A super strategy to always win chess – does it exist?

Chess is a fascinating game: it is over 500 years old, it has many difficulty levels and it looks great on your resume if you are a chess grandmaster. The question of today is:

Is there a strategy available for chess, such that you can print it on paper and you can win a battle against Garry Kasparov by just following the instructions on the paper?

Game types

Let’s look at the fundamentals: according to game theory, games are divided in different groups based on their characteristics. Characteristics like if players cooperate or compete, if players play in turns or simultaneously, etc. Chess (just like Checkers and Tic Tac Toe) belongs to a category called “perfect information games”, based on the following characteristics:

• Per turn, one player makes one move (Sequential)
• There is no chance involved (Deterministic)
• All future moves can be known.

Zermelo

In 1913, a German mathematician named Zermelo came up with an idea called ‘Zermelo’s Theorem’. He claimed that all perfect information games have a strategy available. This strategy is either to make White force a win, to make Black force a win or to make White force a tie.

Wait a minute. But that means that if someone knows this strategy, he will always win or play a tie if he plays the right colour? Correct.

Awesome! Lucky enough there is a catch: we can proof that Zermelo is right and thus that such a strategy exists, but to compute such a strategy we need a lot of computer power. Chess has so many possible moves that we still don’t have enough computing power to calculate this strategy for chess. Something that chess players can be happy about, as  Zermelo noted:

“if you know the winning strategy, the game is meaningless to play.”

Proof

So how do we know that this is true?

The easy way is to make a diagram (game tree) with all the possible states in which the game is finished (terminal nodes) and mark who won the game. Add all the possible states just one step before the game is finished and derive who will win the game in this state based on the end state. You can do this until you are in the beginning state of the game and then you have found the full strategy. This is an oversimplified version of what mathematicians call backward induction. 

And of course, a picture says more than a thousand words. As an example I created a diagram for Tic Tac Toe. In the most upper corner you see the starting point of the game, further down you see all the end states. The yellow boxed outcomes are ties, the blue boxed are wins for player X and the red are wins for player O. While creating the logic, I started by drawing a few boxed endgames and worked my way up to create possible gamestates before the end state. 

Now, let’s assume that the player always chooses a move which is best for himself, i.e. Player X plays a blue action, and if not possible a yellow one. Player O plays a red action, or if not possible a yellow one. Then we can conclude that in the beginning situation, Player X will win if he just follows the blue lines. Player O can only win, if Player X makes a mistake.

Conclusion

So, the answer is that yes, there is a winning strategy available for chess in such that either Black or White can force a win or White can force a tie. We can proof that this strategy is available, but we don’t know what the strategy is, because we cannot compute it.

Huh, but did chesscomputer Deep Blue not win from Gary Karsparov in 1997? Yes, it did, but not by using the winning strategy, but by using smart A.I. tricks to win the game. In one of the next posts I will explore those tricks, stay tuned :)

Special thanks to ABCartoons.nl for the awesome cartoon of Ernst Zermelo.