@MARattigan, wouldn't you agree that saying "a fundamentally different strategy" to solve chess is much like saying "we need faster than light drive to travel around the galaxy"?
. the truth is that there is almost certainly no such strategy that will take us a large fraction of the way to a solution being possible (on a log scale). Rather the large majority of what we need is an increase in computatational resources, whatever method is used.
When comparing here, I am thinking on a log scale. Say we need 10^15 more computing power (not a precise number), we might pull that down by a factor of, say, 10^2 with brilliant advances in strategy, but the large majority of the gap remains (on a log scale).
No. I wouldn't agree.
Consider the following two player game.
At the start of the game the index is set to 3.
White moves first and chooses a positive natural number.
If in a set prearranged time Black can find another positive natural number such that when the two numbers are raised to the index and added the result is some other natural number raised to the same index he wins.
Otherwise the index is increased by 1 and Black moves next with the roles reversed.
Thereafter the players alternate moves, the index increasing by 1 each time.
It was suspected for a long time that the game was drawn and some results were established such as, like chess, the game could not be won on the first move. But relatively recently the game was completely solved as drawn.
Note that the game tree, game states and branching factor are all infinite.
But the solution was not found by a BFI routine run on a computer. It was, in fact, a fundamentally different strategy.
I think if chess is ever solved the same will probably be true.
Edit: Now I think about it, it is trivial to prove the game I outlined is drawn, but still by a fundamentally different strategy.
Stockfish evaluates this position as +13.6 for white. Should be enough, surely? (Chess.com analysis doesn't correct it, but uses some heuristic to conclude what the value is).
It doesn't matter for practical chess.
@playerafar mentioned excluding all bishops and immediate stalemates. This should be a better example at -14.4
I meant that 13.6 pawns should be enough to win.
So, @playerafar, what is your algorithm for disposing of that one?
There's the problem. There are so many "special" positions that a set of exclusion criteria will never be enough.
Nice position. Took me a while to realise black can't stop white saving it (duh).