I agree with almost all of that except this part:
"Adding the missing pieces at the 7 or 8 man tablebase level is relatively minor"
The idea that 'adding a piece' gets easier wouldn't seem to follow.
Even though you'd get more 'repeats'.
This was discussed some time ago.
For reference - look at how tough it was adding just one piece to just six pieces.
How long it took.
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Every time you add another piece - as the number of pieces on board increases - then that piece relates to more other pieces.
Another factor that I don't think has been discussed much -
how the number of moves immediately available increases each time you add a piece.
Many might say 'well no not if you're adding a pawn because that pawn doesn't add many moves' ...
missing the point that that's only for one move deep.
You add anything at all - increases the number of moves available -
but then that grows with a depth of 2 ply three ply and so on 'ahead'.
Totally neglected factor so far.
---------------------------------------
Trying some relevant math.
Twenty to the 10th power and twenty-five to the tenth power.
For the first I got an answer of about ten trillion.
For the second I got about 95 trillion.
Idea: correspondence with a position that averaged about twenty moves available over ten ply versus correspondence with a position that averaged twenty-five moves available over ten ply.
Ten ply is only five moves deep.
The computers are computing far deeper than that.
-----------------------
Then I tried the same two numbers on an exponent of 30.
For the first I got a number of about 1000 x (a trillion cubed)
For the second I got a number about 100,000 times greater.
I meant the missing "pieces" of the tablebase, i.e. castling positions et al. A good example of why using weak and strong here is not advisable. I should not have said "pieces" without clarifying.
Skimming through all this I will say that I should have said castling rights and/or en passant (and/or any other exclusions made for expediency). The important part is that while tablebases at the 6/7/8 levels can be called incomplete without including everything, using the terminology weak or strong just causes confusion, and that technically tablebases will always be incomplete (since they do not include draws, if nothing else).
Adding the missing pieces at the 7 or 8 man tablebase level is relatively minor...and as Elroch mentioned it's only going to be a tiny fraction of positions added. That would still require significant effort later down the road...if we're going to calculate 10^40+ positions, then adding various moves would require calculating say another 10^35. Trivial enough at each stage, but significant in total.
I agree with almost all of that except this part:
"Adding the missing pieces at the 7 or 8 man tablebase level is relatively minor"
The idea that 'adding a piece' gets easier wouldn't seem to follow.
Even though you'd get more 'repeats'.
This was discussed some time ago.
For reference - look at how tough it was adding just one piece to just six pieces.
How long it took.
-------------------------
Every time you add another piece - as the number of pieces on board increases - then that piece relates to more other pieces.
Another factor that I don't think has been discussed much -
how the number of moves immediately available increases each time you add a piece.
Many might say 'well no not if you're adding a pawn because that pawn doesn't add many moves' ...
missing the point that that's only for one move deep.
You add anything at all - increases the number of moves available -
but then that grows with a depth of 2 ply three ply and so on 'ahead'.
Totally neglected factor so far.
---------------------------------------
Trying some relevant math.
Twenty to the 10th power and twenty-five to the tenth power.
For the first I got an answer of about ten trillion.
For the second I got about 95 trillion.
Idea: correspondence with a position that averaged about twenty moves available over ten ply versus correspondence with a position that averaged twenty-five moves available over ten ply.
Ten ply is only five moves deep.
The computers are computing far deeper than that.
-----------------------
Then I tried the same two numbers on an exponent of 30.
For the first I got a number of about 1000 x (a trillion cubed)
For the second I got a number about 100,000 times greater.