@MARattigan
I think your post #2948 was in response to my post # 2945 a few before.
This one: https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?cid=68837185&page=148#comment-68837185
Looks like some posts have been deleted - I get an access violation on that link and #2948 is one of Elroch's.
A main point of mine in that post (among other points) is the relevance of strong to weak.
Much earlier in the forum I was talking about 13 to the 64th and factorials about 32 squares having to be empty and two Kings only.
Those posts of mine got good reaction at the time.
Strong math - to get strong results.
When the discussion 'converges' on weak solving - which its been doing for about 3000 posts - then 'strong' is still relevant.
Including as part of the process before 'weak' and also to contrast with 'weak'. So that its clearer what's being omitted.
The main point is a weak solution solves only the starting position but a strong solution solves all positions. But that is using the term "position" to mean all aspects of the situation that are relevant to possible contiuations - a diagram is only one aspect and doesn't determine the possible continuations.
Terminology and worry about 'positions' was not intended.
There's quite a lot of controversy here about 'games' versus 'positions'.
'Positions' can be defined according to the context.
That's true.
In the context of solving chess, I would say "position" should be equivalent to a FEN less the ply count field if "chess" is taken to be the game under basic rules, but chess under competition rules is a different game with different solutions (weak or strong and possibly also ultra-weak) and, in the context of a forward search, "position" should be equivalent to a FEN less the ply count field + a list of positions with the same material that have previously occurred and how many times each has occurred. (The latter is also equivalent to a FEN with ply count 0 + the moves leading to the position, but in that case different specifications could represent the same position.)
If its relevant in the context whose move it is - then that's included.
If its not then it isn't.
Relevant in the context of solving either game.
In some of the discussion we even had a suggestion that positions that would have to be illegal - like adjacent Kings - should be allowed in advance. And then cleaned up later.
I disagreed with that.
But maybe that's valuable in the programming aspects of it.
The point is that adjacent kings are just one case of the side not to move being in check. Those positions are all illegal and have to be removed anyway. (Note that I have to say "those positions" - the diagrams may or may not tell you if the situation is legal.)
Tromp deemed it easier or more efficient to leave that to the legality checker. The number of positions from which his sample was taken would be higher, but the sample would contain a higher fraction of illegal positions. That's OK for estimating the true number of legal positions; he's not trying to find an accurate upper bound.
(Though the legality checker couldn't be guaranteed to do a complete job, because the legality problem is not yet solved.)
Definitions according to context.
By the way - when I went to the Tromp page you linked - there wasn't much there. Something about 'complex formula'.
Just now I went to a Wikipedia article about Claude Shannon (yes I believe Shannon was mentioned earlier) - he's got a neat formula that also ends up around 10 to the 44th.
Saw this too: But some of it is wrong:
https://chess.stackexchange.com/questions/5592/what-is-the-number-of-legal-positions-in-a-chess-game
I think Tromp's number is agreed to be the closest. This link and this link are the only links I provided for Tromp and both make the code available, so I don't see what more you would want. So far as I know the code for the improved upper bound of 10^45.888 has not been published, nor has the figure been firmly asserted by Tromp.
Shannon's formula actually seems to give something between 10^42 and 10^43 but the formula itself could be distinctly more accurate. He only needed to show a 32 man tablebase was impracticable and it's already impracticable at 10^42.
I want to learn how to debate. Any advice?