You know how to save a position better than I do. I will show you. ;) If someone else finds the solution I am sure the whole world will marvel in it. If there is a case for it is winning like ten perfect games in a row a solution? How many games before the moves can not improve and both players are trying the most to win?
@vsdgniuz said in #18:
> To prove that chess is not a solved game, I needed to prove that neither white nor black can force win or draw.
there is need to prove chess is not solved. It enough to observer that such proof has not been presented (most likely will not happen). Equally to there is no need to prove that chess in theory solvable as all complete information games are solvable.
and whether game is solved obviously means nothing. I keep losing my games in first ten moves which is not necessary all required information to survive that long can in practice tabulated. And mostly is
> To prove that chess is not a solved game, I needed to prove that neither white nor black can force win or draw.
there is need to prove chess is not solved. It enough to observer that such proof has not been presented (most likely will not happen). Equally to there is no need to prove that chess in theory solvable as all complete information games are solvable.
and whether game is solved obviously means nothing. I keep losing my games in first ten moves which is not necessary all required information to survive that long can in practice tabulated. And mostly is
@vsdgniuz said in #18:
> So, why did I not mention Black initially? It is just because of statistics.
I asked out of curiosity because I would be really interested if there is some elegant way to actually prove it. To be honest, I would be very surprised if the result were anything else than "it's a draw, win cannot be forced by either side".
> To prove that chess is not a solved game, I needed to prove that neither white nor black can force win or draw.
I think you mean "solvable" hear, "not solved" rather means noone presented a strategy ensuring a win or a draw (draw for both sides). But the fact that chess can be (theoretically) is a simple consequence of the graph being finite which is guaranteed by the 50-move rule imposing a fixed limit on maximum number of moves in a game (together with limited number of possible moves in any position). We are just not able to brute force the graph yet (and it's not clear if we ever will).
> So, why did I not mention Black initially? It is just because of statistics.
I asked out of curiosity because I would be really interested if there is some elegant way to actually prove it. To be honest, I would be very surprised if the result were anything else than "it's a draw, win cannot be forced by either side".
> To prove that chess is not a solved game, I needed to prove that neither white nor black can force win or draw.
I think you mean "solvable" hear, "not solved" rather means noone presented a strategy ensuring a win or a draw (draw for both sides). But the fact that chess can be (theoretically) is a simple consequence of the graph being finite which is guaranteed by the 50-move rule imposing a fixed limit on maximum number of moves in a game (together with limited number of possible moves in any position). We are just not able to brute force the graph yet (and it's not clear if we ever will).
@petri999 said in #22:
> there is need to prove chess is not solved. It enough to observer that such proof has not been presented (most likely will not happen). Equally to there is no need to prove that chess in theory solvable as all complete information games are solvable.
OP mentioned chess is a solved game, hence, chess is dead. That point of view led me to the analysis I shared earlier. On the same note, I wholeheartedly agree with you that this is not an important question. I don't care if chess is solved or not, that's not going to stop me from playing and enjoying the game.
@mkubecek said in #23:
> I asked out of curiosity because I would be really interested if there is some elegant way to actually prove it. To be honest, I would be very surprised if the result were anything else than "it's a draw, win cannot be forced by either side".
Let's look at the trend of white wins, black wins and draws for the matches between top two chess engines as they have evolved.
Below is the result of games played between the top two engines:
2011, Season 1 (tcec-chess.com/#div=sf&game=1&season=1) - White wins: 10 [25%], Black wins: 7 [17.5%], Draws: 23 [57.5%]
2013, Season 5 (tcec-chess.com/#div=sf&game=1&season=5) - White wins:10 [20.83%], Black wins: 8 [16.67%], Draws: 30 [62.5%]
2017, Season 10 (tcec-chess.com/#div=sf&game=1&season=10) - White wins: 20 [20%], Black wins: 4 [4%], Draws: 76 [76%]
2019, Season 15 (tcec-chess.com/#div=sf&game=1&season=15) - White wins: 19 [19%], Black wins: 2 [2%], Draws: 79 [79%]
2021, Season 20 (tcec-chess.com/#div=sf&game=1&season=20) - White wins: 22 [22%], Black wins: 0, Draws: 78 [78%]
2021, Season 21 (tcec-chess.com/#div=sf&game=1&season=21) - White wins: 25 [25%], Black wins: 1 [1%], Draws: 74 [74%]
2022, Season 22 (tcec-chess.com/#div=sf&game=1&season=22) - White wins: 37 [37%], Black wins: 0, Draws: 63 [63%]
2022, Season 23 (tcec-chess.com/#div=sf&game=1&season=23) - White wins: 35 [35%], Black wins: 2 [2%], Draws: 63 [63%]
2023, Season 24 (tcec-chess.com/#div=sf&game=1&season=24) - White wins: 36 [36%], Black wins: 0, Draws: 64 [64%]
2023, Season 25 (tcec-chess.com/#div=sf&game=1&season=25) - White wins: 50 [36.23%], Black wins: 1 [0.72%], Draws
87 [63.04%]
The best chess engine in 2011, Houdini had an Elo rating of 3011. The best chess engine in 2023, Stockfish had an Elo rating of 3673. That is an improvement of about 650 points over 12 years.
