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

TetsuoShima   Nobody says chess is a draw because chess players think it is a draw.  I don't say that.  Maybe your command of English is not so good and you do not understand?  I am saying it is an indication that chess is a draw--I am not saying it proves chess is a draw.

You keep saying the same thing and you are misquoting when you say this.

Also, I have given much evidence which you seem fit to say it is "not evidence"  You seem to have an odd definition of "evidence"

@George_jetson5: First of all, chess is only a math problem until it is solved. The moment we have a 32 pieces tablebase it becomes a query program and not math anymore. It is therefor not a real mathematical problem.

Second, you don't have to know perfect play before acquiring some sound principles. They have been proven to be good in a lot of situations. Do you make calculations with pi although you are not using the whole number? (I know it is an irrational and transcendental number.) Isn't math using complex numbers? That are numbers that by definition do not exist, yet they do. Just as we all know that we must not be very strict all the time, you should not be. 1. d4 is a better move then 1. a4. Intuition will tell you and some chess principles too. They are good.

Third, in this discussions have some mathematicians the idea that it is only evidence when it can be proven mathematically. Any other type of evidence is not rational. That makes it quite hard to discuss. Not only because I am not a mathematician, but also because there are definitely other types of evidence. When I presented mathematicians with a mathematical challenge, there came no response.

Finally, anyone in any professional field can tell you that it is very hard to know if you are on the right track before you have reached it. That is not the sole experience of mathematicians. And no other type of problem is that complex as another human being. It is for instance easier to prove a mathematical thesis than to convince you that you are wrong. Believe me. :-)

Q.E.D.

Here is the definition of "evidence" I was going by--Free online Dictionary

Evidence  A thing or things helpful in forming a conclusion or judment.

Is there a different definition of "evidence"?

I will repeat there will never be a 32 piece tablebase.

Some here say throw out all the evidence that is not a 32 piece tablebase.  Why?  I don't think they understand "evidence"

richie I was going by the dictionary as to the definition of "evidence"

However much of my evidence was empirical anyway.

emperical:    based on testing and experience.

This is a very long and wordy thread for such a simple answer: no one knows for sure.

The consensus of master level players and experts on the subject theorize that chess is probably always a draw with perfect play on both sides, but to determine that in certainty is far beyond our capabilities right now.

I would be surprised if that was the case. Personally it doesn't bother me one way or the other. It would be nice to know for sure, but at the moment we don't (as far as I can tell).

One of your points is that computers are stronger than humans. However humans with the help of computers are stronger than that.

It is called Centaur Chess and right now it is the strongest chess we have.

Centaur Chess consists of very many drawn games. That is an indication that chess is a draw. 

If chess is a draw which is my hypotheis you will see things happening.

One thing you will see is that at the very highest levels there will be more and more draws over time. This is happening now.

I base my confidence chess is a draw because of evidence. I cannot prove 100% chess is a draw but there is enough evidence there that it is very likely chess is a draw when played without error.

Jaas gave some positions which were very complicated and beyond the skill of human chess players to solve.  However such positions are very rare.

If you have a random position generator then approximately 95% of the positions would be solvable by a strong human.  

But I am not sure what the point is? So about 5% of all positions are not solvable [easily] by humans--please explain what this has to do with if chess played without errors is a draw?

The math guys were taling about all the possible positions in chess.

The vast majority one side or the other has a tremendous advantage.

Those theoretical end games are very rare.  Probably less then one tenth of one percent of all postions.  

But my question is  so there are some postions that are very hard for a human to evaluate  what does this have to do with is chess a draw with perfect play? 

@george_jetson5: Since you are a mathematician, can you answer my question? I asked the same question to jaaas, but he never took the opportunity to answer or even directly react to this question. I am still curious.

My question is if you can show how and when evaluations of chess positions will significantly change (from a draw to a win)? With basic openings are the first set of moves more or less equal. I call those openings basic in which both players start playing in the centre. Chess engines show consistently evaluations around and circling around 0. The bigger the number of plies get and the longer the evaluations stay around 0 (in the QG or RL for instance), the smaller the probability that there will be an overall change in evaluation (to a win for white or black).

