Chess is too complicated with a total of 10^50^50 theoretical games possible, a total of 10^120 reasonable games possible, and a total of 10^70 good games possible which is too large for the current technology to work with, it is far from being solved.
No solution in chess is known or expected in the near future. The traditional brute force calculation implemented by Stockfish, as well as the prowess of neural networks such as Alphazero is not enough to solve chess.
Solving a game preemptively means having a straight strategy to always force a particular result by following a plan, it occurs in some games. Solving chess means having a strategy that can result in a win or draw 100% of the time.
I have wondered if chess is close to being solved, and if not, what developments in the future can we expect regarding this case.
It will after all have a significant impact if it were to happen, is chess a solved game? This is the topic for today.
If something were to even come close to being solved it would make the game pretty bland since it eliminates the value of competition, if something is solved what’s the point of even playing?
Luckily, chess has some qualities that make it hard for one battle plan to work all the time, which is why you shouldn’t worry about having a silver bullet to destroy all the fun in this game.
Is chess too complicated to be solved?
There are a total of 10^50^50 chess games possible from all 32 pieces on the board but should only be around 10^120 if we are only counting reasonable moves. If only the good moves are accounted for, there should only be 10^70 possible chess games.
10^50^50 is a much larger number than you can imagine, in fact, there are probably aren’t enough numbers in the observable physical realm to compare such a quantity.
For example, there are only 10^15 (estimated) total hairs on all the human heads in the world, and a single person has a lot of hairs that would take months if not years to count.
And that is accounting for all of the human heads in the world! Which are billions of people that have a lot of hairs on their own.
In fact all of that combined is not even equivalent to the number of potential games in chess, this is an overwhelming comparison and it’s not even close.
Grains of sand in earth versus potential chess games
If human hair wouldn’t suffice shouldn’t we use something that is smaller, something that is too small for the human eye? How about grains of sand?
How does it fare to the total amount of potential chess games that can theoretically be played back and forth?
Well, there are about 10^23 grains of sand on Earth (estimated), which is a lot more than the total of human hairs combined but is still too small to be compared with potential chess games.
And we are talking about grains of sand! something that is too small which you can imagine would take a lot of space accounting for the whole earth.
A 10^23 definitely is no match for 10^50^50 and you can double or even triple the amount and there are still larger theoretical chess games possible.
Atoms in the universe versus potential chess games
We are going beyond all the scales and compare the potential chess games against all the estimated atoms in the observable universe.
Atoms are probably one of the smallest units we can go into in hopes of achieving this quantity. There are a total of 10^81 atoms in the observable universe (estimated) which is a huge number but is still smaller than the theoretical number of chess games.
And we are talking about atoms, something that is so small that there probably are a lot of units out there with all the numbers it takes to form just a single element.
In fact, the number of typical chess games is as many times as great as all those numbers added together (human hairs, grains of sand, and atoms in the observable universe).
The point is there are just too many variations in chess that it is pretty hard to come up with a counter-strategy against every individual move, it would take a strong processor unit to do that.
Just the sheer number of potential games would allow any competent player to deviate from any force draw/win which means that solving chess is pretty difficult if not impossible.
Potential chess games vs. Reasonable chess games
But let’s take a step back for a moment and acknowledge that some moves in the position wouldn’t really make sense and something that one wouldn’t normally play.
This means that not all theoretical chess games are actually reasonable games that are likely to appear in matches played by human or computer players.
Even though there are many potential games not every single move in the game will appear as reasonable, if we don’t count unreasonable moves it should only equate to around 10^120.
After all, sacrificing a pawn for little or no positional advantage whatsoever is something that no one plays (if they are good).
Technically such moves are possible, but it doesn’t make it reasonable, so in this context it is becoming more sound that chess can be solved.
However, we still need to remember that 10^120 is a huge number and still greater than all the atoms in the observable universe (10^81).
If we are only looking at this count, chess being solved is still a bleak possibility since there is still a huge amount to be accounted for.
Good moves vs. Reasonable moves
Now just because something is reasonable doesn’t make it automatically good, just because a move doesn’t give up material (which makes it reasonable) doesn’t mean it is a good move to attain objectives in the game.
In fact even beginners can play moves that don’t give material but are still not considered to be good moves, especially if there isn’t any thought behind it.
