play chess extremely well too, but they will never "solve" chess. Chess is much more complicated. A computer could not play a "perfect" game of chess if every sub-atomic particle in the universe contained a bit of chess information. (That has been mathematically proven also)."
No, that has not been proven. It is true if we are talking about solving every position that could possibly arise in a chess game, but it is not necessary to do so to provide a "weak" solution to chess. I'll explain in a minute.
To be fair, it's quite possible that a weak solution to chess is a mathematically intractable problem. However, that has not been proven and I doubt it would be possible to prove it. I believe it's one of those problems where you can't prove that it's unsolvable, but you could possibly prove that it isn't (by simply solving it).
MostFamousDane wrote:Regarding the point that keeps coming up that checkers is solved - it is simply wrong. Checkers has not been solved in anyway near the normal understanding of the word. The Chinook team has done some long searches on some openings that are not guaranteed to be 100 % correct. That has very little to do with solving checkers and people have done the exact same thing in chess
http://chessbase.com/newsdetail.asp?newsid=8047.
Unofrtunately, virtually nothing in this statement is correct. It's already been pointed out that the article is a hoax, so we won't dwell on that, but actually checkers has in fact been solved in something "near the normal understanding of the word". If you play against Chinook, you will lose or maybe draw -- period. It doesn't matter if you're God; you cannot win. And, barring an undiscovered flaw in the proof (which is unlikely; I'm sure they've checked everything up down and backwards), we do know this with 100% certainty.
What Chinook
hasn't done -- and I've seen some probable confusion about this later in the thread -- is solve checkers for any given position that can possibly arise in the game. This is called a "strong" solution, and is not possible because the game tree is too large for any computer to ever handle. Chinook found what is called a "weak" solution: it has solved the game's starting position. In any game it plays starting from that position, it will never turn a winning position into a drawing or losing position, nor ever turn a drawing position into a losing position. (EDIT: Some posts later I found out this is wrong!! It can indeed turn a winning position into a drawn position, but never a drawn position into a losing position.) To manage this, it only needs to analyze a tiny fraction of the possible positions in the game.
This may sound counterintuitive, but with some thought, it should be obvious. Suppose we have a position P where player 1 is considering two moves, A and B. It finds that move A will definitely win -- it's a mathematical certainty. Why, then, should it analyze move B? Since move A already produces the best possible result, move B cannot be an improvement (it could possibly win sooner, but that doesn't matter -- we just want to know whether it wins, loses, or draws). Whether it wins, loses, or draws is irrelevant. Thus the position created by move B will never be analyzed (unless perhaps a different sequence of moves -- a transposition -- elsewhere in the game tree results in the same position). Since position P allows the winning move A, then position P is a winning position for player 1 -- and so player 2 knows that any move that results in position P is a losing move. This means that player 2, if he is playing optimally, will never allow position P to arise! (Unless he's already lost and has no better alternatives...) This concept is behind the game tree analysis technique called "alpha-beta pruning", which can severely reduce the number of branches in the tree while having no impact at all on the mathematical soundness of the analysis.
But since so many branches are pruned, it is still possible to set up a position (even one that might have occurred in an actual game between humans) that Chinook hasn't analyzed -- like a game where player 2 allowed position P to occur, and player 1 did indeed play move B -- and it will not necessarily play optimally in such positions since it's never seen them before. It's just that these positions will never occur in a game against Chinook if you start the game from the beginning, because Chinook will always move to prevent those positions from occurring.
Of course, whether checkers has been solved or not should have no impact on whether it's an interesting game for humans -- unless of course somebody devises a way to memorize the solution, but that may not be possible. But who knows... maybe another Marion Tinsley will come along and figure out a way.