Chess is one of the most studied games in human history.
Grandmasters have analyzed it for centuries, and modern computers can defeat the best human players.
Yet despite all that progress, one simple question remains unanswered:
What is the true outcome of chess with perfect play?
If both players made the best possible move every time, would the game always end in a draw?
Could White force a win?
Or is Black secretly winning from the very first move?
Surprisingly, we still don’t know.
And the reason is simple: the game of chess is astronomically large.
When Is a Game “Solved”?
In mathematics and computer science, solving a game means something very specific.
A game is considered solved when we can determine the exact outcome assuming both players play perfectly.
There are different levels of solving a game:
Weakly solved
- We know the outcome from the starting position with perfect play.
Strongly solved
- We know the optimal move from every possible legal position in the game.
Some simple games have already been solved this way.
For example, tic-tac-toe has been strongly solved. Every possible position has been analyzed, and we know that if both players play perfectly, the game will always end in a draw.
The reason this is possible is that the game is small. There are only about 255,168 possible games of tic-tac-toe, which computers can analyze easily.
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But chess is a completely different story.
A Real Example: Checkers Was Solved
In 2007, researchers led by Jonathan Schaeffer solved the game of Checkers.
After analyzing hundreds of billions of positions, they proved that perfect play from the starting position always leads to a draw.
This means checkers is weakly solved.
Computers now know the optimal strategy from the beginning of the game, although not every single possible position has been mapped perfectly.
Even solving checkers required:
- decades of research
- massive databases
- enormous computing power
And chess is vastly more complex.
The True Size of Chess
Every move in a game creates new possible futures. If you imagine every move branching into many more moves, you get what computer scientists call a game tree.
Game Tree Chess
In chess, the average position offers roughly 35 legal moves. This number is known as the branching factor.
That means the number of possible positions grows extremely quickly:
After 1 move → about 35 positions
After 2 moves → about 1,225 positions
After 3 moves → about 42,875 positions
After 4 moves → about 1.5 million positions
And it keeps growing exponentially.
A typical chess game lasts 40–60 moves, which causes the number of possible game sequences to explode.
Claude Shannon, one of the founders of information theory, estimated that the number of possible chess games is roughly: 10¹²⁰
This estimate is known as the Shannon Number.
For comparison, scientists estimate that the observable universe contains roughly 1⁰⁸⁰ atoms.
The number of possible chess games is therefore vastly larger than many numbers we encounter in everyday science.
Why Computers Can’t Simply Calculate Everything
At first glance, it might seem like this is just a matter of computing power. Modern computers are incredibly fast, and chess engines analyze millions of positions every second.
But brute-forcing chess is still far beyond our reach.
Even if a computer analyzed one billion positions per second, it would still take far longer than the age of the universe to explore the entire game tree.
And time is only part of the problem.
Solving chess would also require:
- unimaginable amounts of memory to store positions
- enormous energy to perform the calculations
- sophisticated methods to manage the enormous search space
Because of these limits, modern chess engines take a different approach.
How Modern Chess Engines Actually Work
Instead of trying to calculate every possible future move, chess engines focus on searching the most promising parts of the game tree.
They rely on techniques such as:
- Alpha–beta pruning, which eliminates branches that cannot influence the final decision
- Evaluation functions, which estimate how good a position is
- Pattern recognition and neural networks, which help identify strong strategies
For example, the engine Stockfish searches extremely deep variations using highly optimized algorithms.
Meanwhile, systems like AlphaZero, developed by DeepMind, use neural networks and self-play to learn strong strategies.
These programs play at superhuman levels, but they do not know the true mathematical solution of chess.
They simply make extremely strong predictions about which moves are best.
Is Chess Actually Solvable?
In theory, yes.
Chess is a finite game with clear rules and a limited board. That means a complete solution must exist in principle.
But in practice, solving chess would require exploring an enormous number of positions, far beyond what current computers can handle.
It may take:
- centuries of computing advances
- entirely new algorithms
- or breakthroughs in hardware
before such a solution becomes possible.
For now, chess remains unsolved.
The Beauty of an Unsolved Game
In many ways, the fact that chess remains unsolved is exactly what makes it so fascinating.
Some games eventually become mathematically closed. Once the optimal strategy is known, there is little left to discover.
But chess is still full of mystery.
New strategies continue to emerge. Grandmasters still discover ideas that have never appeared before. Even powerful engines occasionally reveal surprising concepts that humans had never considered.
A simple 3×3 grid like tic-tac-toe can be completely mapped.
But the 64 squares of a chessboard still hold an immense universe of possibilities — one that continues to challenge players, mathematicians, and computers alike.
And for now, the final answer to chess remains one of the most intriguing open questions in the world of games.
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