Who would win a perfect game of chess?

[mfb]

I believe this means in the end white always wins in a perfect game.

Why would it mean that? Why would it give any indication of that?
We have chess programs that can perform beyond the level of the very best humans - and as far as I know you are not among them - and even they can't answer the question about a perfect game because they are far away from perfect play.

 

[MathematicalPhysicist]

Why would it mean that? Why would it give any indication of that?
We have chess programs that can perform beyond the level of the very best humans - and as far as I know you are not among them - and even they can't answer the question about a perfect game because they are far away from perfect play.

How would one know when a perfect game has been played?

 

[zoki85]

While chess hasn't been solved yet, other games have. For example, I know that in in some games, like connect four, if both players play perfectly, the player who goes first will always win. On the other hand, some games, like tic tac toe, a perfect game will result in a draw; in fact, I recently found out that this is true for checkers as well. What I'm wondering though, is if it's possible to predict which scenario a perfect game of chess would lead to even without having fully solved it yet, and if it is possible, what the answer is.

Gardner chess (5x5 board) is weakly solved by help of computers analysis.
Result of the perfect play of both sides is a draw.
See the paper:
https://arxiv.org/abs/1307.7118

It is naturally to expect that chess on 8x8 board is a draw as well.

 

[MathematicalPhysicist]

Gardner chess (5x5 board) is weakly solved by help of computers analysis.
Result of the perfect play of both sides is a draw.
See the paper:
https://arxiv.org/abs/1307.7118

It is naturally to expect that chess on 8x8 board is a draw as well.

A 5x5 board wouldn't include all of the chess pieces of the original 8x8 game, so I don't see how is your conclusion any valid here.

We might as well play a game of 16x16 chess on a round table...
Well it's of course makes you generalize the chess game to a 2nx2n or 2n+1x2n+1 chess board... quite tough indeed.

 

[zoki85]

A 5x5 board wouldn't include all of the chess pieces of the original 8x8 game, so I don't see how is your conclusion any valid here.

It includes pawns and one of each kind. That's something

 

[MathematicalPhysicist]

It includes pawns and one of each kind. That's something

Still, it's a different game.

I wonder how would one solve the generalized problem?
Certainly not in this millennium...

 

[zoki85]

Certainly not in this millennium...

Only if powerful enough quantum computer find a forced win for one side.
But, that's not going to happen since game chess is most likey a draw

 

[MathematicalPhysicist]

Only if powerful enough quantum computer find a forced win for one side.
But, that's not going to happen since game chess is most likey a draw

It's just a game... (and white wins in the end ;-)).

 

[MathematicalPhysicist]

Well I've beaten myself again.

This time it took only 86 steps.
Quite an improvement.

 

[mfb]

How would one know when a perfect game has been played?

A perfect player - an entity that can fully analyze the remaining game tree - will be able to tell you. Otherwise you can't be sure. It's still possible to spot errors even without having a perfect player, of course.

 

[MathematicalPhysicist]

A perfect player - an entity that can fully analyze the remaining game tree - will be able to tell you. Otherwise you can't be sure. It's still possible to spot errors even without having a perfect player, of course.

Well, in the two games that I won I didn't necessarily make the first option of move the computer hinted me to make; unless of course it was the red option and not pink which from what I gather is the optimal move in that instance.(edit: it seems the red is on green square, so it doesn't really matter).
I understand that the algorithms that the computer uses in level 10 are just not optimal.
How many games should one win in white until it is settled?
I don't know how to start calculating all the number of perfect games needed.

 

[jbriggs444]

How many games should one win in white until it is settled?

If you are adopting this proof technique then the answer is: "all of them until all opponent strategies have been exhausted".

 

[MathematicalPhysicist]

If you are adopting this proof technique then the answer is: "all of them until all opponent strategies have been exhausted".

how many are there exactly?
How would you calculate this number on the simple original 8x8 game?

