Not sure what you mean or whether you are being serious, but it's simply a proposition that requires proving. A very familiar situation to those who have experience of mathematics, computer science, game theory and all other rigorous disciplines.
Chess will never be solved, here's why
Sort:
<<Is the twin prime conjecture solved?
The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved.>>
Fascinating, although not as fascinating as Cecil Blanche Woodham-Smith's book on Queen Victoria.
Elroch wrote:
Not sure what you mean or whether you are being serious, but it's simply a proposition that requires proving. A very familiar situation to those who have experience of mathematics, computer science, game theory and all other rigorous disciplines.
I don't think an axiom, such as the one I outlined, which is necessary for his hypothesis to be true, can come before at least a partial solution of chess. Yet tygxc seems to conclude that the proof can precede the partial solution. He has therefore partially solved chess, in his own mind.
Oct 23, 2022
0
#6305
It is essential that @tygxc responds to post #6465 to support his previous claim.
You see, to tygxc "deduction" means à la Sherlock Holmes (to say the best); it is not a strict process like in mathematics or in formal logic. He pretends, imo, to not understand that such type of reasoning is inadequate for solving games.
Oct 23, 2022
0
#6307
tygxc wrote:
@6454
"discarding all variations the committee of GMs don't like"
++ No, I mean: discarding all variations that are clearly worse e.g. 1 e4 e5 2 Ba6? and occasionally adjudicating positions that are clear draws e.g. many opposite colored bishop endings. It is not a matter of liking or disliking, but of being 100% sure.
"His incorrect idea (for me) is that this is a definitive solution of the game."
++ Why incorrect? Then a strategy is determined to achieve the game-theoretic value against any opposition. That satisfies the definition of weakly solved.
What you define as "clearly worse" is, in many cases, what I define as "what the committee of GMs don't like", as their opinion is what you propose using to determine better and worse.
Eliminating so many possibilities is what makes me unsatisfied with any solution reach through this method.
@6474
"What you define as "clearly worse" is, in many cases, what I define as "what the committee of GMs don't like", as their opinion is what you propose using to determine better and worse."
++ Let us look at a few examples, where humans save engines irrelevant calculations.
1 e4 e5 2 Ba6? is clearly worse than 2 Nf3. It even loses to checkmate in 82.
It loses a whole bishop and all the rest is the same i.e. there is no compensation of any kind.
So the move 2 Ba6? can be safely discarded.
https://www.iccf.com/game?id=1164313 This was agreed a draw because it is a fortress.
Engines can go on for many moves until a 3-fold repetition.
https://www.iccf.com/game?id=1164259 This was agreed a draw because the opposite colored bishops make it impossible for either side to win.
Engines can go on for many moves until a 3-fold repetition.
@6465
"a sequence of logical deductive steps starting with a set of axioms and additional definitions and ending with the desired proposition as a conclusion." ++ Yes
The set of axioms are the Laws of Chess. https://handbook.fide.com/chapter/E012018
"PROP 1: the value to white of the position after 1. Nh3
<= the value to white of the position after 1. Nf3"
++ This is what this paper did https://arxiv.org/abs/2111.09259
It was fed with no human input but the Laws of Chess i.e. axioms,
and it only performed boolean operations i.e. logic. It arrived at:
d4 > e4 > Nf3 > c4 > e3 > g3 > Nc3 > c3 > b3 > a3 >
h3 > d3 > a4 > f4 > b4 > Nh3 > h4 > Na3 > f3 > g4.
In human terms it requires a set of intermediate theorems deduced from the Laws of Chess.
One such intermediate theorems is that control over the center increases the value.
The center functions like high ground in the military: if you hold it the opponent fights uphill.
From the Laws of Chess follows that
Queens, Bishops, Knights, Pawns, and Kings control more squares from the center.
Thus control over the center increase the value.
That is the same in other games:
in Checkers the center is more important, in Losing Chess only 1 e3 wins,
in Connect Four only 1 d1 wins, in Nine Men's Morris: the best starting moves are b4, d2, d6, f4.
1 Nf3 controls 2 central squares and 1 Nh3 zero.
A knight on the rim is dim.
