[The King’s Gambit has been solved.]( According to ChessBase:

> Fifty years ago Bobby Fischer published a famous article, “A Bust to the King’s Gambit”, in which he claimed to have refuted this formerly popular opening. Now chess programmer IM Vasik Rajlich has actually done it, with technical means. 3000 processor cores, running for over four months, exhaustively analysed all lines that follow after 1.e4 e5 2.f4 exf4 and came to some extraordinary conclusions.

Rajlich’s response to the question of solving a chess gambit is fascinating:

> 1.e4 e5 2.f4 exf4. We now know the exact outcome of this position, assuming perfect play, of course. I know your next question, so I am going to pre-empt it: there is only one move that draws for White, and that is, somewhat surprisingly, 3.Be2. Every other move loses by force.

> *CB: How can you have worked that out, aren’t there gazillions of possible continuations?*

> Actually much more than “gazillions” – something in the order of 10^100, which is vastly more than the number of elementary particles in the universe. Obviously we could not go through all of them – nobody and nothing will ever be able to do that. But: you do not have to check every continuation. It’s similar to Alpha-Beta, which looks at a very small subset of possible moves but delivers a result that is identical to what you would get if you looked at every single move, down to the specified depth.

> *CB: But Alpha-Beta reduces the search to about the square root of the total number of moves. The square root of 10^100, however…*

> Yes, I know. But think about it: you do not need to search every variation to mate. We only need to search a tiny fraction of the overall space. Whenever Rybka evaluates a position with a score of +/– 5.12 we don’t need to search any further, we have our proof that in the continuation there is going to be a win or loss, and there is a forced mate somewhere deep down in the tree. We tested a random sampling of positions of varying levels of difficulty that were evaluated at above 5.12, and we never saw a solution fail. So it is safe to use this assumption generally in the search.

This notion of a “problem space” or a “solution space” is something worth exploring more, both for what it might do for humanities research but also for possible research into as a phenomenon itself.