Chess will never be solved, here's why

What exactly is your number meant to be, Ghostess? The same as below?

As you say, OEIS has the 26% higher number 69,352,859,712,417 for the number of possible 10 ply chess games (and is a very reliable source). On the other hand the number of _positions_ after 10 ply is surely much smaller due to transposition. And there are surely _not_ enough short mates to make up the difference. In fact _all_ of the games with 0 to 9 plys added together are only a few percent of the number of those with 10 plies. (See OEIS).

Even if your calculation is not working as intended, kudos for trying to do such a computationally demanding thing. Probably none of the others here have dared to try!

To try to determine the reason, I would suggest doing the same calculation for 1, 2, 3 ... ply.

More misinformation.

Shannon never said that the number of possible chess games was 10¹²⁰ - read his paper.

The number of possible games under FIDE basic rules is infinite (ℵ₀ if you count only finite games, ב‎₁ if you count games of length ω).

The number of possible games under FIDE competition rules is estimated to be somewhere between 10²⁹²⁴¹ and 10³⁴⁰⁸² according to this paper.

Hi MEGA
when considering tygxc's motivations including the ones you and I have mentioned ...
such motivations are usually not exclusive of each other.
In other words and/or instead of just 'or'.
A or B. Or both.
And if more than two - possibly all.
It may seem that one might knock out another as a possibility ...
but with the internal psyche of those who don't care whether they believe themselves or not and thereby 'lose track' of that - there's typically internal oscillations and vacillations and cycles regarding how much they believe of their nonsense.
Its a transient situation.
And it shows as whoever trolling/disinforming moves around a clock face of different retorts and tactics.
Which can take weeks or days or even just minutes - to move around that dial.
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With tygxc though - while he's pushing his disinfo - he's never that far from the forum topic plus he's minimally personal.
O - that's @Optimissed - is much much worse.
tygxc's posts appear to reflect that he wants the discussions to be about the forum subject - even as he also obviously wants it to be about his disinformation regarding same.
whereas O basically wants the discussions to be about O personally and everyone else personally too especially those who disagree with or criticize O.
In other words O trolls constantly and in ways almost all members know to not do.
That is O's life's work.
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O was 'badly damaged' (because of his fragile delicate nature) in a recent exchange in this forum a few days ago).
But instead of then getting himself muted by chess.com for a third recent time ..
(desperately and pathetically needing to go 'far over the top' in retorting)
this time he instead averted that and simply took a break for a few days.
Something he needs to learn to do regularly.
Something fester told him to do.

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.

@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.

tygxc not understanding that 'optimal play' hasn't been figured out yet and doesn't understand that there isn't 'optimal play' by saying there is.
Differences between a comment and a proof.
tygxc perhaps depending on an incidence of people making mistakes while rightly refuting and debunking his disinformation.

Say a game began d4 d5 and then the two players agree to a draw.
Or - there's a flood or an earthquake and the game ends abruptly.
In both cases - as far as 'perfect game' is concerned - the game is incomplete.
Can be distinguished from 'perfect end result'.
If there's only two kings left - or there's a king and single minor piece against a lone king then those are perfect end results in both cases and are perfect draws in both cases.
When or where does 'perfect' begin to break down?
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King and rook versus lone king. And the lone king isn't stalemated.
Is that a 'perfect win'?
Not if the rook side flag drops.
And if that side doesn't know how to mate there and doesn't get it right in time or goes over 50 moves or repeats the position three times - those become 'perfect draw results'.
So those still aren't perfect wins.
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A perfect win result only occurs if:
1) checkmate happens.
2) resign happens. Or a player forfeits somehow.
3) flag drops and the other player has sufficient mating material.
Those happen constantly.
But those are end results - not the games in their entireties.
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now try 'perfect tablebase positions'
one side's up a rook.
There's no clock. No 50 move rule. No 3 fold repetition rule.
And its not stalemate.
Is such a position a 'perfectly won position from there'?
Yes. But that doesn't mean that position came from a perfect game.
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Can we prove it couldn't have?
Not necessary. Its a win.
Plus apparently we wouldn't define such a game leading to such a position as Perfect anyway.
But its the same situation with King and rook versus King and rook. A book draw.
There's no way to prove that all games producing that are perfect.
You may as well try to prove the universe is finite. Or infinite.
Neither has been done. Won't be.