This is normal statistics as you will know. Can you give a general formula showing those type of boundaries and the development of the probability that the game will change to another evaluation? The formula must already exist, I think, because it is independent from chess.

The truth is that chess machine evaluations and strong human evaluations of almost all positions areaccurate.  There are some rare end game positons where humans cannot evaluate.  

This really has nothing to do with "Is chess a draw".  It only says humans are not perfect in rare evaluations.  

However these postions in question can be and have been evaluated correctly with humans with the help of chess engines. I have always said to evaluate a postion best to use humans with the aid of chess engines.

@george_jetson5: I asked you the question just to give it another try. You clearly are not avoiding it, but your interpretation is absolutely not my question.

It is about statistics. I have had that more than twenty years ago. At that time I was quite good at it. Scored maximum for it and taught my fellow students. But applying it properly will take time and I do not have the books anymore.

Let me try to rephrase it, although this rephrase changes perspective and might give you the idea that your interpretation was what I was asking for. It is different from your interpretation.

How big is the chance that the best move in a position creates a win (for either one of them) when the x moves before kept the position equal?

How big is the chance that, if not happening in that move and the evaluation is still more or less equal, in the next position there is a move that creates a winning position for either one of the players?

If not happening in that move and the evaluation is still more or less equal, how big is the chance that there is in the next position a move that ...?

My hypothesis is that the chance on such a move becomes smaller and smaller with every new position being still more or less equal.

@george_jetson5: do you agree with my hypothesis?

George, I have never claimed there is absolute mathematical proof that chess is a draw. I have claimed that there is ample evidence to surmise that chess is a draw with perfect play. I have not seen any evidence to the contrary.

The closest I've ever seen to anyone who has studied the game in depth claiming that white wins were Kurt Richter's work on 1.e4 which led to the Richter-Veresov variation of the Sicilian and several other critical attacking lines,  and Hans Berliner's work in The System on 1.d4. Neither proved a win. Berliner's work is a very strange read, but essentially he argues that with best moves white retains a slight advantage that is not sufficient by itself to win. Of the two, Berliner's approach was more compelling, but even he, a former correspondence World Champion, agreed that chess is a draw with best play.

Again, although I did not provide a mathematical proof that chess is a draw (none exist), there is plenty of evidence for a practical player to accept the theoretical evaluation of the initial position as a draw and no credible evidence to the contrary.

That is a good point--all the evidence points one way.  

george You greatly underestimate the chess playing ability of strong chess players. Just because there are some very few problems they cannot solve--I mean that is hardly significant and they have solved those problems using table bases which humans created.

You also seem to ignore that my hypothesis is coming true.

We cannot solve the problem "is chess a draw" using math as we will never have a 32 piece tablebase.  

You really just do not understand because you have never been in that kind of situation.

The fact that a chess machine can win from the best human has no bearing on the question.  Remember humans are allowed to use their own knowledge plus the chess machine.

Let me ask you this: if you had to guess if chess is a draw or if White should win or if Black should win--what would be your guess and what level of confidence would you have in your guess.

Do agreed draws count? I'm not convinced they should, and that we must count only those games played out to the bitter end Carlsen-style, at least to a position that is known to be a draw.

Are you sayng that humans are flawed, machines are flawed, but machine + human = perfect play ?

This particular argument sounds suspect !

to the rest of the post : george aswered the arguments you say he ignored multiple times through his posts. They may not be very simple to understand because they use a lot of math. However, I encourage you to read them a second time. I think he accurately points why the "evidence" you give should not be blindly trusted.

Tronchen  No, I am  not saying that at all. Where did you get the idea I was saying machine and human = perfect play?  Plese reread what I said.

So what you call "suspect" is something I never said. This is a strawman argument--misquote me and then knock down the misquote.

Also, when you say ""why the "evidence" you give should not be blindly trusted."  Again you misquote me. I never said the evidence I give should be blindly trusted.  This is a strawman argument.  Misquote someone and then knock down the misquote.