Having a reasonable move is different from having a good move, the so-called good moves are of different class and would further cut the total possible games (for good players) which should be around 10^70.
But still, not everyone is capable of playing good moves, a reasonable move occasionally appears into the equation especially if it is a middle-rated match.
This means that in most cases the 10^70 is actually not being followed since other just reasonable moves are being played, so there is a blurry line here.
Professionals can probably narrow even further by classifying it as great moves which would decrease the number of potential chess games, but that only means that the game is only solved for a few people.
Even if it is solved (which it is not) you still have to be at the peak of the rankings in order to actually execute the ultimate plan, which still means that it is not solved for most people.
There are just so many potential games to account for that tailoring a set of moves to force a draw/win is almost impossible.
Are there any entities that could force a draw or a win in chess?
Although there are huge volumes of draws in professional games, a decisive match still happens around 20% of the time (depending on the time control). Both human and computer games had unpredictable results even with optimal play.
One of the best ways we can identify whether a draw or win can be forced in chess is to look at the strongest entity to ever play it, the chess computers.
If such an ultimate strategy does exist then the engines would have been able to implement it to force a draw/win each and every time.
This is of course not the case, battles between chess computers do end in a draw most of the time but are not something one would consider forced, decisive games occur here and there.
Even a chess engine that is supposed to be the pinnacle of chess play is unable to force a win/draw against one another, this is an indication that chess is still not solved.
Otherwise, these entities would have figured out how to draw/win on each of their games.
One cannot force a win with white
Another assumption is that white having the first move could potentially force a win eventually if the said color played correctly. This is not the case since black can indeed pull out an unpredictable result even when white is being played by a chess computer.
The one wielding the white pieces definitely has an edge over black, this advantage however is not a forced win which means that it is still not solved.
Both the best human players in the world/ best computer are unable to secure a win with absolute certainty just by playing with white, black can still win based on the results.
Openings can be deciphered but not the result
This question of chess being solved is probably the result of endless theoretical study that forces a certain result to a degree, but here’s the thing, players can deviate from such openings to avoid particular results.
Even if a line is played through should force a draw for example, doesn’t necessarily mean that such a line is the only way to play the variation, one can choose another.
The pursuit of theoretical openings does indeed make the games more drawish, but we can still see some decisive games even from drawish lines such as the Berlin (defense).
Vladimir Kramnik for example has defeated Garry Kasparov with the drawish Berlin without Kasparov winning a single game, this means that Berlin no matter how drawn-oriented it is, is still not a forced draw.
This could be applied into opening lines that are extensively memorized even until the endgame which should lead to a draw, there will be opportunities down the line to play another move that would give chances for the players.
The consequences of a complicated game
Chess is too complicated to have a simple solution, any forced win/draw if it does exist is likely to be complex and non-applicable in most cases.
It’s likely to be something that takes skill to properly execute and can only be accessed by the elite players, it’s not gonna only cost one to five moves to force these results, likely to be a lot of moves.
I can imagine that a chess computer would be the first to have access to such a variation, and even then there is a doubt if human players can do the same thing.
Even if chess was eventually solved one day only a handful of individuals (or none at all) will be able to implement the idea, chess is just too complicated.
Then if it is the case that it is unachievable in practical play does that really make it different from not being solved at all?
Most people when they ask this question are trying to have a step-by-step guide to implement the solving idea, if it cannot be done by human players then it’s like it doesn’t exist in the first place.
Could chess be solved in the near future?
Information scientist Shannon has predicted that it would take 10^90 years to solve chess with a 1 MHz computer, however technological advancement has doubled every year.
There have been 7-piece endgame tablebases that expressed a forced mate-in-546 but not in 32 pieces.
Chess is too complicated, yes, but I cannot pretend that technology has never surprised humanity before, development can be faster than we think.
Chess computers can one day have enough processing power to identify the solving idea, we don’t know that for sure.
I’m saying that chess could indeed be solved if our technology reached the point where it can calculate quadrillions of moves per microsecond where it can completely navigate the tree branch instantly, however, we are still far from that future.
You see chess computers choose between moves based on a fixed depth search as explained by my other article (will open in a new tab).
But there are challenges such as the horizon effect that limits the calculation of current computers, if ways around it can be formulated we perhaps can be close to solving chess.