 

[SSequence]

Maybe this is relevant?
https://math.stackexchange.com/questions/1406919

 

[jedishrfu]

There is really only one answer here: Mary Poppins

Who is practically perfect in every way.

I don't know if she ever played chess though.

 

[BWV]

So, I played the other day against the computer in the level of grandmaster in chess.com (i.e level 10).

You wouldn't expect me to win with white, but I guess this was one of those days everything clicked.
I believe this means in the end white always wins in a perfect game.
I used the hints' option, but I didn't always take the first option it suggested me to do (since if I had done that the game would have ended in a draw).

I am attaching a .txt file with the moves, it took something like 93 moves in total.
Cheers!

that’s hilarious. Beat AlphaZero and then we’ll talk.

here is the results of 1,000 of the most ‘perfect’ chess games that have been played:

https://www.google.com/amp/s/www.ch...ero-crushes-stockfish-in-new-1-000-game-match

 

[Infrared]

@MathematicalPhysicist I don't think this is a persuasive argument for chess being won for white. I imagine one could also beat that engine with the black pieces, but you wouldn't claim that chess is a win for black.

 

[MathematicalPhysicist]

@MathematicalPhysicist I don't think this is a persuasive argument for chess being won for white. I imagine one could also beat that engine with the black pieces, but you wouldn't claim that chess is a win for black.

I don't know to tell you the truth.
I didn't try to win with the black, but I assume the game will always be finished either in a draw or a loss to white.

A funny anecdote:
https://www.chess.com/forum/view/fun-with-chess/white-always-wins
"
Why is it that White always wins in Chess? Every game I've ever played, White wins. It's driving me nuts! Is it because White goes first? That always puts them a move ahead, meaning Black is always having to counter-act what White's doing.

It's also weird how I'm always the Black side."

You can try playing with the black, and let us know if you won in level 10 with black.
Do post your script with the moves.

 

[MathematicalPhysicist]

that’s hilarious. Beat AlphaZero and then we’ll talk.

here is the results of 1,000 of the most ‘perfect’ chess games that have been played:

https://www.google.com/amp/s/www.ch...ero-crushes-stockfish-in-new-1-000-game-match

I would like to play against it, but I cannot find it in google...

Here's what I found:
https://www.quora.com/How-can-I-play-Googles-AlphaZero-in-chess

Anyway, I could not win without the hints given by the software, obviously.
My post is about the thought that perhaps indeed white in the end wins after all.
Obviously to prove that one needs to know all the perfect games that can be played.

 

[BWV]

I have not seen where deepmind released stats on AlphaZeros training games. The stats on a million or so games it plays against itself would be interesting

 

[MathematicalPhysicist]

I have not seen where deepmind released stats on AlphaZeros training games. The stats on a million or so games it plays against itself would be interesting

Well, you can also say that I also play chess games against myself with the chess.com engine. (Though not even close to 1000 games).

My play is assisted by what the engine hints me to do, so in way I witnessed the computer plays against itself with me choosing between the options it offered me.

I tried once (for a game of 135 moves) to play in black but the game ended in a draw; so it make me wonder now how good is this engine of theirs.

BTW, why don't they publish the stats of the million games alpha-zero played against itself?

 

[Infrared]

Do post your script with the moves.

[Site "Chess.com"]
[Date "2020.02.29"]
[Event "Vs. Computer"]
[Round "1"]
[White "Computer Level 10"]
[Black "Guest"]
[Result "0-1"]
[CurrentPosition "8/8/3K4/1q2q1p1/6k1/8/8/8 w - - 8 93"]

