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

I belive it was 10^80 (and not 10^(10^80)).

Never mind, no computer will be able to go through all games.

In fact, a tablebase is much smaller than a listing of all games.  In particular, a listing of all games is much bigger because it includes all kinds of meaningless repetition of positions and is kept finite only by 3-fold repetitions and 50-move raw rules.  Tablebases require much smaller sets.  But ponz is messed again.  Existence of a tablebase solution is an enormous step in this problem.  It means the solution is decidable and well-defined even if we can't do it because of practical limitations. 

"It means the solution is decidable and well-defined even if we can't do it because of practical limitations." 

Sorry, but a "solution" that can never happen is not a "solution" 

"Existence of a tablebase solution is an enormous step in this problem."

Sorry again, but there is no such tablebase solution in existence. If you think there is one please point it out. 

"Sorry, but a "solution" that can never happen is not a "solution" "

Not true but sorry you think it is.  I'm trying to give you some elementary education here.  Proving existence without giving a solution is a central kind of math problem.

"Sorry again, but there is no such tablebase solution in existence. If you think there is one please point it out."

Sorry again that you are an uneducated idiot.  I do not have to construct something to prove it exists.  This is high school mathematics that you missed. 

zborg wrote:

Have you noticed how often this thread's posts get caught up in an infinite regression argument?  Post #101 is good example, but there are many, many others.

Calling Georg Cantor.  Georg, we really need you now!

 http://www.amazon.com/Mathematics-The-Loss-of-Certainty/dp/B003VT4WZG/ref=sr_sp-atf_title_1_3?s=books&ie=UTF8&qid=1378219146&sr=1-3&keywords=mathematics+loss+of+certainty

Well yes except it's not infinite, is it. It's finite. It only seems infinite because it's currently impossible.

in 1970 Bobby FIscher said a computer will eventually be stronger than every chess player. Im not sure maybe they invented it but in one of the books about him written by russian they said he indeed said so..

But its funny how a great genius can only be a genius on the chess board

Fischer was by far not the only one who was convinced that early that computers could one day play even of better to human.

Botvinnik has worked on chess program algorithms without having brute force computers at hand.

There's no need for ad hominem in arguments.

You are making the positive claim that a 32 piece table base solver has been made.

This is obviously false because the highest table base in existence today is a 6 piece table base.  They are working on a 7 piece table base.

For your claim to have any merit, you have to offer proof. You can't just say unicorns exist hypothetically and say that mathematically this is true and proven to exist because maybe there's alternate dimensions or parts of this universe unexplored with an infinite probability of them being somewhere.

It's silly that you're calling me uneducated when you're saying things exist when they simply don't. Now it is highly unlikely that  a 32 piece tablebase can be made in the future, and currently, there is no 32 piece tablebase.

And as I've said before, as you increase the number of pieces in a chess table base, the time it would take a supercomputer to calculate it also increases exponentially.

I can concede at least that a solution that won't be solved before humans go extinct is a still solution, what I'm saying is, if you completely missed the point, that it is infeasible that the solution will be ever found before the sun explodes. 

Ah, you primitive humans of 2013 don't know anything, by 12046 C.E. Chess was solved using a Xarkon quantum-matrix. It's a win for black BTW.

What it comes down too is that chess has not been solved and will not be for a long time. Honestly, I think once it is solved it will turn out to be a draw but that is just speculation. You did not prove mathematically that it was solved and if you think you did you need help. Ponz if you had any intelligence you would just say it is your opinion that chess is a draw and try to support it, instead of claiming false proofs. 

6 minutes ago · Quote · #130

johnsmithson: "Clearly not.  Claiming that something exists is surely not the claim that someone has constructed it or knows what it looks like or anything else about it.  This is fundamental math."

He is claiming that it exists. He is not claiming that it is possible. Obviously, it is possible. A very rudimentary way of doing it would be to just make a program that can calculate every possible position after the opening position based on the rules of the game of chess, but doing so would probably take so long that a computer calculating it will degrade. 

Also, this isn't exactly "math". This is simply logic. Heck, it's simple English. He is using the word "exist". I am taking this into the context that he's saying there actually is a written program that can solve 32 piece table bases and that it has calculated it. Not "oh it's possible to make". The main argument here either way, is that even if we went ahead and made one, there's no way we could calculate it all the way through.

Let's say I took an 8x8 space on my monitor and made a program that increments the colors on the screen between black and white. Starting with a full white image, the top left pixel becomes black first. On the next iteration, the second pixel and black and the first is white. After going through all 64 of these different iterations, now it will cycle through the next 64 where two pixels are black. Eventually, the program cycles through all black and white images in this space until the entire screen is black.

To find how many different images this combination can produce, we take the number of colors (black and white) to the power of the number of pixels. The number of colors is one bits per pixel and is represented as 2^1. The number of pixels is just the resolution, 8x8. Even if I restrict it to (2^1)^(8*8) which is two colors to the power of the size of the screen, that's still 2^64 or 18,446,744,073,709,551,616. (18 quintillion, 446 quadrillioin, 744 trillion, 73 billiion, 709 million, 551 thousand, and 616 different images.)