2 > 0, thus 1 Nf3 has a value >= 1 Nh3
Another such intermediate theorem is that greater mobility increases the value.
That is also true in other games like Nine Men's Morris. If you have played b4, d2 and your opponent f4, d6, then it is better to play d7, d5, e4, or g4 that limit your opponent's mobility than a4, c4, d1, or d3 that limit your own mobility.
In the initial position white has 20 legal moves.
After 1 Nf3 white has 23 legal moves.
After 1 Nh3 white has 21 legal moves.
23 > 21, thus 1 Nf3 has a value >= 1 Nh3
There is a hierarchy in the intermediate theorems:
King safety > material > center > mobility
A lone knight can defeat a whole army with a smothered checkmate.
King safety also explains why
Nf3 > Nc3
g3 > b3
c4 > f4
b4 > g4
c3 > f3
"I merely have a couple of relevant degrees and many years of relevant experience and further knowledge to draw on" ++ Me too
Oct 24, 2022
0
#6310
So there we have it.
@tygxc doesn't know what "deductive logic" means and doesn't know what "relevant degree" means either.
Oct 24, 2022
0
#6311
Perhaps I was wrong to think he would be one of those who understood what the value of a position is. For clarity: V(given position) is defined in three simple stages:
Let W be a white strategy and B be a black strategy (always assumed to be deterministic)
V(W, B) is defined as the (deterministic) result when these strategies are played against each other.
V(W) is defined as minimum over all black strategies B of V(W, B),
V(given position) is defined as maximum over all white strategies W of V(W)
@6478
There is no contradiction of any kind.
Your formalistic descriptions simply mean 'the outcome if all participants play optimally.
So V = min [V(W)] is indeed no higher for 1 Nh3 than for 1 Nf3. q.e.d.
tygxc wrote:
@6465
"a sequence of logical deductive steps starting with a set of axioms and additional definitions and ending with the desired proposition as a conclusion." ++ Yes
The set of axioms are the Laws of Chess. https://handbook.fide.com/chapter/E012018
"PROP 1: the value to white of the position after 1. Nh3
<= the value to white of the position after 1. Nf3"
++ This is what this paper did https://arxiv.org/abs/2111.09259
It was fed with no human input but the Laws of Chess i.e. axioms,
and it only performed boolean operations i.e. logic. It arrived at:
d4 > e4 > Nf3 > c4 > e3 > g3 > Nc3 > c3 > b3 > a3 >
h3 > d3 > a4 > f4 > b4 > Nh3 > h4 > Na3 > f3 > g4.
It's wrong. In my view, e4 is a little less good and b4 is far better than that. Logically, Na3 cannot be worse than h4, for reasons there's no need to go into here. It should be obvious that d3 cannot possibly be worse than a3 and c3, as well as some others. You do not realise that no computer is competent to put opening moves in order of worth. If it were possible, then it would be a big step on the road to solving chess.
In human terms it requires a set of intermediate theorems deduced from the Laws of Chess. One such intermediate theorems is that control over the center increases the value.
The center functions like high ground in the military: if you hold it the opponent fights uphill. From the Laws of Chess follows that Queens, Bishops, Knights, Pawns, and Kings control more squares from the center. Thus control over the center increase the value.
Logically, not for white's opening move. White may be playing a black system reversed and we can assume that black is worth a draw anyway. So illogical.
That is the same in other games:
in Checkers the center is more important, in Losing Chess only 1 e3 wins, in Connect Four only 1 d1 wins, in Nine Men's Morris: the best starting moves are b4, d2, d6, f4.
1 Nf3 controls 2 central squares and 1 Nh3 zero. A knight on the rim is dim.
Next, you'll be saying "never miss a check, it might be mate".
2 > 0, thus 1 Nf3 has a value >= 1 Nh3
Another such intermediate theorem is that greater mobility increases the value.
That is also true in other games like Nine Men's Morris. If you have played b4, d2 and your opponent f4, d6, then it is better to play d7, d5, e4, or g4 that limit your opponent's mobility than a4, c4, d1, or d3 that limit your own mobility.
In the initial position white has 20 legal moves.
After 1 Nf3 white has 23 legal moves.
After 1 Nh3 white has 21 legal moves.
