@12789
"I only inspected and found none can result from optimal play by both sides."
++ You can verify yourself. Here is the random sample file of 10,000 positions without promotions to pieces not previously captured. The file is raw, before legality check, i.e. contains illegal positions. The file is labelled 'noproms', meaning no promotions to pieces not previously captured, i.e. it contains only positions from 1 box of 32 chess men, but some positions have e.g. 2 dark-square bishops on one side. I inspected the positions and found none that could result from a reasonable, let alone perfect game with optimal play from both sides.
If you think one of these could, then try to come up with a reasonable game that leads to it.
You do not have to prove optimal play, only present reasonable play.
"but not why you should be starting with 10^38 in the first place"
++ The number of legal positions is (4.82 +- 0.03) * 10^44.
However, the 3 random samples shown cannot result from optimal play by both sides,
as both sides have multiple underpromotions to rooks and/or bishops,
and such underpromotions only make sense to avoid a draw by stalemate,
and it cannot be optimal play for both sides to avoid the draw.
Per Tromp the breakdown of raw position count before legality check is:
promotions: 0 positions: 19201527561695835455154058755564594798074
promotions: 1 positions: 382355871178268365234183218244670372695068
promotions: 2 positions: 3666683498600457464891752992187014354136188
promotions: 3 positions: 22267499667290257736558400874926183060238400
promotions: 4 positions: 95095065373967146179514528215894174339720228
promotions: 5 positions: 300571414300527313744528888013946849776424304
promotions: 6 positions: 721668497316402902485416452421325823057710432
promotions: 7 positions: 1329934072135692805837128923570048899100334756
promotions: 8 positions: 1874962044164806332602085236357597905810647344
promotions: 9 positions: 1980800128935921108339671872170042183548439128
promotions: 10 positions: 1492529839915108301878747832838229979840571492
promotions: 11 positions: 722080907452760073481816196266539169729817880
promotions: 12 positions: 175351843526979273665005184194531833618491680
promotions: 13 positions: 7338473695924787177946719990630518998574920
promotions: 14 positions: 45087168602668580254351850721788483191140
promotions: 15 positions: 55323182237139471340692375109727946960
promotions: 16 positions: 11716401834002951530424702440978260
Total: 8726713169886222032347729969256422370854716254
Promotions to pieces not previously captured occur in master games and in ICCF WC Finals draws, but positions with 9 promotions to pieces not previously captured make up the lion's share of the (4.82 +- 0.03) * 10^44 legal positions. That is why 10^44 is no good starting point.
A better starting point is 3.8521 * 10^37 from An upper bound for the number of chess diagrams without promotion.
'Without promotion' here is short for 'without promotion to pieces not previously captured'.
For some positions you can prove a piece is original, not promoted,
and for some positions you can prove a piece must be promoted, not original,
but generally you cannot tell from a position if it contains promoted pieces or not.
'Without promotion' means 'without promotion to pieces not previously captured',
or, in other words, positions possible from 1 box of 32 chess men.
The 10^37 is too restrictive, as positions with 3 or 4 queens do occur in master games,
and in perfect games with optimal play from both sides as we know from ICCF WC Finals draws.
I arbitrarily multiply by 10 to include such positions, leading to 10^38.
That is why starting from 10^38.
"what optimal play has to do with anything"
++ Weakly solving chess is about optimal play by both sides: positions that cannot result from optimal play by both sides are not relevant to weakly solving chess.
The 110 draws out of 110 games of the ongoing ICCF WC Finals are examples of optimal play by both sides and constitute at least part of a weak solution of Chess.
Moreover it is redundant, as it shows several strategies to achieve the game-theoretic value instead of the required one.
On the second comment, @tygxc said that chess hasn't been solved yet
On the seventh, he said it's a draw
what?
Well spotted.
But then you'll see he tried to qualify it by posting different definitions of 'weakly solved' and that terminology is the gremlin at the center of much of the discussion here.
tygxc tries to maintain that 'perfect games' exist and that they resulted in a draw because they were 'perfect'.
That is Disinformation.
Bobby Fischer suggested publically to the effect that 'if nobody makes a mistake the game ends in a draw'
but that is misleading because 'if nobody makes a mistake' is an Abbreviation of the actual reality.
The actual reality is:
'If neither player makes a big enough mistake that is both detected and exploited sufficiently for a win by the opponent - or neither player makes a mistake that is otherwise sufficiently exploited for a win by the opponent or that otherwise leads to a loss for the player making the big enough mistake - then obviously the game ends in a draw Unless somebody's flag falling on their chess Clock also results in 'not a draw' too or instead'
That's the actual reality. Happens constantly all over the world.
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And there's another Gremlin about terminology there too.
In that second case - word phrasing that is meant as an abbreviation resulting in saying something else and spreading disinformation.
The continuing improvement of engines indicates there aren't any known 'perfect' games because tomorrow's engines are finding wins (in other words 'mistakes') that yesterday's engines didn't find.
But tygxc will keep pushing his disinformation that there are 'known' perfect games and pretend that that 'proves' his Disinformation that 'chess is a draw with optimal play'.
Which would mislead beginner and novice players and other players.