Chess will never be solved, here's why

@MARattigan, do you accept my point that we can ignore all positions where both sides have extra rooks or bishops?

With the way positions for black and white have dual use in a solution (i.e. a legal move that reaches a position that has already occurred in the analysis tree for the other side need not be analysed further) we need only deal with positions where "side B" has <=2 bishops and <=2 rooks.

That should save a useful amount on the Tromp number. Or at least what would be a useful number if a solution was close to feasible.

I wonder how much it saves?

@MARattigan, do you accept my point that we can ignore all positions where both sides have extra rooks or bishops?

which seems not to be understood by people who are rather weirdly in my estimation keen on deductive reasoning. I tend to look at such people with a critical and sceptical eye. It should be possible to meet in the middle somewhere.

<<<<"the 10^7 sample of master games"
++ Chess games are no random events, they follow logic, especially at higher levels.

You don't understand the notion of a sample of variation.>>>
Here it might be best to briefly explain what it is you feel isn't understood. What tygxc is saying, as indidated by "especially" is that there's a greater tendency at higher levels for chess games to be accurately played. It really is a communication problem. It takes two people to communicate.

His error is in thinking there is any conflict between the two. For example, imagine you play two super-engines (as consistently logical as you can get in chess) against each other for a million games . Like all real top engines, such as the latest Stockfish, I assume there is some random variation in their play.

This is enough to have very good statistical knowledge of the long run results you would get between the two engines. Suppose, for example, one of the engines wins 1000 games and the other wins 1000. You have a good estimate of the win rate of each engine (around 0.1%).

You also now know that if you sample 100 games between these engines, you can expect to usually see 100 draws roughly 80% of the time. (Exact number can be calculated)

Under 20% of the time you will see 99 draws. About 4% of the time 98. And so on

Hopefully the stochastic nature of the results and the appropriateness of treating them as such is clear (it is the basis of all use of Elo type rating systems, and others).

"You are arguing for making an entire class of legal moves illegal" ++ No, I am arguing that the game stays the same if underpromotions to pieces not previously captured were illegal.

A claim which definitely can't be justified. You are appalling at reasoning logically.

Again, rather than respond like this, perhaps explain the exact context. I commented on this and explained why in my opinion tygxc's assumption is prone to inaccuracy by pointing out a situation where it would be inaccurate.

I have explained how ignoring the possibility of underpromotion (or inappropriately large classes of underpromotion) could sometimes makes a generated weak solution strategy fail. 

Specifically, suppose @tygxc's suggested algorithm reaches a position where underpromotion to an extra rook is the only way for black to win. His algorithm literally can't see that the underpromotion exists - it's effectively illegal - and says "this position is fine for white, giving a draw". The strategy is invalid and this is indetectible to the algorithm (because it does not know about the possibility of underpromotion in that position).

It's worth pointing out that this situation is very rare, but it seems totally impractical to prove that it is never relevant. If someone can do that, I will buy them a beer!

"it is a sample of 3" ++ All positions counted by Tromp look like that.
Most have 9 promotions to pieces not previously captured.
99.95% have 3 to 16 promotions to pieces not previously captured.

"I was for a few months the highest rated daily chess player on chess.com."
++ chess.com daily is a joke. One may think for a day and the opponent for a minute.
One may play one game and the opponent 100 games simultaneously.

"No engines, no tablebases" ++ Impossible to verify.

"very unusual things happen occasionally" ++ Chess is a very logical game.

"As many master games show."
++ Show one real master game with an underpromotion to a piece not previously captured.
Not a Nakamure trolling blitz game with 6 knights, not the Lasker trap.

"If that happens once in less than 10^7 games, that might happen 10^10 times in 10^17 games" ++ But a rare exception should not change the total count.

"in an enormous sample"
++ It is no random event, there is an iner logic resulting from the Laws of Chess.
A pawn needs time to reach the back rank, and in that time pieces get exchanged,
therefore promotion to a piece not previously captured is rare.
An average Tromp position has 9 promotions to pieces not previously captured.

The most reasonable piece to promote to is a queen.
Promotion to a knight is rare, but happens sometimes for the unique properties of the knight. Promotion to a rook or even bishop is even more rare,
and only happens to avoid a draw by stalemate.

Underpromotion to a piece not previously captured is the product of two rare events that does not occur in master games, not because the sample is tiny, but because of the inner mechanics of Chess.

That is why 10^38 is more reasonable than 10^44.

Even the 10^37 is too many: here is a legal position as counted in the 10^37, but which cannot be reached by reasonable play, let alone optimal play by both sides:

2398 is very good if you achieved it here. Well done.

My peak was 2225, both here and the same on Chess World. I found that I would have had to put a lot more time into it to get higher, like you by limiting it to a couple of game maximum, at a time and being willing to analyse for several hours per week. I wasn't willing to do that.

I found, at the time, that playing Daily chess here had a very positive effect on my otb play at classical speeds. In this incarnation I maxed at 2125 because I was less willing to put in time and effort than before and I had thought I had noticed that it was adversely affecting my performance in classical. I didn't play at all here for about a year except Chess960 and then after a break of a few months, played over 6000 5 mins blitz games over a year and a half. That was very beneficial for my return to otb chess and I won a rapidplay with 5/5 and have an otb rapidplay grade once again. ECF seems to have lost my last grade and details even though my last rated game was only 5 years ago.

I completely get where you are regarding tygxc but I also feel I understand him and that he's making a good point, but in his own way, which seems not to be understood by people who are rather weirdly in my estimation keen on deductive reasoning. I tend to look at such people with a critical and sceptical eye. It should be possible to meet in the middle somewhere.

I'm aware you don't know the meaning of the word "compromise but this conversation is not for you. I find it difficult enough to find people who have some kind of idea of reality as it is without you wanting to join in.

Either read what I'm saying, understand it and understand what I'm doing, which you cannot manage, or don't expect your comments to be taken seriously. Various layers of interaction go on and leave you as an uncomprehending bystander.

One person at a time pls. Also, I'd prefer to talk to someone who is more my intellectual equal than you are, thanks.

Watson.

I don't need to. You do. I know you were full of incandescent rage and fury because Elroch and I were talking about something and you felt left out. He's all yours again.

Dioinnnnng.