Tromp does indeed estimate 4.8 x 10^44 legal positions with promotion, and your wish to ignore all promotions is ridiculous. The reasoning that underpromotions to bishop and rook by the proponent only of a drawing strategy can be ignored is valid. This means that we can manage with positions where one side only promotes to queens and knights. [Note you can't assume the opponent of a strategy will not underpromote because that risks reaching a position where the opponent can win only by underpromotion. Evaluating this as a draw would be fatal.

Where is the estimate of the number of these positions where one side has unlimited promotions and the other is only permitted to promote to queen or knight? On a log scale it is nearer the number for all legal positions than the number for all legal positions without promotion (because one side has all the possibilities and the other has a lot of them). Somewhere around 10^42.

Tromp (github)

Nah once we are done with this conversion everyone's braincells will deplete to one and yours will probably be .5

Heading for another mute in a hurry I see...

...and gone already a few hours later.

Interesting as this might be in itself, we should be able to agree it is irrelevant to a weak solution of chess that consists of two drawing strategy. The reason is that it suffices that a strategy doesn't ever blunder away a basic rules chess loss. If the strategy ignores FIDE rules, the only surprise that can happen is that the game is unexpectedly drawn, which is the objective!

Constructing such a strategy is a challenge but only in the same way that it was in checkers (other than the size). While in both checkers and basic rules chess it is possible for two players to keep the game drawn and never simplify it down or end, checkers was solved by showing it was possible to either force a drawn tablebase position or to repeat an earlier position in the analysis tree. This works because to refute a drawing strategy the opponent has to be able to completely avoid both of these. No need to wait for a 3-times repetition or even to have a rule that such a repetition is a draw, since a strategy is shown to draw if you disprove the existence of a win for the opponent against it).

@tygxc:

"chess has been solved - we have 5000 drawing moves from the latest ICCF snoozefest so we don't need to worry about dealing with as many as 10^40 other positions.

In fact it's better than that. The moves are not consistent with being in just one strategy for each side, so we actually have an even smaller number of moves from each of several alternative incompatible drawing strategies for each side, which may be even more incomplete, but it is more redundant!"

(paraphrased)

[And yes, we certainly don't really even know all of those positions are drawing. Especially the first one]

https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?page=1#comment-66772169

That's probably the most downvotes that I've seen.

The arguments against tygxc's positions all stand.
Its his positions that were always very dusty.
What has tygxc said right so far?
He has conceded that chess cannot be solved with current technology.
Regarding tygxc's obtuseness in avoiding the arguments made to him - such obtuseness is technically 'his fault'.
But 'fault' isn't the best word there.
Its his choice.
Some would argue that his obtuseness is 'trolling'.
I think that 'trolling' would be a word better describing the ten-year behaviour of @Optimissed - not tygxc.

Did optimissed get muted again he hadn't been online recently

Optimissed has gone very quiet. Suddenly.
Has not been online on chess.com for three days.
Maybe decided he couldn't afford three mutes.
Maybe finally realized to take a rest like fester suggested to him.
During O's absence - HP becoming very shrill and strident.
HP refers to a member literally named " @hapless_fool "
I kid you not. That really is his account name.
Regarding O - not hard to guess his likely strategies.
He will let tygxc 'take the heat' for now.
But it won't work because tygxc has shown he is not fragile and delicate -
and can hold his head up and take all kinds of heat while O - that's Optimissed - constantly panics and trolls when opposed.
Does O likely have an alt to watch these forums for him - while HP shills for him in another forum ?
O likes to accuse people of having alt accounts.
And he constantly projects.
Suggests that that is what he's doing.
If its not - I don't care either way.
There's a difference between passivity and not caring.