True or False Chess is a Draw with Best Play from Both Sides - Chess Forums - Page 127

ponz111

Aug 28, 2019

0

#2521

I do not understand how anyone cannot realize that there have been more and more draws in World Championship matches? [just as I predicted]

MARattigan

Aug 28, 2019

0

#2522

Optimissed wrote:

MARattigan wrote:

Optimissed wrote:

Yes, you understand that despite Champagne and advanced years, you can't really compete. That must seem like a problem but just accept that you aren't here to compete but to learn. All will be well. Exponential series can be elusive. At first they seem cool but take your eye off them and they get out of hand. Then the fish really jump out of the basket.

Exponential series normally refers to 𝟏+𝔁/𝟏!+𝔁²/𝟐!+𝔁³/𝟑!+ … and I always thought it was very well behaved. You're a little skimpy on the details of how this relates to OP's question. Perhaps if you elaborated it would make it clearer.

I think you may have failed to fully take into account the formula 𝐎𝐩ₜ(𝒊ₘ) = 𝝅.>>

Broadly, an exponential series is any series that increases (or decreases) exponentially. It ought to be obvious (but it obviously isn't) that the possible variations of moves in a game of chess form such a series.

Don't worry about it.

If by "the possible variations of moves in a game of chess" you mean the number of different legal games of length 𝓷 ply (let's call it 𝓰ₙ) then you're right that it obviously isn't obvious to me that 𝓰ₙ is an exponential series. In fact it's obvious to me that it isn't.

In an exponential series 𝓰₁,𝓰₂,…𝓰ₙ,…, 𝓰ₖ₊₁/𝓰ₖ must be constant. By inspection 𝓰₁=𝟸𝟶, 𝓰₂=𝟸𝟶² but 𝓰₃ >𝟸𝟶³. The series is therefore not exponential.

That applies whether or not the 75 move rule is in force. If the 75 move rule is in force then it's also obvious that 𝓰ₙ=𝟶 whenever 𝓷>2.75(16.5+30)=16,500.

But mainly you still haven't explained what this has to do with OP's question.

Prometheus_Fuschs

Aug 28, 2019

0

#2523

Optimissed escribió:

Prometheus_Fuschs wrote:

Optimissed escribió:

None of your comments are to the point, MAR. You seem to be obsessed with the idea that no-one plays perfectly or that mistakes will always happen, without realising that it's these mistakes which cause games to be won and lost.

Are you trolling?

The odds are stacked against you on that one.

In your mind.

If I was wrong and you were right then GMs wouldn't be losing games at all.

lfPatriotGames

Aug 28, 2019

0

#2524

ponz111 wrote:

I do not understand how anyone cannot realize that there have been more and more draws in World Championship matches? [just as I predicted]

That's like predicting the sun will come up. You dont know until it does, but it's a pretty easy prediction. The reason there are so many draws is because they are so evenly matched. Do you think there would be as many draws if the world championship consisted of a contest between the worlds best human and the worlds best computer? Both are the best of the best, it's best play from both sides.

In world championship games that are not draws, how often does white vs black win?

Prometheus_Fuschs

Aug 28, 2019

0

#2525

Ponz showed that there is a correlation between the level of human play and the prevalence of draws. The issue is that he hasn't shown why that implies a causation.

zborg

Aug 28, 2019

0

#2526

ponz111 wrote:

I believe from 62 years of playing chess and thousands of my own games that chess is a draw unless one side or the other makes a mistake.

I would suggest that out of billions of chess games that one cannot find even one game which was won or lost without one of the players making a mistake. If anyone thinks they can find such a game please post it here.

I believe Ponz111's bold assertion (roughly 6 years ago) is eminently reasonable.

Has anyone yet posted an example of "that game," requested above?

"Put Up or Shut Up," one just might say.

Is there an empiricist (anywhere) in this tread??

