True or False Chess is a Draw with Best Play from Both Sides

1. Related games are draws (e.g. checkers, mini-chess, etc.)
2. If black has a winning stratedgy, then white can steal it, unless the initial position is a Zugzwang.
3. We know from the 6-man tablebase: balanced/separated material/position = draw (is it always?  I am not sure).  The initial position is balanced and separated.
4. The chess game tree has been fully explored to depth-N (not sure what N is), but there is no forced win, nor even an obvious significant advantage.  For black/white to win, it means that in these trillions (?) of positions (i.e. all balanced positions at depth N) all must also be forced wins -- this does not seem likely.

These explain my intuition that chess is a draw.  Not sure if they are new, but there does not appear to be much discussion about them. Of course, they are completely irrelevant to a mathematical proof that chess is a draw.

That's complete nonsense (the bolded part is the most blatantly wrong, as no mathematically literate person could ever make such an idiotic argument as the bolded sentence), and I'm not sure there's a much point in discussing it with you, since you don't seem to have any scruples about ignoring parts of discussions and then reconstructing the past discussion as you fancy while ignoring the parts that contradict your "memory". Had you already forgotten that I had corrected you once already, or did you remember and knowingly utter misrepresentations a second time?

The entire tone of George's discussion was to encourage skepticism that it is so close to certain that the possibility of being wrong is not even worth considering seriously, not to argue for a specific position. He was saying that there are reasons to believe the chance of something other than a draw is greater than the infinitesimal chance most of us give it, because at root this is a mathematical problem (combinatorial game theory, to be precise), and there have been cases in math where all the instincts, the heuristics, the impressions by the experts in that sub-discipline hinted toward one solution, only to be dashed when a proof to the contrary was found.

Jetson gave the example of the Q+P vs Q endgame that features some positions that human heuristics aren't sufficient to solve or even categorize adequately. We are still stuck at a 7-man tablebase and have no idea what surprises we will find if we get to larger tablebases. It's possible that there might be positions that we think are drawish but actually have counterintuitive wins that we would never have thought possible (at more than an infinitesimal probability) were it not for the tablebase proof that it is mate in 789, for example, because Black can't avoid a certain configuration of pieces that results in loss of a material after a 700-move sequence.

I do in fact believe that a draw is most likely, as did Jetson, for much the same reasons as you probably do, but after thinking about the possibilities of there being unexpected surprises buried amongst the enormous combinatorial space that is still unexplored, I no longer think that the chance of it being anything other than a draw is something like 1 in a thousand. I wouldn't put it higher than 1 in 10, and probably no higher than 5%. Jetson's estimate was more extreme, but the spirit of the discussion was not about any particular number, it was to counsel caution, because the lesson of mathematics is that gut instinct and the heuristic-based forms of reasoning that we employ when doing most things other than mathematics can be misleading when navigating nearly inconceivably large state spaces like that of chess and many other combinatorial and other mathematical problems.

There are a few positions that are so complex that they cannot be evaluated bu humans except with help from devices invented by humans.  So the point is not that humans alone could not evaluate these postions--as these positions were evaluated by humans with the help of table bases.

It does not matter if humans had the help of chess engines or table bases-the fact is these very rare postiions were evaluated correctly by humans.

It does not make a very big difference if I think chess is a draw is 99% likely and someone else thinks this is more than 95% likely. These are our opinions based [in my case] on a ton of evidence. 

Is chess a draw with best play on both sides?  The answer is an opinion as very likely we will never "solve" chess.  It is my opinion from a ton of evidence and also my hypothesis coming true that chess is a draw.

I think there may be a correlation that the better a player you are the more you will value heuristics and thus the more likely to believe chess is a draw.

However, it is not all heurestics as there is much evidence outside of heurestics.

but first how do you come up with 600 billion games? -I thought databases only have a few million games recorded.

did really every GM say so?? I dont think they really asked everyone.

their are really many ways to get an winning advantage, zugzwang and checkmate.

Computer cut certain path of circulation because they are negative, but some of those could be good along the line.

To me its still a 50 50 chance if chess is a draw or a win. Because experience has no influence on the question if chess is a win or not.

if there are for example billions over billions of ways that lead to a draw and only a hundred that lead to a win any experience and knowledge we have is totally meaningless.

TetsuoShima    Did I say 600 billion games?  Thought I said 100 billion games? Please check this out.  I am guessing 100 billion chess games have been played.  Data bases only record a small fraction of games played. Once I had a 4000 game winning streak and none of these games were recorded. 

Also you misquote me by indicating I said EVERY GM SAYS chess is a draw--I did not say that at all.  

And of course, not every GM was asked that question.  However many were asked in different situations and almost all said they thought chess was a draw. Do you really doubt that the vast majority of grandmasters think chess is a draw with best play??

