> Yes, that's pretty much the human intuition for why no one doubts that White will win. But it is very, very far from a mathematical proof.
White will win if he plays perfectly: this is mathematically assured because white has an advantage of nine points. The only way for white to lose or to draw is by extreme error. The article assumes a perfect game, so I too assume that white will play a perfect game.
> Let me remind you that each ply has a branching factor of about 20, which means each move has a branching factor of several hundred. In most positions you'd be lucky to be able to calculate even one or two forced exchanges, let alone all the way to the end of the game.
As I recall, Deep Blue was calculating at a depth of more than eight moves...
> The Deep Blue chess computer which defeated Kasparov in 1997 would typically search to a depth of between six and eight moves to a maximum of twenty or even more moves in some situations. -- http://en.wikipedia.org/wiki/Deep_Blue_(chess_computer)
I find it difficult to believe that this wouldn't have improved or could not be improved upon, since this was based on the technology available in 1997. It's safe to say we've made progress since then.
While you may not be able to calculate an entire game, you could certainly calculate all the exchanges required to reach a properly winnable and calculable endgame. This is pretty damn close to being able to calculate a whole game...and you're assured victory.
As I said, once you get to a point of two kings and a queen, it's trivial.
I think one important point you're missing is that a chess engine looking to mathematically prove a victory is very different from the ones that play against grand masters. Deep Blue may have been able to calculate 6 to 8 moves in advance, but that was after it pruned all the moves that were obviously incorrect. When you're trying to prove something mathematically however, you have to assume that even something as silly as sacrificing a queen for a pawn with no obvious positional gains is a valid move and calculate all possible branches taken from that move until checkmate some 30 moves down the road.
For example, checkers is a vastly simpler game than chess. Yet, it took 18 years of constant computation to solve it [1]. Even a game as simple as tic-tac-toe has 255,168 possible games [2]. The estimated number of chess games is 10^10^50 [3].
It is important to remember that "the value of 1 Queen is equivalent the value to 9 Pawns" is only an heuristic. It helps the players to make decisions but nobody wins only because he has more points.
And the values are not written in stone. For example, Knights and Bishops usually have the same value, that is like tree pawns for each one. But if the position is open the Bishops are usually more valuable and if the position is closed the Knight are more valuable.
I'm also completely sure that in "Chess with Queen" White has a wining strategy, but being completely sure is not a proof. (I have been wrong before!)
White will win if he plays perfectly: this is mathematically assured because white has an advantage of nine points. The only way for white to lose or to draw is by extreme error. The article assumes a perfect game, so I too assume that white will play a perfect game.
> Let me remind you that each ply has a branching factor of about 20, which means each move has a branching factor of several hundred. In most positions you'd be lucky to be able to calculate even one or two forced exchanges, let alone all the way to the end of the game.
As I recall, Deep Blue was calculating at a depth of more than eight moves...
> The Deep Blue chess computer which defeated Kasparov in 1997 would typically search to a depth of between six and eight moves to a maximum of twenty or even more moves in some situations. -- http://en.wikipedia.org/wiki/Deep_Blue_(chess_computer)
I find it difficult to believe that this wouldn't have improved or could not be improved upon, since this was based on the technology available in 1997. It's safe to say we've made progress since then.
While you may not be able to calculate an entire game, you could certainly calculate all the exchanges required to reach a properly winnable and calculable endgame. This is pretty damn close to being able to calculate a whole game...and you're assured victory.
As I said, once you get to a point of two kings and a queen, it's trivial.