At the start I must admit that I am not the brightest chess player, so this just might be a stupid question but: Calculated Chess moves have been determined to be infinite, as I am given to understand. But of what use is this knowledge to the game, or player when the guestimate (this can probably be calculated) is half or even far less than half would constitute legitimate moves or moves that make no sense at all (a move because it can be moved to "x" without reason. The question that should be quired is, "how many legitimate moves are there in chess that lead to a legitimate conclusion 'win, draw, or forfeit'?" Who knows that actual legitimate moves that can be made which evolves into a legitimate conclusion?
From Shannon's Programming a Computer for Playing Chess:
From these remarks it appears that to improve the speed and strength of play the machine must:
- Examine forceful variations out as far as possible and evaluate only at reasonable positions, where some quasi-stability has been established.
- Select the variations to be explored by some process so that the machine does not waste its time in totally pointless variations.
The first can be done by evaluating all checks, captures, and threats - a true and tested method to avoiding blunders.
But notice "some process" in the second bullet point has to be set by you. There's an easy way to choose this, and it's also noted in Vukovic's Art of Attack:
If the threat move is the same on two consecutive plies (with one ply in between them to account for the side to move), the threat move is a serious one and the search is extended.
Threat moves are moves that, if the other side were to (illegally) 'pass' on this move, they would be mated, material loss would occur, or some other favorable advantage would occur.
If I attacked your queen with my knight, and your queen moves to some spot but is still attacked by my knight, that is a serious threat move. Then we check the other possible squares that the queen can move to, and if any resulting position is unfavorable, then the position of my knight is superior and considerable for my next move.
So what else?
If a side makes a move and it leads to a mating attack in one variation without compromising your position in all variations (one of the variations is a serious threat), it is a good candidate for your next move.
We can also turn this around.
If we attack the king and the defending side has to compromise his position (by making his surrounding squares weak, for example), that is a considerable candidate move. Because it's more forcing, this is of a higher category.
Of the highest category is attacks on the enemy king with certainty of mate. Huge compromises like a queen sacrifice would have to occur to stave off this attack.
Granted that there might be an infinitesimal number of possible moves in a chess game, in reality only a few really make sense on any given turn, so the vast majority can be excluded. Nevertheless, the tree of the total number of reasonable moves in a game would probably still be beyond calculation, but I can't think of any good reason to know what that possible number might be anyway.