Yes, of course there are many ways to get a winning advantage. However you will not get a winning advantage unless your opponent makes a mistake.

"Computer cut certain path of circulationj because they are negative, but some of those could be good along the line."  I think you mean here that the chess engines delibertly do not consider certain lines [example giving the queen away for nothing] but some lines could later be found to be good lines. [I think this is what you mean.]  It is possible this could happen but it is quite rare,.  However centaur chess mostly solves that problem.

To you there is a 50-50 chance that chess is a draw or a win.  Question, if it is a win--who wins Black or White??? Please answer this question.

"Because experience has no influence on the question if chess is a win or not."  This I disagree with completely.

Your last paragragh is conjector. However very strong players would tell you that the chances of your idea being true are very slim. 

ok its either a 50 50 chance or a 33 33 33 chance.

we cant give the percentages because the evidence is not big enough to give more weight in any favor.

when the games are not recorded the dont add to the pool of knowledge because the most often vanish.

Also centaur chess also doesnt kill the flaws mostly, otherwise GMs wouldnt always find new ideas.

also centaur chess is still prone to mistakes as you saw with grischuk in the candidates, when he said oh computer said bad so i left it that way, he didnt even look further because he thought Svidler wouldnt play it.

such lapses happen all the time.

The truth is our knowledge is no real evidence and has absolutly no bearing on the question.

my idea cant have smaller chances because there is no indication it is wrong.

TetsuoShima  You are using a logical fallacy which says if there are only two possibilities both are equally likely.  For example there are polar bears on Mars.  There are polar bears on Mars or there are not polar bears on Mars.

But one statement is quite a bit more likely.

Yes, games not recorded do not add to the pool of knowledge.

Yes, Centaur Chess sometimes can be wrong

However I do not agree that our knowledge is no real evidence or that the knowledge of the best players has no bearing on the question.

"Evidence" is anything which points towards a conclusion.  There is much evidence which points to the conclusion that chess is a draw. You can say "there is no real evidence" but to do this you have to ignore a whole lot of evidence. 

TetsuoShima  You are using a logical fallacy which says if there are only two possibilities both are equally likely.  For example there are polar bears on Mars.  There are polar bears on Mars or there are no polar bears on Mars.

But one statement is quite a bit more likely.

Yes, games not recorded do not add to the pool of knowledge.

Yes, Centaur Chess sometimes can be wrong

However I do not agree that our knowledge is no real evidence or that the knowledge of the best players has no bearing on the question.

"Evidence" is anything which points towards a conclusion.  There is much evidence which points to the conclusion that chess is a draw. You can say "there is no real evidence" but to do this you have to ignore a whole lot of evidence. 

I think sapientdust made a fine post above summarizing some of the points now lost.  A few points:

a) I'm surprised he is not banned after that outrageous remark " no mathematically literate person could ever make such an idiotic argument as the bolded sentence" about ponz.  Are you saying ponz isn't mathematically literate?  Really? 

b) The non-response of ponz was nauseating concluding with "However, it is not all heurestics as there is much evidence outside of heurestics."  The fact is there is this guy who doesn't know how to spell heuristics, didn't know the word yesterday, can't spell "conjecture" and he is arguing math.  And he is doing everything he can to silence people who are trying to help him understand something interesting.  I'm not sure if this is a ponz problem, chess.com problem, or some broader societal issue. 

c) Ponz has told us his opinion on whether chess is a draw 100's of times.  Why he thinks anybody cares is an interesting thing to ponder.  Why he even cares given that there is a huge discussion that he clearly doesn't understand is an interesting thing to ponder.

There have been repeated threads on the Ponziani here on chess.com.  Someone started one the other day about "ponziani without the spam" because the Ponziani threads all get destroyed.  Ponz won't even let a discussion about chess go on without trying as hard as he can to destroy discussion in the service of making him appear right.  He has vastly more credibility in discussing the Ponziani than in discussing mathematics. 

Making mistake is human. That is what makes chess different from

Tic-Tac-Toe. Chess is too too too too ... complicated that current intelligence level of humans has not found this answers.

chiaroscuro62

Yes, I did not spell "heuristics" correctly.  It is not true that I did not know the word "heuristics" until yesterday.  Also, I did not spell "conjecture" correctly.

There is evidence that chess is a draw outside of heuristics.

I am not stopping any discussion on this forum. Rather than the personal attacks--why not give your points of discussion on how you think I am wrong?

[I do not know of any Ponziani threads which were destroyed]

A possible response of the kind that furthers discussion.  Perhaps if we could get some intelligent discussion going on here this thread would be interesting.....

"Perhaps I mischaracterized Jetson's position.