At a constant 60fps (frames/images per second) on my screen, it would take 5,209,497,168,964,272 hours to go through every black and white permutation of an 8*8 space. That's 594,284,413,526 years. My computer would probably break down before that happens.

Considering a 64x64 board, 32 pieces with the different moves they can make, there is MUCH more entropy than 8x8 pixels with 2 colors. There's no way we'll ever be able to calculate this. The solution does not exist (has not been found), nor will be found. Sure it's possible, given infinite resources (or at least, trillions of years), but that doesn't change that there is no such solution now. It doesn't matter what kind of processors are developed in the future, it's still doubtful that we'll make a computer fast enough to calculate this in less than billions of years.

It doesn't matter if Aristotle or anyone understands the operations, when the operations can't be calculated in a useful timeframe.

It's not going to happen, and here you guys are saying it's already here.

To put part of the above more simple way

1. You claim a 32 piece tablebase exists

2. Your proof is you can tell me how to construct a 32 piece tablebase.

3. Therefore a 32 piece tablebase exists.

Here is an analogy:

1. I claim that there is 1000 story hotel on Mars.

2.  My proof is I can tell you how to construct a 1000 story hotel on Mars.

3. Therefore a 1000 story hotel on Mars exists.

Now back to what this entire thread is about anyway.

We can't objectively [100%] prove if a game with out errors  will result in a draw. I'm saying, in my opinion, that it will be a draw. [To me the evidence is overwhelming ] One of my basis for this is that with higher level chess players (SuperGrandmasters and the best Centaur players), most of their games end in draws. This is one reason why I think it's  likely that a perfect game is a draw. If it so happened that the majority of games from this level of chess players were wins for white, I would be saying a perfect game is likely to result in a win for White as well.

However, seeing as games at higher levels (closer and closer to perfect) result often in draws, I believe it's likely that a perfect game results in a draw.

[I am now just giving one of my reasons why I think a perfect game will end in a draw]

Firstly, have you ever played a game of chess? Chess isn't played on a 64x64 board. That quote alone makes me think you're trolling. Also, pretty much all computers nowadays can calculate at more than 1 megabyte/second easily - the 60 bytes/second you used in oyur calculations is slightly low methinks, not to mention future advances in technology. Eventually we probably will have a 32-piece tablebase.

lol. have I ever played a game of chess!  [I have a rating over 2500]

 sorry, that was a typo, I meant 8x8.

And yes 60 fps is slow, you could probably do 8x8 much much faster with a normal computer. I used 60fps because I was thinking about an animation showing the pixels changing on screen and most media such as online videos/movies or video games run at 60fps if I recall correctly. I apologize for using a bad example, as underlying calculations in a computer would definitely be much faster than displaying images on a screen one by one. Either way, 8x8 with 32 pieces is still many times more complicated than 8x8 with two pixels.

I am considering looking a little more into the math of calculations of that depth, but I imagine it will still result in something that will take thousands of years.

By  the way I am saying chess has not been proved mathematically.  I am also saying there is overwhelming evidence that chess is a draw.

I am also saying that because something can be constructed does not mean it exists.

I am also saying a 32 piece tablebase solving chess just will not happen in the lifetime of humans. 

They will not get to a 9 piece tablebase in the next 100 years.

We can disagree on how long it would take to construct a 32 piece tablebase but chess is not going to be solved 100% anytime soon.

Therefore to have an opinion of if chess is a draw with best play we have to look at other evidence and I have looked and posted other evidence.

Most people  who think the only way to prove chess is a draw 100% is to use  a 32 piece tablebase.

I do not think we have to prove something 100% to have an opinion. 

billions of games of chess have not been played though

There is no need for such mean-spirited argumentation. All you have to say is that you are talking about construction and existence with regards to mathematical proofs, not in the common-language sense.

johnsmithson

Using personal attacks says something about you, not me.

Now if sapientdust is correct and you are not using common-language re "exists" then you could have said so.

Is not there a difference between mathematical proof that something can exist and something that actually exists? [I am asking a question here for anyone to answer] 

With best arguments from both sides this debate should be drawn.

On the topic of how long it would take to calculate a 32 piece tablebase, there's already approximations:

http://en.wikipedia.org/wiki/Shannon_number

"However, even at this figure there will be 10^120 variations to be calculated from the initial position. A machine operating at the rate of one variation per micro-second would require over 10^90 years to calculate the first move"

Saying a solution to an NP-complete problem exists because we have an algorithm for it, isn't a true statement. The algorithm exists, not the solution. The solution will take way too long to actually calculate through that algorithm and the solution has not really been found yet (doesn't exist), so I think ponz makes sense with what he's saying.

I think the problem is that john is misinterpretting ponz as saying there is "no solution" when he's saying "the solution has not been found". I mean, if the solution did exist, you could go Google it right now and this entire thread would be pointless.

imo, john's just trolling. You can tell by his post that he didn't even read ponz's last response. (Particularly, response #141). Infact, if you look real closely at his avatar...

edit: man that guy sure sounds angry at something. since when are children allowed on forums.