Calls to a non-existent algorithm are just like believing in the paranormal. There's no basis for it. There's only one method currently underway to solve chess, and that is building tablebases backwards from all possible mates. Significant enough progress on that will not happen in our lifetimes, or even within any possible technological future that we can make concrete plans toward. This thread, like all the other threads on this topic, was over before it began.
As I have pointed out in the past, trying to build a bridge to the steel structure that tablebases represent using the mud and reeds and Tygxc proposes is not a worthwhile effort. But at least it's an attempt of some sort, deluded as it may be, which is more than can be said for Optimissed's talking in circles, which is pure trolling and pseudo-intellectual twaddle.
Just a small quibble. A brute force search isn't practicable. Looking at all permutations of moves takes billions of years, even with the latest computers. So solving chess isn't really possible until and unless an algorithm is developed, which can recognise accurately a bad move and cut it out. It's necessary to leave the fuzzy area which consists of moves that are only probably bad. Of course, a human that can't tell that 1. e4 e5 2 Ba6 definitely loses for white isn't going to help to define good and bad moves. For practical reasons, their lack of willingness to try to cut out bad moves means that this project of solving chess is a non-starter, so they really shouldn't be involved. They're the human equivalent of "bad moves".
For the purposes of solving, a bad move is any move that changes the game state and a good move is one that doesn't. The game state can be defined as the theoretical outcome of any position, given best play by both sides. You say that random moves are a sample of all possible moves and would give an accurate representation of game length; but I don't think that's correct because a game of chess is a different thing from a random permutation of legal moves. The latter isn't suited to solving chess in any meaningful way. A solution won't be viable until an accurate way is found to cut out obvious errors and, of course, most random moves are obvious errors.
There's definitely a lack of focus in thinking about this subject, which is clearly displayed on this thread and which isn't helped by incompetents like btickler and a couple of others getting involved, because they're bored and want to troll. I wouldn't count Mr Desperate among these, although his thinking is not error-proof. Some of the others aren't even capable of considering interesting questions because their determination to troll is so powerful. Unfortunately there's no thread owner to block them.
Let's not pretend we don't know who is willfully trolling here. The only reason you are pivoting to "incompetents" now is because you were recently called out about your other "I" words, also historically used for trolling. You talk a lot, but you don't have much to say. Just another day of fuzzy logic and bitterness, 'til your wife comes to make you go to bed.