...However, it can safely be ruled out that if chess is either a win for White or Black, losing in 16 moves is not a perfect game...
I don't think that has been proven. There may be a perfect game where one side can force a win in 16 moves. Or do you know of a mathematical study that shows it's impossible?
If there was a forced win in 16 moves, it would have been found a long time ago.
Very good point!
...If there was a forced win in 16 moves, it would have been found a long time ago.
There may be no forced wins in a perfect game of chess with 16 moves - but I don't consider this to be a mathematical proof. Using Shannon's assumptions for the average number of moves for each player there's about 10^48 games of chess with 16 moves. I'm pretty sure nobody has done an exhaustive search to confirm none of them are forced wins.
Haha! We don’t know.
However, it can safely be ruled out that if chess is either a win for White or Black, losing in 16 moves is not a perfect game. actually this cannot be safely ruled out. if chess is solved to be a draw then it would be quite probable that there would be billions of 16 move games ending in a draw which were perfect. there would be billions of games ending in a draw which were 21 moves long also.
The only way it could be perfect would be if chess is a draw and certain moves must be played to avoid losing (in rather a lot of moves), and at some point in the opening a perpetual check position would be reached. [this also is not correct there are more ways
to draw than to perpetual check--lack of material to mate is one of them...]
You can also try to prove the drawishness of chess ad absurdam, in that it would be almost unthinkable that the most perfect of perfect games, a king's game, would turn out to be imperfect enough that there was a single line for one side that would lead irrefutably to a win.
...You’re just repeating the same idiocies, like some 16-moves games are perfect....
Just to clarify: You haven't concluded that a 16 move game cannot be perfect, have you?
Maybe thats possible. But if a 16 move game could be perfect, why are there 17 move games?
Because if chess is a draw [as most of the very top players believe]
Now he’s back to belief, no more stating to know—from the top players. Still not understanding the difference.
It is a lie that i do not undersand the difference between " believe" and
"know". What you repeatedly failed to understand is that someone can both "believe" and "know" at the same time.
capablanca invented his 2 extra chess pieces (combinations of rook and knight and rook and bishop ) because he thought chess would be solved quickly. We are not there now and people like caruana and grischuk dont think we will get there soon. Openings will be partly solved (as today for example the marshall is considered to be a draw- yet people play it because nobody knows all the lines) Opening theory however will go deeper, in the future you might have to learn 30 moves deep insted of 20.
If you use them to mean the same thing ... fine. Other people here apparently do not. Thus, we have miscommunication. Would you like to improve communication or further disrupt it?
I use the two terms to have slightly different meanings.
Because top players believe chess is a draw may or may not mean those top players know chess is a draw.
Most top players assume chess is a draw from the opening position. When they study openings [often using Centaur chess] they are assuming chess is a draw. They never study openings assuming chess is a win for either side.
Some top players say chess is a draw. Some top players both assume chess is a draw and say chess is a draw. Some top players who assume chess is a draw will also say they believe chess is a draw.
The 3 terms are very similar in meaning and a top player may use any one of the three terms or any two of the three terms or all three of these terms.
Because a top player may say he believes chess is a draw does not mean he does not assume chess is a draw and it does not mean he does not know chess is a draw.
...It took me all of 5 minutes to figure that a forced mate in <13 moves is probably impossible logically. If any rigor were applied here I'm pretty sure the people on this thread could prove a forced mate in 16 not possible...
Probably...pretty sure...?
I was asking about a mathematical proof. Not guesswork or speculation.
...and this was how far in got the 5 minutes I spent before going to bed. It's very clearly stated in a preeeeetty short post. Can you just not comprehend what you read? Even this analysis was more rigorous than anything you've *ever* done on this thread, by the way (since your only real attempt at an analysis around page 60 wass riddled with double-counting errors and other inaccuracies that would only take minutes to suss out).
Since I didn't have time to go further, this would perhaps have been a great chance for you jump in and show me up with your dazzling brilliance by taking it the rest of the way, or just improving/shoring up my back of the napkin premises. But instead, you showed us exactly what you've always got in your tank...nothing.
Most top players assume chess is a draw from the opening position. When they study openings [often using Centaur chess] they are assuming chess is a draw. They never study openings assuming chess is a win for either side.
I would be so bold as to posit that when they study openings they don't really ponder that question much, if at all. I would also be so bold as to posit that that broader and greater question is something they don't really give a rat's a$$ about when they are prepping beyond "this opening produces XYZ results with current theory, but MVL tried a novelty I think has potential, and my engine says it's not outright losing, so...let's take it for a spin". Sure, they might try to determine if an opening tends to draw or have a slightly higher winning percentage *for current/recent human and engine play*. But then, that play is imperfect...which everyone seems to understand except you. Even your vaunted Centaur chess at the very highest level is imperfect...it sure as heck cannot support your 99.99% certainty (oh wait, didn't you add a zero recently? I can't even remember anymore)...
This thread isn't really about human guesses or analysis. It is supposed to be about computers solving chess. Has anyone proposed any method other than brute force to solve chess using computers?
