guys who cares
The obvious answer is the people reading and posting on this thread. The more puzzling question is what are you doing here? Punishing yourself? You clearly have other important topics to consider, like whether dogs really are forever...
I never went very far on computer science type topics. Other than a mathematician, I feel like maybe someone who has knowledge on the topic of data structures would be able to answer the interesting question: how to estimate the ratio for number of games to number of unique positions.
But since I've made the prior assumption that we're only considering "sensible" moves, a lot of purely mathematical tools simply wouldn't work. You're probably better off taking something like a large database of engine games, and brute forcing it i.e. counting all the unique positions.
Regarding 'nodes per second' when 'considering' positions -
that looks ridiculous - in the context of greatly varying difficulties of positions.
Positions with 10 pieces in them instead of 5 - would average far more than double the number of possible ensuing moves ... 'orders of magnitude' higher.
Each position would have much more move possibilities at each stage because of the five extra pieces. And much more depth.
The concept that 'nodes per second' could be a constant through these situations - looks ridiculous. Very much so.
No 'background' in mathematics needed.
High school math sufficient.
The difficulties of positions vary - everyone knows that.
So aggressively trying to defend 'nodes per second' by ignoring that variation in difficulty - looks more and more blatant.
More and more exposed.
'Passive aggressive'. How would the thinking go?
"Yes - I know the difficulties in positions vary - but I just won't talk about that. Won't acknowledge it. Won't acknowledge what that does to 'nodes per second' as a constant. Nobody will be able to make me so acknowledge or concede ! And some people will then continue to fall for 'nodes per second' ! "
If a computer student was trying to do his dissertation for his degree and started pushing 'the cloud computers put out work at a very high constant of nodes per second so therefore we could weakly solve chess in five years' - then I can see the likely reaction of a Review Board.
Groans. One of the professors offers "I liked that young man. So disappointing that I will have to vote No to his degree !"
One of the others: "Yes. Quite. It makes me wonder how he got this far."
Another: "Probably by 'cramming'. But he did seem to understand most of the work up to now."
Senior professor: "Somehow he talked himself into this. I imagine even most if not all of the professionals in the project itself would not subscribe to 'nodes per second' as a constant here.
I'll have the Fail notice sent out.
Thank you Gentlemen. See you tomorrow."
#1926
++ That is an interesting post indeed.
"let's say there are, on average, 5 reasonable options per move."
++ I calculated before that 4 candidate moves per move yields 1 error per 10^20 positions.
That is also consistent with chess knowledge: 1 e4 1 d4 1 c4 1 Nf3 are the 4 top moves, the others need no consideration.
1 e4 e5, 1 e4 c5, 1 e4 e6, 1 e4 c6 are the 4 top moves, the others need no consideration.
So that makes 4 per move
It is not necessary to consider alternatives for black: if a table base draw is reached then that retroactively justifies all black moves as optimal
28 moves per game may be not enough, maybe 40.
Now chess has many, many transitions:
1 e4 e5 2 Nf3 Nc6 = 1 Nf3 Nc6 2 e4 e5 = 1 e4 Nc6 2 Nf3 e5...
"so maybe 10^30 sensible positions."
++ This may well be right.
It is consistent with 10^37 * 10 / 10^6 = 10^32
10^37 from the Gourion count
* 10 to allow 3 or 4 queens
/ 10^6 Tromp's conjecture that only 1 in 10^6 positions without promotions to pieces not yet captured can occur in a reasonable game
#1927
Very cunning
Now you finally proved that C70 is wrong and that black should play the Berlin 3...Nf6 instead of 3...a6 like Lasker already said.
#1926
++ That is an interesting post indeed.
"let's say there are, on average, 5 reasonable options per move."
++ I calculated before that 4 candidate moves per move yields 1 error per 10^20 positions.
That is also consistent with chess knowledge: 1 e4 1 d4 1 c4 1 Nf3 are the 4 top moves, the others need no consideration.
1 e4 e5, 1 e4 c5, 1 e4 e6, 1 e4 c6 are the 4 top moves, the others need no consideration.
So that makes 4 per move
It is not necessary to consider alternatives for black: if a table base draw is reached then that retroactively justifies all black moves as optimal
28 moves per game may be not enough, maybe 40.
Now chess has many, many transitions:
1 e4 e5 2 Nf3 Nc6 = 1 Nf3 Nc6 2 e4 e5 = 1 e4 Nc6 2 Nf3 e5...
"so maybe 10^30 sensible positions."
++ This may well be right.
It is consistent with 10^37 * 10 / 10^6 = 10^32
10^37 from the Gourion count
* 10 to allow 3 or 4 queens
/ 10^6 Tromp's conjecture that only 1 in 10^6 positions without promotions to pieces not yet captured can occur in a reasonable game
#1935
Of course chess is solvable, that has already been proven.
The only question is if that is feasible: how much time it would take.
I believe GM Sveshnikov when he said it can be done in 5 years, but others dispute this.
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#1927
Very cunning
Now you finally proved that C70 is wrong and that black should play the Berlin 3...Nf6 instead of 3...a6 like Lasker already said.
Ah, but I needed you to show me the way.
It's the same method you're using to discount 2.9 x 100 x 10^44 x 3^(2.9 x 100 x 10^44) other positions.
(Figure probably exaggerated somewhat - got that idea from you too.)
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Stop spamming.
Uggh ... no I do not willingly go into this thread again. The mental power that has gone into this thread could have instead at least quarter solved the problem.
1. Proofs of a solution that shows chess is computable makes you famous.
2. Random conjectures that no such proof exists does not.
3. If your assertion is that no such proof exists, then proving non-existence would also make you famous.
Those are three outcomes you could pursue. Stop using the forum bandwidth for nonsense chatter. Prove something, indeed prove ANYTHING THAT WOULD CONTRIBUTE TO SOLVING THE PROBLEM, or stop posting, please.