Over time, as the chess engines have been improving, the win rate as black pieces has been decreasing. It was about 17.5% in 2011 and was near 0% in 2023.
On the contrary, the win rate for white pieces had been stable for 10 years at about 20% and then started increasing from 2021 onwards to reach about 35%.
The draws increased from 57.5% in 2011 to about 80% until 2021, when it started decreasing again and is currently near 65%.
The following conclusions can be drawn from the above observations:
- Black wins: As the engines improved, it became more and more difficult for black to win the game. Meaning white was able to at the least draw the games that black could have won.
- Draws: The draws increased until 2021. As the win rate of white was stable, this means that the increase in the percentage of draws came from games that were earlier won by black.
- Wins: From 2022, onwards, white's win rate increased from near 20% to near 35%. As black wins were already near zero from 2019, this increase came from the games that were previously drawn. White is getting better at using its advantage. The only advantage I know that white has over black is the first-move advantage.
To summarize, as chess engines are getting better, they are getting better at using the first move advantage when playing as white.
PS: The conclusion that neither side can force a win would require win rate of both white and black reaching 0% and percentage of draws reaching 100%. The current trend during the evolution of the chess engines is not heading in that direction.
@mkubecek said in #23:
> I think you mean "solvable" hear, "not solved" rather means noone presented a strategy ensuring a win or a draw (draw for both sides). But the fact that chess can be (theoretically) is a simple consequence of the graph being finite which is guaranteed by the 50-move rule imposing a fixed limit on maximum number of moves in a game (together with limited number of possible moves in any position). We are just not able to brute force the graph yet (and it's not clear if we ever will).
Proving a game is solved and proving a game is solvable are two very different problems. I provided evidence for only the first problem. To prove that a game is not solved yet, it is sufficient to prove that no strategy has been found that allows a player to force wins or draws. Proving a game is not solvable would require one to prove that there exists no strategy which could be used to force wins or draws.
> there is need to prove chess is not solved. It enough to observer that such proof has not been presented (most likely will not happen). Equally to there is no need to prove that chess in theory solvable as all complete information games are solvable.
OP mentioned chess is a solved game, hence, chess is dead. That point of view led me to the analysis I shared earlier. On the same note, I wholeheartedly agree with you that this is not an important question. I don't care if chess is solved or not, that's not going to stop me from playing and enjoying the game.
@mkubecek said in #23:
> I asked out of curiosity because I would be really interested if there is some elegant way to actually prove it. To be honest, I would be very surprised if the result were anything else than "it's a draw, win cannot be forced by either side".
Let's look at the trend of white wins, black wins and draws for the matches between top two chess engines as they have evolved.
Below is the result of games played between the top two engines:
2011, Season 1 (tcec-chess.com/#div=sf&game=1&season=1) - White wins: 10 [25%], Black wins: 7 [17.5%], Draws: 23 [57.5%]
2013, Season 5 (tcec-chess.com/#div=sf&game=1&season=5) - White wins:10 [20.83%], Black wins: 8 [16.67%], Draws: 30 [62.5%]
2017, Season 10 (tcec-chess.com/#div=sf&game=1&season=10) - White wins: 20 [20%], Black wins: 4 [4%], Draws: 76 [76%]
2019, Season 15 (tcec-chess.com/#div=sf&game=1&season=15) - White wins: 19 [19%], Black wins: 2 [2%], Draws: 79 [79%]
2021, Season 20 (tcec-chess.com/#div=sf&game=1&season=20) - White wins: 22 [22%], Black wins: 0, Draws: 78 [78%]
2021, Season 21 (tcec-chess.com/#div=sf&game=1&season=21) - White wins: 25 [25%], Black wins: 1 [1%], Draws: 74 [74%]
2022, Season 22 (tcec-chess.com/#div=sf&game=1&season=22) - White wins: 37 [37%], Black wins: 0, Draws: 63 [63%]
2022, Season 23 (tcec-chess.com/#div=sf&game=1&season=23) - White wins: 35 [35%], Black wins: 2 [2%], Draws: 63 [63%]
2023, Season 24 (tcec-chess.com/#div=sf&game=1&season=24) - White wins: 36 [36%], Black wins: 0, Draws: 64 [64%]
2023, Season 25 (tcec-chess.com/#div=sf&game=1&season=25) - White wins: 50 [36.23%], Black wins: 1 [0.72%], Draws
87 [63.04%]
The best chess engine in 2011, Houdini had an Elo rating of 3011. The best chess engine in 2023, Stockfish had an Elo rating of 3673. That is an improvement of about 650 points over 12 years.