Nope, not a single credible premise that goes beyond brute force augmented with the best pruning we can manage. Some people don't even make it past "somebody 70 years ago said there should be another method" and then resting on someone else's laurels and calling it a day.
alpha zero is not using brute force
alpha zero is not using brute force
Alpha Zero is not doing a damn thing towards solving chess, either.
Lets take the chess variants that have already been solved like antichess, did not think i would go so quickly.
Lets take the chess variants that have already been solved like antichess, did not think i would go so quickly.
Anti-chess/losing chess etc. is obviously waaaaaaay easier to solve, because captures are mandatory. It's just strings of long forcing lines stuck together.
...If there was a forced win in 16 moves, it would have been found a long time ago.
There may be no forced wins in a perfect game of chess with 16 moves - but I don't consider this to be a mathematical proof. Using Shannon's assumptions for the average number of moves for each player there's about 10^48 games of chess with 16 moves. I'm pretty sure nobody has done an exhaustive search to confirm none of them are forced wins.
Hey Vick, thanks for pointing out that brute force is the only way to be sure 
...thumbs up. You finally figured it out for the larger question!
Sadly though, you're also wrong in this case, because proving that black can simply survive for 16 moves *from the opening position* where pieces are occluded and distant from the goal, which requires no forced win, loss, *or* draw by the way, is a whole lot easier than trying to solve chess. It's a completely different problem, with a completely different magnitude.
Maybe you'll understand if we reduce it down further...
69,352,859,712,417 moves in the first 10 play of a chess game. Clearly, a number far beyond brute force calculation for the human mind, yet that is a 5 move game. It is ridiculously easy to prove that white or black has no forced win in 5 moves...
alpha zero is not using brute force
Alpha Zero is not doing a damn thing towards solving chess, either.
I wouldn't say it is doing nothing towards solving chess. At the very least, it is analysing some of the lines required for a bute force solution (as every engine does). But, it is making progress in discerning which lines deserve more attention than others.
If there is a forced win, then all lines do not need to be searched. If a person finds a forced mate, then do you really need to look further? There could be another forced mate, but even one forced mate is enough to declare the game solved.
It is doing this effectively no more or less than anyone playing a chess game, so...
Also, you seem to think that an engine just playing down a line is accumulating useful data (in terms of solving chess)...it is not. The data is only useful if you can carry it to a provable conclusion, not simply because you evaluated a position with an imperfect evaluation method that is just floating in the ether tethered to nothing. I mean, will you think that when websites show 3-4 engine evaluations of Carlsen vs. Caruana during match games that they are also helping to solve chess while they do it?
That's why tablebases work their way backwards from mate. That is conclusive. You can't take a tablebase-like algorithm and just start applying it to random middlegame positons, you have to build the solution step by step, proving as you go.
You can also try to prove the drawishness of chess ad absurdam, in that it would be almost unthinkable that the most perfect of perfect games, a king's game, would turn out to be imperfect enough that there was a single line for one side that would lead irrefutably to a win.
Your premise is flawed in that chess *evolved* to it's current state...it's been effectively designed by committee over the centuries. It is far from a scenario of purposeful and perfect game design. What it has evolved into is remarkable, and as close to perfectly a balanced game as I think has ever evolved over that length of time (thus, its enduring popularity). But it is nowhere close to perfect. The key for chess is that the game's complexity of calculation ensures that those imperfections it still has are hidden from human comprehension OTB, so we cannot exploit them effectively.
Ways in which chess could be arguably "more perfect" as a game design/construct:
- Reduce first move advantage to zero or effectively zero
- Fix clunkiness of en passant
- Fix bishop/knight imbalance (bishop pair = better than pair of knights)
- Fix clunkiness/smooth out rough edges of castling
- Remove clunkiness of 3-fold repetition and 50/75 move rules (tournament play only)
...I'm sure I could come up with more if I spent more time.
...and this was how far in got the 5 minutes I spent before going to bed...
It is possible that a perfect game with 16 moves exists based on what is currently known about chess. Then you replied with a statement qualified by "probably" and "pretty sure". Obviously that is guesswork - not much interest to me.
...and this was how far in got the 5 minutes I spent before going to bed...
It is possible that a perfect game with 16 moves exists based on what is currently known about chess. Then you replied with a statement qualified by "probably" and "pretty sure". Obviously that is guesswork - not much interest to me.
Well, true, you don't like to think for yourself and would always rather quote someone else's work as absolutes, and true, you like to argue technicalities that allow you to escape any real rigor in any of your analysis/numbers, and so any debate where you have to get your hands dirty by using the old noggin' is a stretch for you, but...I mean...you like to create chess variants. Surely, you have some ability to be creative and/or thoughtful. I haven't seen it, but...why would you enjoy said hobby if you didn't have those things in you somewhere? I *have* noticed that you're not all that good at actually playing the variants you design, so that is honestly kind of a puzzler, but still...it's a creative endeavor, in theory.
...However, it can safely be ruled out that if chess is either a win for White or Black, losing in 16 moves is not a perfect game...
I don't think that has been proven. There may be a perfect game where one side can force a win in 16 moves. Or do you know of a mathematical study that shows it's impossible?
If there was a forced win in 16 moves, it would have been found a long time ago.