1.e4 d6 2.d4 Nf6 3.Nc3 g6 4.h3 Bg7 5.Nf3 O-O 6.Be3 a6 7.a4 b6 8.Bc4 e6 9.O-O Bb7 10.d5 exd5 11.exd5 Nbd7 12.Re1 Re8 13.Qd2 Nc5 14.Bd4 Qd7 15.Qf4 Nh5 16.Qh4 Qf5 17.Bxg7 Kxg7 18.b4 Nd7 19.Qd4+ Qf6 20.Qd2 Ne5 21.Nxe5 Rxe5 22.Rxe5 dxe5 23.Bb3 Nf4 24.Ne4 Qf5 25.f3 Bxd5 26.Bxd5 Rd8 27.c4 c6 28.g3 Nxh3+ 29.Kg2 h6 30.Re1 Ng5 31.Nxg5 hxg5 32.a5 bxa5 33.bxa5 cxd5 34.cxd5 f6 35.d6 g4 36.f4 g5 37.fxe5 Qf3+ 38.Kg1 Qxg3+ 39.Kf1 Rf8 40.e6 Rh8 41.Qg2 Qxd6 42.e7 Qf4+ 43.Kg1 Qd4+ 44.Kf1 Qc4+ 45.Kg1 Re8 46.Qf2 Qd5 47.Qb6 Qd2 48.Qe6 Qxa5 49.Kg2 Qc7 50.Qe4 Qc5 51.Re2 a5 52.Qe6 Qa7 53.Kf1 Qb7 54.Kg1 g3 55.Re5 Qb1+ 56.Re1 Qh7 57.Re2 a4 58.Qe3 Qh4 59.Rg2 Qb4 60.Re2 a3 61.Kg2 Qh4 62.Qxg3 Qc4 63.Qf2 Kf7 64.Re1 Qg4+ 65.Kf1 Qh3+ 66.Kg1 Rxe7 67.Rxe7+ Kxe7 68.Qa7+ Kf8 69.Qb8+ Kg7 70.Qb7+ Kg6 71.Qe4+ Kh6 72.Qe7 Qg3+ 73.Kh1 Qf3+ 74.Kg1 Kh5 75.Kh2 f5 76.Qa7 Kh4 77.Kg1 Kh3 78.Qh7+ Kg4 79.Qa7 Qd1+ 80.Kf2 Qd2+ 81.Kg1 Qe1+ 82.Kg2 Qe2+ 83.Qf2 Qxf2+ 84.Kxf2 a2 85.Ke1 a1=Q+ 86.Kd2 f4 87.Kd3 f3 88.Kc2 f2 89.Kb3 f1=Q 90.Kb4 Qb2+ 91.Kc5 Qfb5+ 92.Kd6 Q2e5# 0-1

The chess.com computer "missed" 25...Bxd5 after which black was much better/winning. Anyway, I don't think this (or any) engine is strong enough to deduce the result of a perfect game of chess. Chess seems mostly balanced, and with a relatively large drawing margin, the general consensus is that the first move advantage shouldn't be enough to win in a perfectly played game. Of course this isn't proof, but I'd be very surprised if it weren't true...

 

[BWV]

In Alphazero’s 100 game tournament against Stockfish8 it scored 28 wins, 25 as white and 3 as black (the other 72 games were draws)

 

[MathematicalPhysicist]

[Site "Chess.com"]
[Date "2020.02.29"]
[Event "Vs. Computer"]
[Round "1"]
[White "Computer Level 10"]
[Black "Guest"]
[Result "0-1"]
[CurrentPosition "8/8/3K4/1q2q1p1/6k1/8/8/8 w - - 8 93"]