Prometheus_Fuschs

Aug 28, 2019

0

#2527

Optimissed escribió:

zborg wrote:

ponz111 wrote:

I believe from 62 years of playing chess and thousands of my own games that chess is a draw unless one side or the other makes a mistake.

I would suggest that out of billions of chess games that one cannot find even one game which was won or lost without one of the players making a mistake. If anyone thinks they can find such a game please post it here.

I believe Ponz111's bold assertion (roughly 6 years ago) is eminently reasonable.

Has anyone yet posted an example of "that game," requested above?

"Put Up or Shut Up," one just might say.

Is there an empiricist (anywhere) in this tread??

The empiricists are all believers that one day, a forced win will be found, so they're withholding judgement until that day. I'm a rationalist as regards this subject. Empiricism isn't always appropriate if there are no observations possible. After all, who knows what perfect play is?

You don't need to show the perfect game to prove the game state of the initial position in chess.

Prometheus_Fuschs

Aug 28, 2019

0

#2528

Optimissed escribió:

Prometheus_Fuschs wrote:

Optimissed escribió:

Prometheus_Fuschs wrote:

Optimissed escribió:

None of your comments are to the point, MAR. You seem to be obsessed with the idea that no-one plays perfectly or that mistakes will always happen, without realising that it's these mistakes which cause games to be won and lost.

Are you trolling?

The odds are stacked against you on that one.

In your mind.

If I was wrong and you were right then GMs wouldn't be losing games at all.

Because they make mistakes and outwit one-another. It seems to be a simple thing to understand and yet you cannot seem to do it.

I understand it perfectly, otherwise I wouldn't have said what I said.

Prometheus_Fuschs

Aug 28, 2019

0

#2529

zborg escribió:

ponz111 wrote:

I believe from 62 years of playing chess and thousands of my own games that chess is a draw unless one side or the other makes a mistake.

I would suggest that out of billions of chess games that one cannot find even one game which was won or lost without one of the players making a mistake. If anyone thinks they can find such a game please post it here.

I believe Ponz111's bold assertion (roughly 6 years ago) is eminently reasonable.

Has anyone yet posted an example of "that game," requested above?

"Put Up or Shut Up," one just might say.

Is there an empiricist (anywhere) in this tread??

Even if we offered a correct example, he (and we) wouldn't have the means to verify it so asking for the game is completely useless.

MiyaTheBird

Aug 28, 2019

0

#2530

?

jtang2018

Aug 28, 2019

0

#2531

"Perfect" is a relative term. Stockfish would define "perfect" differently from Lc0. Without chess being a solved game, we can't say anything about "best play".

Billkingplayschess

Aug 28, 2019

0

#2532

MARattigan wrote:

Excalibr4 wrote:

AlphaZero says white wins...

My big brother says Black wins.

Even if your Big Brother Is the strongest chess computer on Earth AZ still whips him like a wet baby seal!

ponz111

Aug 28, 2019

0

#2533

We should stop using the term "perfect game" as people use that term differently and we talk past each other.

To me an optimum game is a game where neither side makes an error which would change the theoretical result of that game.

Thus there would probably be billions of ways to play the first few moves of such a game.

ponz111

Aug 28, 2019

0

#2534

same goes for "best play" people use the term differently. "Best play" should [for our purposes] simply mean play that preserves your win or draw. It is obvious that any one position --there may be many

ways to play "best play" from the great majority of positions.

MARattigan

Aug 28, 2019

0

#2535

Excalibr4 wrote:

MARattigan wrote:

Excalibr4 wrote:

AlphaZero says white wins...

My big brother says Black wins.

Even if your Big Brother Is the strongest chess computer on Earth AZ still whips him like a wet baby seal!

Joke. I don't use smileys because I think they're a bit insulting.

MARattigan

Aug 28, 2019

0

#2536

Optimissed wrote:

MARattigan wrote:

Optimissed wrote:

MARattigan wrote:

Optimissed wrote:

Yes, you understand that despite Champagne and advanced years, you can't really compete. That must seem like a problem but just accept that you aren't here to compete but to learn. All will be well. Exponential series can be elusive. At first they seem cool but take your eye off them and they get out of hand. Then the fish really jump out of the basket.