But if we are strictly talking about modern technology I personally think that it will take some 50 years for this to be even on the table, a lot of development has to take place.
It is indeed possible though since there was a time where everyone thought that computers could not best humans in chess but it did happen, technology is indeed surprising.
Chess is different from other games
This idea of solving chess was brought up by other games being solved, but we have to understand that chess by nature is different from those.
Other games such as tic-tac-toe have been solved due to the clear finite amount of potential moves in its game which does not apply to chess.
In tic-tac-toe there are only limited options each turn that even get reduced whenever each player makes a move, the options are just too few.
This is why the ultimate plan to solve tic-tac-toe is pretty simple, the options are fewer and therefore it is easier to make a combination.
How about checkers, a game that is synonymously similar to chess? Checkers is actually a solved game but is clearly different from chess.
Checkers has been solved since the pieces move in a predictable pattern (all of them move the same way) unlike in chess where every piece has unique movements that are different from one another.
This means that the more the game progresses in chess the more complicated it becomes due to these unique movements, this makes checkers similar, but is a totally different breed from a complex game such as chess.
Some endgames have been solved
Though it cannot be denied that there isn’t any ultimate plan to force a win/draw from the start of the game there are certain endgames that have definite win/draws.
An opposition (in the endgame) for example can force a win/draw if played correctly despite the material advantage/disadvantage.
But even going beyond that, models have been created to solve endgames that contain fewer amounts of units, particularly 7-piece endgame tablebases.
There are 7-piece endgame tablebases (basically endgames that only contain 7 pieces) that have been created which gives a forced mate-in-546, however, this is only in the endgame (though even chess engines can’t replicate it without access to these tablebases).
These 7-piece endgame tablebases are theoretically known as drawn but are actually a forced win in 546 moves; these endgames have been solved but chess in general (not just in endgames) is far from such a state.
The difficulty of solving chess
In 1949 information scientist Shannon produced an estimate that it would take 10^90 years to solve chess with a 1 MHz computer.
Computer power and storage technology have improved considerably since then (aka Moore’s law), where computer power and storage capacity doubles every year.
If taken into account, it would take approximately 300 years to come up with a computer that would be 10^90 times more powerful than Shannon’s 1 MHz machine.
Now you could make the argument that even the doubling advancement of technology can change to triple or quadruple over the course of years, which may be true.
But even then it would take at least 50 years to have access to such technology and to have that technology work on chess specifically, which is still a long time.
It is likely that the trend of doubling every year will continue and we wouldn’t solve the game until 300 years or so.
This is not accounting for the ceiling to which computer storage can actually reach, there might be a certain point where the computer space cannot go any higher.
Or even the opposite where technological advancement will slow down from the doubling trend that we are seeing right now, and makes this pursuit much longer.
It is unclear if chess can be solved even with future technology
If you look at our current state of knowledge it is almost impossible to truly solve chess, however, the advent of technological advancement has surprised us before so that may change.
Chess can in fact be solvable where there is a force win/draw for either white or black theoretically, but it is hard to imagine if it can be applied to practical conditions.
Even if a computer has the computer space to solve chess, it would still take a long time to think of the moves (possibly for days) due to the complicated branches.
This is why modern chess computers do not calculate all the possible positions right off the bat, they only calculate until the position gets stable.
This is to accommodate the time it takes to play chess, primarily the time control that suggests each player’s allotted thinking time when choosing the moves.
I imagine that it is very hard to imprint all the possible chess games and embed them in the computer before the matches, the sheer amount might cause a complication.
These are just one of the many challenges that solving chess presents, but as of today, there’s definitely no ultimate plan to force a draw/win in chess.
Do you now know why chess is not solved yet?
If we are ever hoping to solve chess then the bet should be on the computers and not on the human players, the complication deserves that.
It takes a lot to force a draw/win from the start of the game and the memory required is too much for elite human competitors.
However with the current trend in computer technology, it is clear that such hope will be far in the future, so we still have to wait if it is possible.
I personally don’t think that it is good for chess since it would make the game more boring thinking that there is an unavoidable outcome available.
What makes chess great is the power of customization, that the result can be determined by our own power only. This is definitely an interesting thought, that is all, sleep well and play chess.