1.e4 d6 2.d4 Nf6 3.Nc3 g6 4.h3 Bg7 5.Nf3 O-O 6.Be3 a6 7.a4 b6 8.Bc4 e6 9.O-O Bb7 10.d5 exd5 11.exd5 Nbd7 12.Re1 Re8 13.Qd2 Nc5 14.Bd4 Qd7 15.Qf4 Nh5 16.Qh4 Qf5 17.Bxg7 Kxg7 18.b4 Nd7 19.Qd4+ Qf6 20.Qd2 Ne5 21.Nxe5 Rxe5 22.Rxe5 dxe5 23.Bb3 Nf4 24.Ne4 Qf5 25.f3 Bxd5 26.Bxd5 Rd8 27.c4 c6 28.g3 Nxh3+ 29.Kg2 h6 30.Re1 Ng5 31.Nxg5 hxg5 32.a5 bxa5 33.bxa5 cxd5 34.cxd5 f6 35.d6 g4 36.f4 g5 37.fxe5 Qf3+ 38.Kg1 Qxg3+ 39.Kf1 Rf8 40.e6 Rh8 41.Qg2 Qxd6 42.e7 Qf4+ 43.Kg1 Qd4+ 44.Kf1 Qc4+ 45.Kg1 Re8 46.Qf2 Qd5 47.Qb6 Qd2 48.Qe6 Qxa5 49.Kg2 Qc7 50.Qe4 Qc5 51.Re2 a5 52.Qe6 Qa7 53.Kf1 Qb7 54.Kg1 g3 55.Re5 Qb1+ 56.Re1 Qh7 57.Re2 a4 58.Qe3 Qh4 59.Rg2 Qb4 60.Re2 a3 61.Kg2 Qh4 62.Qxg3 Qc4 63.Qf2 Kf7 64.Re1 Qg4+ 65.Kf1 Qh3+ 66.Kg1 Rxe7 67.Rxe7+ Kxe7 68.Qa7+ Kf8 69.Qb8+ Kg7 70.Qb7+ Kg6 71.Qe4+ Kh6 72.Qe7 Qg3+ 73.Kh1 Qf3+ 74.Kg1 Kh5 75.Kh2 f5 76.Qa7 Kh4 77.Kg1 Kh3 78.Qh7+ Kg4 79.Qa7 Qd1+ 80.Kf2 Qd2+ 81.Kg1 Qe1+ 82.Kg2 Qe2+ 83.Qf2 Qxf2+ 84.Kxf2 a2 85.Ke1 a1=Q+ 86.Kd2 f4 87.Kd3 f3 88.Kc2 f2 89.Kb3 f1=Q 90.Kb4 Qb2+ 91.Kc5 Qfb5+ 92.Kd6 Q2e5# 0-1

The chess.com computer "missed" 25...Bxd5 after which black was much better/winning. Anyway, I don't think this (or any) engine is strong enough to deduce the result of a perfect game of chess. Chess seems mostly balanced, and with a relatively large drawing margin, the general consensus is that the first move advantage shouldn't be enough to win in a perfectly played game. Of course this isn't proof, but I'd be very surprised if it weren't true...

The consensus changed over the centuries according to wiki.
We don't even know how to estimate the number of perfect games which are possible to be played.
In my first post in this thread I thought to myself that it must be a tie just like checkers, but my opinion has changed after playing a few games.

How can one prove that it would end in a draw or not without playing the game?
It's like in the proof of the 4-colours mapping theorem, that was shown by computer computation, why should we believe that it indeed considered every possible outcome?
Heck, human programmers code the programme?
And humans are known to err...

 

[Infrared]

The consensus changed over the centuries according to wiki.

I'm not sure which article you're referring to, but https://en.wikipedia.org/wiki/First-move_advantage_in_chess#Drawn_with_best_play suggests a very strong consensus that chess is drawn.

In my first post in this thread I thought to myself that it must be a tie just like checkers, but my opinion has changed after playing a few games.

You can have whatever view you like, but it's not clear why you think this. Is it just that the chess.com computer can lose (with either color)? A large majority of computer vs computer games are drawn. Even the the most recent alphazero-stockfish match finished with 839/1000 draws, and this was still considered a substantial victory for A0. Both of these engines are much stronger than the chess.com level 10 program.

 

[MathematicalPhysicist]

@Infrared in the same article in the beginning:
"Since 1988, chess theorists have challenged previously well-established views about White's advantage."

