Can Chess Be Solved? [Hint: Probably Not!]

This is quite a big question, not least because when people speak of “solving chess” they rarely specify exactly what they mean by “solving”. If we assume that what they mean is, “is there an optimal strategy for playing chess by which a perfectly played game must result in either a victory or a forced draw?” then we can begin to answer the question.

Can chess be solved? In theory, chess can be solved because the rules create a closed, predictable system. In practice, however, chess cannot be solved because it’s beyond the capacity of any human mathematicians and beyond the capabilities of computers. There are 10120 potential variations of games in chess and around 1043 different potential positions on the board. To fully solve chess, every single one of these must be compared against the other.

So, let’s take a deeper look into chess and see what makes it such a complex sport and whether there might ever be a solution for a “perfect game” that could allow a player to either dominate the game or, alternatively, to ensure that no-one every won another game of chess.

Can chess be solved? - ChessPulse.com
Can chess be solved? – ChessPulse.com

The Current State Of Solving Chess

Chess is possibly the most famous “intellectual” sport in the world and thus, it attracts a huge amount of interest in the potential for solving the game. Of course, the most likely way to solve chess is via computer and as you probably know, the best computer players are already some way better than the best human players.

However, because of the incredible combinations of possibilities involved to weigh up the 10120 potential variations of games in chess and around 1043 different potential positions on the board, it would take a human being 1090 years to solve chess.

Computers are quite a bit faster than human beings at calculating things but, even with their power – this would still take longer to solve than the expected lifespan of the universe.

Some Progress Has Been Made On Solving Chess Endgames

This is not to say that there is no progress on this front and to date there are some interesting results based on endgames. These are studies based on what they call “all non-trivial endgames” that have no more than 7 pieces in total on the board (this count includes both of the kings).

There are quite a few of these endgames but there are rather less than 10120 of them. So, a “tablebase” that is a collection of every single permutation can be built and, indeed, has been built of these endgames.

A 546 Move Forced Mate!

They’ve discovered some very peculiar circumstances in just this tiny selection of games. For example, there is a position on the board in which it is possible to force a mate in 546 moves though you have to ignore the 50-move rule in order to pull it off. (This is a rule which says the game is a draw if the same position appears on the board 5 times – though if playing against a human being after 3 times, a player may require the draw).


You can set this up on a board yourself. You will need to put White: Queen h1, Knight h2 and King on d3.

You will need to put Black: Bishop on d1, Knight on h7, Rook on a7, and King on f4.

It is black to move.

You shouldn’t feel bad if you can’t figure out this 546-move checkmate, no human being can. Nor can any chess computer that doesn’t have access to the tablebase. Yes, even the greatest chess playing computers aren’t capable of seeing 546 moves into the future and playing perfectly to arrive at mate.

And this is a simple example of a chess position! There are 25 pieces missing from the board already and many moves have already been made (exactly which moves we don’t know in this theoretical exercise).


Can Chess Be Solved?

This has become a matter of some debate in recent years. You see, it is not essential for a computer to test every possible variation on the board or indeed potential position. Some of these positions and variations are innately and obviously bad. What if we could somehow cut down the amount of results that needed to be compared?

Can We Make The Problem Smaller?

Then there is the fact that some of the greatest grandmaster games have taken place over the course of a fairly few number of moves – 16 is a record. If the greatest players in the world can come to an ending in 16 moves is it possible that the “perfect game” isn’t very long? Of course, it is.

Thus, potentially there might be a way to solve chess by reducing the size of the problem that we were to attack. Yet, to date, no-one has worked out how this might be done.

The Limits Of Computers And Chess Problems

However, in 1965, Hans-Joachim Bremermann, a mathematician at UC Berkeley published a paper on the limits of computing. He noted that there are three hard limits on how powerful a computer can be – the speed of light (“the light barrier”), the “quantum barrier” (the number of potential superimpositions in a quanta of data) and “the thermodynamical barrier” (awkwardly phrased but hot must run to cold and not the other way around – this defines the flow of time).

These 3 limitations made it certain that a computer cannot solve chess by brute force. It is simply impossible for even a machine many times more powerful than the ones we make today, to crunch the numbers before the universe runs out of time.

The Solution of Checkers And The Implications For Chess

In 2007, the game of checkers was solved (though “weakly” which indicates that a solution to checkers has been found that shows an “ideal” game where both players play optimally – there is, of course, no guarantee that both players, unless computer programmed to do so, will play optimally – so it is not a “strong” solution which would allow a player to win any game or at least force a draw against any opponent).

Many thought that this meant chess would soon be weakly solved. However, the truth is that there are an order of magnitude fewer positions in checkers than there are in chess. The lead on the checkers project, Jonathan Shaeffer, has stipulated that even to “weakly” solve chess, would require quantum computers.

Speculation On The Solution Of Chess

This hasn’t stopped intense speculation that a weak solution for chess is impending and 2035 seems to be the agreed-on date for when such powerful quantum computers will arrive and propel our understanding of chess further ahead.


Chess Solved! (Sort Of)

There are some variants of chess which are much, much simpler than actual chess such as “Mahrajah and the Sepoys”, “Gardener’s Minichess” and “Losing Chess” which have been solved by computer algorithm. Though, in the case of Losing Chess, it has only been “weakly” solved.

As a general rule of thumb, the smaller the board used to play on – the easier a game is to solve. Which is why tic-tac-toe can be solved by almost anyone and without a computer and why the Chinese game of Go! is probably the hardest game of all to solve by dint of having more move options than any other.


Conclusion

Can chess be solved? In practical terms, probably not. However, that’s not to say that there won’t be a “soft solution” in the next 20 or so years. This might spoil a lot of people’s fun when it comes to chess because it will mean that a “near perfect” game will have been found and that there will be a fairly reasonable model for a highly-skilled chess player to base their entire game upon.

The big question, of course, is if there ever were to be a “perfect game”, would you want to know what it was? The sport of chess depends on the outcome being uncertain. If there were a way to ensure you always won or, at the very least, you never lost – this would remove any joy from playing and it wouldn’t take long for others to copy your lead.

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