Over time, as the chess engines have been improving, the win rate as black pieces has been decreasing. It was about 17.5% in 2011 and was near 0% in 2023.
On the contrary, the win rate for white pieces had been stable for 10 years at about 20% and then started increasing from 2021 onwards to reach about 35%.
The draws increased from 57.5% in 2011 to about 80% until 2021, when it started decreasing again and is currently near 65%.
The following conclusions can be drawn from the above observations:
- Black wins: As the engines improved, it became more and more difficult for black to win the game. Meaning white was able to at the least draw the games that black could have won.
- Draws: The draws increased until 2021. As the win rate of white was stable, this means that the increase in the percentage of draws came from games that were earlier won by black.
- Wins: From 2022, onwards, white's win rate increased from near 20% to near 35%. As black wins were already near zero from 2019, this increase came from the games that were previously drawn. White is getting better at using its advantage. The only advantage I know that white has over black is the first-move advantage.
To summarize, as chess engines are getting better, they are getting better at using the first move advantage when playing as white.
PS: The conclusion that neither side can force a win would require win rate of both white and black reaching 0% and percentage of draws reaching 100%. The current trend during the evolution of the chess engines is not heading in that direction.
@mkubecek said in #23:
> I think you mean "solvable" hear, "not solved" rather means noone presented a strategy ensuring a win or a draw (draw for both sides). But the fact that chess can be (theoretically) is a simple consequence of the graph being finite which is guaranteed by the 50-move rule imposing a fixed limit on maximum number of moves in a game (together with limited number of possible moves in any position). We are just not able to brute force the graph yet (and it's not clear if we ever will).
Proving a game is solved and proving a game is solvable are two very different problems. I provided evidence for only the first problem. To prove that a game is not solved yet, it is sufficient to prove that no strategy has been found that allows a player to force wins or draws. Proving a game is not solvable would require one to prove that there exists no strategy which could be used to force wins or draws.
We should be a bit cautious when judging whether chess gets solved in the future by the success rate of programs at forcing a win or a draw. We, and the chess engines, could all quite possibly be missing things.
The part of chess which is already truly solved are those positions which have seven or fewer pieces on the board. During the development of these so-called endgame tablebases certain strategies were revealed which neither human players nor engines had been able to discover. For example, a particularly tough way of defending with K+R vs K+Q was revealed by the tablebases (although it did not succeed in changing the result to a draw). And the endgame K+Q vs K+B+B, previously thought to be drawn, was revealed to be generally a win for the queen.
If exhaustive analysis of these simplified positions with 7 or fewer pieces can reveal truths which neither humans nor conventional engines could, who knows what secrets an exhaustive analysis of the entire game, were that to be possible, might reveal?
The part of chess which is already truly solved are those positions which have seven or fewer pieces on the board. During the development of these so-called endgame tablebases certain strategies were revealed which neither human players nor engines had been able to discover. For example, a particularly tough way of defending with K+R vs K+Q was revealed by the tablebases (although it did not succeed in changing the result to a draw). And the endgame K+Q vs K+B+B, previously thought to be drawn, was revealed to be generally a win for the queen.
If exhaustive analysis of these simplified positions with 7 or fewer pieces can reveal truths which neither humans nor conventional engines could, who knows what secrets an exhaustive analysis of the entire game, were that to be possible, might reveal?
@vsdgniuz said in #24:
> Let's look at the trend of white wins, black wins and draws for the matches between top two chess engines as they have evolved. ...
I'm afraid you don't understand me. I was asking about a proof of the statement that initial position cannot be "black wins". What you present are strong hints that it's unlikely but not a proof (in mathematical sense) that it's impossible, that would have to look completely different.
> Let's look at the trend of white wins, black wins and draws for the matches between top two chess engines as they have evolved. ...
I'm afraid you don't understand me. I was asking about a proof of the statement that initial position cannot be "black wins". What you present are strong hints that it's unlikely but not a proof (in mathematical sense) that it's impossible, that would have to look completely different.
@mkubecek said in #26:
>
I'm afraid you don't understand me. I was asking about a proof of the statement that initial position cannot be "black wins".
I think you misunderstand. All I am proving is chess is that chess is not solved yet.
If I can prove that as on date, no strategy has been found where white can not force a win or draw = black can win even when playing against the best chess engine, it is sufficient to prove that chess is not solved.