Exponential series normally refers to 𝟏+𝔁/𝟏!+𝔁²/𝟐!+𝔁³/𝟑!+ … and I always thought it was very well behaved. You're a little skimpy on the details of how this relates to OP's question. Perhaps if you elaborated it would make it clearer.

I think you may have failed to fully take into account the formula 𝐎𝐩ₜ(𝒊ₘ) = 𝝅.>>

Broadly, an exponential series is any series that increases (or decreases) exponentially. It ought to be obvious (but it obviously isn't) that the possible variations of moves in a game of chess form such a series.

Don't worry about it.

If by "the possible variations of moves in a game of chess" you mean the number of different legal games of length 𝓷 ply (let's call it 𝓰ₙ) then you're right that it obviously isn't obvious to me that 𝓰ₙ is an exponential series. In fact it's obvious to me that it isn't.

In an exponential series 𝓰₁,𝓰₂,…𝓰ₙ,…, 𝓰ₖ₊₁/𝓰ₖ must be constant. By inspection 𝓰₁=𝟸𝟶, 𝓰₂=𝟸𝟶² but 𝓰₃ >𝟸𝟶³. The series is therefore not exponential.

That applies whether or not the 75 move rule is in force. If the 75 move rule is in force then it's also obvious that 𝓰ₙ=𝟶 whenever 𝓷>2.75(16.5+30)=16,500.

But mainly you still haven't explained what this has to do with OP's question.

Yes I did, quite clearly, three times. If that is your level of attention, how can you possibly criticise my discussion if you never saw it, can't remember it and didn't understand it? I'm really not going to repeat it a fourth time. My claim is that the fact that chess with best play is a draw is provable mathematically and such a proof will be based on the overview that I described.

Yes, I must have missed it. My apologies.

Prometheus_Fuschs

Aug 28, 2019

0

#2537

ponz111 escribió:

We should stop using the term "perfect game" as people use that term differently and we talk past each other.

To me an optimum game is a game where neither side makes an error which would change the theoretical result of that game.

Thus there would probably be billions of ways to play the first few moves of such a game.

That is what I mean when I say perfect game.

MARattigan

Aug 28, 2019

0

#2538

ponz111 wrote:

same goes for "best play" people use the term differently. "Best play" should [for our purposes] simply mean play that preserves your win or draw. It is obvious that any one position --there may be many

ways to play "best play" from the great majority of positions.

Except under basic rules since 2017 it's also necessary to win at some stage rather than just preserving a won position. See my post #2522.

Perfect play depends on the 𝓷 move rules in force (these have been various in the history of chess). Hence Syzygy and Nalimov EGTBs. I think this almost certainly applies very soon after the start of the game. Different openings for different rules.

MARattigan

Aug 28, 2019

0

#2539

ponz111 wrote:

We should stop using the term "perfect game" as people use that term differently and we talk past each other.

To me an optimum game is a game where neither side makes an error which would change the theoretical result of that game.

Thus there would probably be billions of ways to play the first few moves of such a game.

You'd need about four moves before you got one billion games altogether even in terms of the American billion. I would guess that the fraction of those games that are perfect would also be rather small. So it obviously depends on what you count as a few.

ponz111

Aug 28, 2019

0

#2540

actually if you go 4 moves--2 moves each side---most move sequences would be moves which do not

change the theoretical result of the game. It takes a lot to turn a game from a draw to a loss and that is why GMs rarely lose [except when they play me.]

I agree that per the new rules of chess you must eventually show the win to be playing perfectly in your sense.

1. d4 Nf6 2. h3 h6 3. c3 c6 is optimum chess in that neither side has made a move which will change the theoretical out come of the game.

1. d3 e5 2. d4 I used to play. 1. a3 Nc6 2. g3 probably a draw.