23 > 21, thus 1 Nf3 has a value >= 1 Nh3
There is a hierarchy in the intermediate theorems:
King safety > material > center > mobility
A lone knight can defeat a whole army with a smothered checkmate.
King safety also explains why
Nf3 > Nc3
g3 > b3
c4 > f4
b4 > g4
c3 > f3
"I merely have a couple of relevant degrees and many years of relevant experience and further knowledge to draw on" ++ Me too
Ah good. Consensus at last.
Elroch wrote:
Perhaps I was wrong to think he would be one of those who understood what the value of a position is. For clarity: V(given position) is defined in three simple stages:
Let W be a white strategy and B be a black strategy (always assumed to be deterministic)
V(W, B) is defined as the (deterministic) result when these strategies are played against each other.
V(W) is defined as minimum over all black strategies B of V(W, B),
V(given position) is defined as maximum over all white strategies W of V(W)
This is a good example of verbal reasoning being far better than the attempt to depict it algebraically, which we see here. I could portray it verbally. It would be much clearer and without need for further explanation. One thing I don't understand is this: why is the interplay of strategies deterministic? What's the reasoning behind that, because I think it's incorrect?
Oct 24, 2022
0
#6315
MARattigan wrote:
So there we have it.
@tygxc doesn't know what "deductive logic" means and doesn't know what "relevant degree" means either.
It is more difficult to believe that someone with a relevant degree would forget what deduction is. A bit like a literature graduate forgetting what a noun is.
Oct 24, 2022
0
#6316
Optimissed wrote:
Elroch wrote:
Perhaps I was wrong to think he would be one of those who understood what the value of a position is. For clarity: V(given position) is defined in three simple stages:
Let W be a white strategy and B be a black strategy (always assumed to be deterministic)
V(W, B) is defined as the (deterministic) result when these strategies are played against each other.
V(W) is defined as minimum over all black strategies B of V(W, B),
V(given position) is defined as maximum over all white strategies W of V(W)
This is a good example of verbal reasoning being far better than the attempt to depict it algebraically, which we see here. I could portray it verbally. It would be much clearer and without need for further explanation. One thing I don't understand is this: why is the interplay of strategies deterministic? What's the reasoning behind that, because I think it's incorrect?
Happy to clarify that by adding a definition that was left implicit (I shouldn't have assumed it was obvious).
A deterministic strategy is one which always plays the same move in any specified position.
If you play two specific deterministic strategies against each other, you always get the exact same game and the same result.
@6482
After this formalistic intermezzo, can we now agree in your lingo that
the value to white of the position after 1. Nh3 <= the value to white of the position after 1. Nf3
and
the value to white of the position after 1. e4 e5 2 Ba6 <= the value to white of the position after 1. e4 e5 2 Nf3
Elroch wrote:
Optimissed wrote:
Elroch wrote:
Perhaps I was wrong to think he would be one of those who understood what the value of a position is. For clarity: V(given position) is defined in three simple stages:
Let W be a white strategy and B be a black strategy (always assumed to be deterministic)
V(W, B) is defined as the (deterministic) result when these strategies are played against each other.
V(W) is defined as minimum over all black strategies B of V(W, B),
V(given position) is defined as maximum over all white strategies W of V(W)
This is a good example of verbal reasoning being far better than the attempt to depict it algebraically, which we see here. I could portray it verbally. It would be much clearer and without need for further explanation. One thing I don't understand is this: why is the interplay of strategies deterministic? What's the reasoning behind that, because I think it's incorrect?
Happy to clarify that by adding a definition that was left implicit (I shouldn't have assumed it was obvious).
A deterministic strategy is one which always plays the same move in any specified position.
Yes, I just wanted that to be clarified: but why is it assumed?? It means that there are no two moves with equal value but that in itself goes against your articles of faith regarding deduction and induction. I'm just pointing out, as I have all along, that you also assume things to be true and so tygxc isn't the only one.
If you play two specific deterministic strategies against each other, you always get the exact same game and the same result.
You would, wouldn't you. But that doesn't reinforce the idea that they are deterministic. Why should they be determinstic?
Oct 24, 2022
0
#6319
It's a definition that is used in the definition of the value of a position.
I mean, edited ^