If one could prove that black can not win, it would be equivalent to saying that chess is a solved game.
The analysis I provided today is the the statement: "it's a draw, win cannot be forced by either side".
>
I'm afraid you don't understand me. I was asking about a proof of the statement that initial position cannot be "black wins".
I think you misunderstand. All I am proving is chess is that chess is not solved yet.
If I can prove that as on date, no strategy has been found where white can not force a win or draw = black can win even when playing against the best chess engine, it is sufficient to prove that chess is not solved.
If one could prove that black can not win, it would be equivalent to saying that chess is a solved game.
The analysis I provided today is the the statement: "it's a draw, win cannot be forced by either side".
@vsdgniuz said in #27:
> All I am proving is chess is that chess is not solved yet.
Well, as long as we put aside the possibility that someone already solved it but keeps the fact secret, this does not really need a proof.
> If one could prove that black can not win, it would be equivalent to saying that chess is a solved game.
It would not. That would only exclude one of the three possibilities. Such proof does not necessarily answer the question which of the other two (white wins, a draw) is correct.
> All I am proving is chess is that chess is not solved yet.
Well, as long as we put aside the possibility that someone already solved it but keeps the fact secret, this does not really need a proof.
> If one could prove that black can not win, it would be equivalent to saying that chess is a solved game.
It would not. That would only exclude one of the three possibilities. Such proof does not necessarily answer the question which of the other two (white wins, a draw) is correct.
@Brian-E said in #25:
> We should be a bit cautious when judging whether chess gets solved in the future by the success rate of programs at forcing a win or a draw. We, and the chess engines, could all quite possibly be missing things.
>
> The part of chess which is already truly solved are those positions which have seven or fewer pieces on the board. During the development of these so-called endgame tablebases certain strategies were revealed which neither human players nor engines had been able to discover. For example, a particularly tough way of defending with K+R vs K+Q was revealed by the tablebases (although it did not succeed in changing the result to a draw). And the endgame K+Q vs K+B+B, previously thought to be drawn, was revealed to be generally a win for the queen.
>
> If exhaustive analysis of these simplified positions with 7 or fewer pieces can reveal truths which neither humans nor conventional engines could, who knows what secrets an exhaustive analysis of the entire game, were that to be possible, might reveal?
Hmm... interesting take. I totally agree with you. However, using chess engine is the easiest way to prove that chess is NOT solved yet as it is the best performing player as on date.
Btw chess engines can find all tablebase moves given sufficient depth and time. Normally, the chess engines are limited to 99 depth because of the 50-move rule.
> We should be a bit cautious when judging whether chess gets solved in the future by the success rate of programs at forcing a win or a draw. We, and the chess engines, could all quite possibly be missing things.
>
> The part of chess which is already truly solved are those positions which have seven or fewer pieces on the board. During the development of these so-called endgame tablebases certain strategies were revealed which neither human players nor engines had been able to discover. For example, a particularly tough way of defending with K+R vs K+Q was revealed by the tablebases (although it did not succeed in changing the result to a draw). And the endgame K+Q vs K+B+B, previously thought to be drawn, was revealed to be generally a win for the queen.
>
> If exhaustive analysis of these simplified positions with 7 or fewer pieces can reveal truths which neither humans nor conventional engines could, who knows what secrets an exhaustive analysis of the entire game, were that to be possible, might reveal?
Hmm... interesting take. I totally agree with you. However, using chess engine is the easiest way to prove that chess is NOT solved yet as it is the best performing player as on date.
Btw chess engines can find all tablebase moves given sufficient depth and time. Normally, the chess engines are limited to 99 depth because of the 50-move rule.
@mkubecek said in #28:
> Well, as long as we put aside the possibility that someone already solved it but keeps the fact secret, this does not really need a proof.
Apparently, to OP that is not the case. He considered chess as a solved game.
> It would not. That would only exclude one of the three possibilities. Such proof does not necessarily answer the question which of the other two (white wins, a draw) is correct.
I finally understand where the misunderstanding is coming from. Indeed, you are right. I stand corrected. It is not sufficient to prove that black can not win to say that chess is a solved game. But, it is sufficient to say that chess is not a solved game if black can win despite white having the first move advantage.
> Well, as long as we put aside the possibility that someone already solved it but keeps the fact secret, this does not really need a proof.
Apparently, to OP that is not the case. He considered chess as a solved game.
> It would not. That would only exclude one of the three possibilities. Such proof does not necessarily answer the question which of the other two (white wins, a draw) is correct.
I finally understand where the misunderstanding is coming from. Indeed, you are right. I stand corrected. It is not sufficient to prove that black can not win to say that chess is a solved game. But, it is sufficient to say that chess is not a solved game if black can win despite white having the first move advantage.