The evidence given by Jetson in mathematical problems that turned out contrary to empirical evidence are not relevant to chess.  For example, the example about some theorem concenring prime numbers being false despite expectations happened because the space of integers is vastly bigger than the space of chess games.  That theorem wasn't true at some number like 10*10^10^100 or something that utterly dwarfs the number of possible chess games.  I would contend that we have explored the finite space of chess games much more thoroughly than we have explored the infinite space of integers.

The example of the Q+P vs Q endgame was interesting and when those results came out of tablebases they were surprising.  But Q vs Q+P endings being wins for the superior side just expand the set of winning positions without changing the fundamental argument that chess is a draw.  N v N+P  is unquestionably winning almost all (all?) the time so adding more winning positions doesn't change much and tablebases haven't changed our understanding of this position.  Chess is a draw not because people can't figure out how to convert wins, but because forcing as much as a single pawn advantage seems impossible.  Tablebases have increased our understanding of chess by showing us how to convert wins in superior positions.  My contention is that these positions are largely irrelevant because they can't be achieved to begin with.

It seems that we all agree (even Jetson) that chess is likely a draw but I think that Jetson's skepticism is misplaced (or maybe even insincere).  Both the tablebase example and the prime number theorem thing are simply not evidence of anything directly relevant to the question."

This is the 1593rd post

That is all no evidence, i dont even mention the pawnless queen endgames were first mover wins.

Seriously Ponz, the knowledge of GMs only applies to the known. If only 100 lines Lead to forced win the knowledge is absolutly not relevant for the topic.

The likeniness of Chess being a draw or a win isnt even in anyway related to the so called evidence

Yekatrinas - I observed this thread for 1000 posts and didn't see even so much as a brief glimpse of an intelligent thought from you.  But periodically you step in and say that the conversation is beyond you thus you think it is stupid.  If you have something to add, please do. 

The bolded sentence was one that smyslovfan said was Jetson's position (nothing to do with ponz). Since the sentence was about Jetson, who is in fact a mathematician and thus certainly mathematically literate, I was effectively saying that Jetson didn't put forward such a silly position, because no mathematician would ever make such a ludicrous argument. It's the sort of fallacy that even a first-year philosophy student would notice.

I think the point of this analogy is rather to show how hard it can be to find a conter-example, and that some results turn out to be wrong even though everyone expected them to be right. The idea is that the number of possible chess games and the size of the counter exampled shown by george are both way beyond human reach. This example suggests that in the same way we shouldn't have trusted the mathematician's intuition on that conjecture on prime, it is not reasonable to trust human's intuition on wether chess is a draw or not. This question is too hard for human alone. That is why we try to build tablebases.

The example of the Q+P vs Q endgame was interesting and when those results came out of tablebases they were surprising.  But Q vs Q+P endings being wins for the superior side just expand the set of winning positions without changing the fundamental argument that chess is a draw.  N v N+P  is unquestionably winning almost all (all?) the time so adding more winning positions doesn't change much and tablebases haven't changed our understanding of this position.  Chess is a draw not because people can't figure out how to convert wins, but because forcing as much as a single pawn advantage seems impossible.  Tablebases have increased our understanding of chess by showing us how to convert wins in superior positions.  My contention is that these positions are largely irrelevant because they can't be achieved to begin with.

I think the most important point is not to know if these position will occur in a perfect game, but to acknoledge they exist. The immediate consequence of such positions existing is that human analysis (using heuristics) can't exhaust the game of chess. In other words, there are positions that resist human analysis. What this means is that we should be extremely careful when we say a position is drawn, because we know there are very simplified positions that we used to assess as drawn and that turned out to be wins. So it is possible that a lot of much more complex middlegame positions that we think are drawn turn out to be wins as well.

To be very clear, the most important point is the following :

We know that playing with heuristics (i.e. experience based methods) fails to achieve perfect play in some situations, so we should be very carefull when using experience-based "evidence" (like grandmaster games or centaur chess) to conclude chess is a draw.

ah.  misunderstood that.  No wonder you aren't banned.

Thanks Tronchen for your intelligent and thoughtful post.  I don't believe any of that stuff I posted; I just posted it as an example of how conversations like this can be productive (i.e., they stimulate thoughtful replies like yours).  I think it would probably just cause a mess if I continued on defending some position I don't believe. 

Centaur chess is not just experience based.  It is experienced based along with brute force chess engines. That is why it is stronger than chess engines alone.

Yes, it is possible that a lot of the more complex middlegame positions that we think are drawn turn out to be wins. It is just not likely. But regardless why even use such a complex middle game positions when there are hundreds of games and positions which have no errors and end up in a draw?  [this is a question]

I think what you are doing is to pick out the one in more than 100 games which are unclear and saying because we do not know the result of this one game [out of more than 100] that we cannot look at the other 99 plus games to see what we can learn from them.