Regarding ' 1. ' above - its very simple and not famous to just argue the upper bound on maximum possible chess positions is finite.
You simply reason that each square of the 64 has a maximum of 13 possible states.
In other words each square must either be empty or have one of 12 types of piece on it - since each side is restricted to six types of chess piece.
So the first upper bound is simply 13 multiplied by itself 63 times.
Which is also stated as 13 to the 64th power.
That's a finite number. So you can argue from there that chess could be solved ...
unlike finding the greatest prime number possible - which Cannot be solved.
You can't. Its proven. There's no such number. Proven. Neatly.
The finite number of chess positions though - doesn't mean it will be solved.
The forum title asserts that chess will never be solved. And 'here's why'.
Proofs as to the difficulty of the task 'contribute'.
Invalid proofs to the contrary 'contribute' too - but its better if they're debunked.
I calculated before that 4 candidate moves per move yields 1 error per 10^20 positions.
[...] the others need no consideration.
1/10^20=10^17/10^37. If you estimate a search space of 10^37 positions, are you saying that policy could miss up to 10^17 positions leading to a different game value than that provided by the proof tree?
"I calculated before that 4 candidate moves per move yields 1 error per 10^20 positions."
That's Extremely far fetched. If only because there are more than 4 legitimate candidate moves in a gigantic number of positions.
And in a percentage of positions that would be far more than one in a billion billion.
Even trying to insist that such situations would occur in under 1% of positions - looks intensely invalid. Arbitrary. Contrived.
Many kinds of exercises are possible as to contrived 'solvings' of chess.
In fact - the possible number of different variations on such contrivances - is Infinite ! Its more than the number of possible chess positions !
I calculated before that 4 candidate moves per move yields 1 error per 10^20 positions.
[...] the others need no consideration.
1/10^20=10^17/10^37. If there are 10^37 sensible positions, are you saying that policy could miss up to 10^17 positions leading to a different game value than that provided by the proof tree?
It's a lot worse than that.
KNNKP has less than 10⁹ positions in basic rules chess.
If you look at the SF14 v. SF14 KNNKP games in this post SF14 blunders between 1 and 9 times under basic rules in each case. The longest of the games contains just 165 positions. The blunder rate appears to rise, if anything, the more think time you give SF14.
In fact @tygxc appears, on the whole, to propose solving the competition rules game, though he's a little evasive on that question. SF14 is also designed to play the competition rules game (its evaluations of diagram + side-to-move + ply count vary according to ply count).
Under competition rules KNNKP has somewhere between 100x557914624 and 100x557914624x3⁵⁵⁷⁹¹⁴⁶²⁴ positions. The factor "100" here represents positions with the same diagram and side to move but with different ply counts (which can have different win/draw/loss evaluations). The figure 557914624 is the Wilhelm reported count of basic rules positions in KNNKP. These are, if you like, "honest" positions taking no account of board or Black/White symmetries. The factor 3⁵⁵⁷⁹¹⁴⁶²⁴ (≓ 10²⁶⁶¹⁹²⁹²⁵) represents, for each KNNKP position the number of possible repetitions (0, 1 or 2) of each position with the same material that my have occurred previously (for each of which, the win/draw/loss value or, where applicable, valid mating sequences, can be different - see, for example, this post).
Under competition rules, SF14, which is designed for the competition rules game, makes only between 1 and 5 blunders in each of the games referred to previously. Again, the blunder rate appears to rise, if anything, the more think time you give it.
I would guess that SF14's blunder rates would rise exponentially with the number of men on the board (so far as I know it makes zero blunders from almost any 4 man position and certainly none from any 3 man position), but since SF14 would typically take less than 60 moves to reach the 7 man tablebases it wouldn't have time to show off anything but a faint shadow of the number of blunders it is really capable of on its first pass. (Though the game would probably be almost all blunders.)
The number of possible chess positions is finite.
That's proven.
So therefore chess is solvable.
That doesn't mean it will be solved though. Nor that it won't be.
Many would argue that its not known whether its solvable until it is -
that doesn't follow either though.
#1935
Of course chess is solvable, that has already been proven.
The only question is if that is feasible: how much time it would take.
I believe GM Sveshnikov when he said it can be done in 5 years, but others dispute this.
It hasn't been proven. Merely inferred, according to a desperately bad inference model.
Can you stop talking b*llocks?
@tygxc has demonstrated that he can keep pushing all kinds of stuff -
like invalid 'reasonableness of moves'
invalid 'square root' reductions
invalid 'nodes per second' speeds
invalid dismissals of FLOPS/second and a general obfuscation of computer speed in general just by invoking invalid 'nodes per second'
how is he able to do this? Well for one - people will be tempted to 'rightly' debunk and refute such claims ...
another is that there's no chess.com policy against it.
If somebody started insisting 'King and two knights can force a win against Lone King - I Know it !' - then could chess.com shut that down?
At first - no. Eventually they probably could and would.
But since computers have not arrived at any verdict as to chess solved or not and might not even be able to do so for millions of years ...
then it remains unestablished and therefore how could chess.com stop the subject?
They'll lock a forum in some instances but that doesn't kill that subject.
So the claims will continue - including the invalid ones.
How often do they need to be debunked? 
#1941
"If you estimate a search space of 10^37 positions, are you saying that policy could miss up to 10^17 positions leading to a different game value than that provided by the proof tree?"
++ No, I am saying that weakly solving chess requires only considering 10^17 positions hence at 1 error per 10^20 positions there remains only 0.1% chance of having made an error.
guys who cares