 

[MathematicalPhysicist]

Makes you wonder what makes something well established...

 

[Infrared]

@Infrared in the same article in the beginning:
"Since 1988, chess theorists have challenged previously well-established views about White's advantage."

I think you misunderstood that quote. Paraphrasing the article, the "well-established" view referred to there is just that white has an advantage. Adorján argued that the first move advantage is overestimated and largely psychological.

The question of how much white's extra move helps him is indeed subject to debate, but almost no strong players think that it's enough to win against perfect play. I'm happy to pull other quotes from the article to show that the consensus is overwhelming if you'd like. I think you should study the game more before jumping to such conclusions- playing "a few games" doesn't override over 100 years of collective human chess understanding.

 

[DaveC426913]

The question of how much white's extra move helps him is indeed subject to debate, but almost no strong players think that it's enough to win against perfect play.

Maybe not enough by itself to win against perfect play, but if both sides are playing perfectly, presumably the edge is sufficient.

A previous poster pointed out that [given perfect play on both sides] black will always be forced to react to white's moves.

The 20 possible opening moves white has will constrain black's potential 20 responses to something less than 20 that are part of a perfect play.

 

[PeroK]

The question of how much white's extra move helps him is indeed subject to debate, but almost no strong players think that it's enough to win against perfect play. I'm happy to pull other quotes from the article to show that the consensus is overwhelming if you'd like.

In addition, collective chess wisdom is codified in the modern chess engines, which use human-specified algorithms to assess any position. Anyone who believes that the game is equal at move one, with white to play, ought to be able to refine the chess algorithm and remove the error made by all current chess engines: which consistently show white having an advantage in all the standrad openings.

I'm not aware of any successful chess engine that assesses the game as equal at the start.

Moreover, if Alpha Zero thought that the game were level, it would have won as many games as black as with white. But, A0 against Stockfish reinforced the practical nature of white's advantage, with A0's wins being predominantly as white.

True, this doesn't prove anything. But, anyone who considers chess to be a level contest between white and black patently has no evidence on which to base this. All the current evidence is that white has a theoretical and practical advantage.

 

[Infrared]

Maybe not enough by itself to win against perfect play, but if both sides are playing perfectly, presumably the edge is sufficient.

Why would you presume that? The general consensus is that a perfectly played game of chess ends in a draw- see the article I linked earlier. Also, chess engines are the closest we have now to perfect chess, and a large majority of computer vs computer games end in a draw. The issue is that chess has a pretty large drawing margin. Often, one side is worse/responding to the opponent for the whole game and still escapes with a draw.

 

[BWV]

I think an analogy is whether there is a first move advantage in tic tax toe - obviously it’s always a draw, but with less than perfect play I would bet that the first move wins more often

 

[PeroK]

Maybe not enough by itself to win against perfect play, but if both sides are playing perfectly, presumably the edge is sufficient.

Again, the modern chess engines give a good measure of what size of advantage is needed to win a game. An advantage of +0.5 is generally enough to put your opponent under pressure, but probably not enough to win. That's generally the maximum advantage that white enjoys.

There is currently no evidence, therefore, that white has enough to force a win.

One clear issue is stalemate being a draw. If stalemate were a win, it might be a different conclusion. A player may eventually have a huge advantage but no way to force a win.

 

[DaveC426913]

Again, the modern chess engines give a good measure of what size of advantage is needed to win a game. An advantage of +0.5 is generally enough to put your opponent under pressure, but probably not enough to win. That's generally the maximum advantage that white enjoys.

Can we assume they're playing "perfect" games?

 

[jbriggs444]

Can we assume they're playing "perfect" games?

Assuming perfect play is a draw...

By "perfect game", one assumes that you mean a game in which no move by white allows black to force a win and no move by black allows white to force a win. Since modern chess engines do not always draw, we can readily see that they do not always play perfectly.