“You told me you could prove it but that's an assertion and not a proof. I don't accept your assertion, which is unproven. Do you actually know what a proof is?”
it’s asserted because it’s already known to be true. That’s how a math proof works.
I even gave the exact formulas for the mirror moves in my original proof
Optimized what did I assert that wasn’t true by definition or widely known to be true?
MEGACHE3SE wrote:
Optimized what did I assert that wasn’t true by definition or widely known to be true?
Optimissed wrote:
The entire claim you made.
Honestly, Megache3se, there are plenty of clever and competent people who comment on this site but there is quite a lot of people who have some mental problem or inability and you don't want to be looking like them. Sure, that kind of person will befriend you. Very often, due to age, people's mental abilities decline and they cover it up by becoming cynical and trolling defensively. Don't take their word for anything. You have to be able to tell who is honest and who is intelligent and knowledgeable ... or you just become like the trolls.
In other words he doesn't know.
Your claim that it's known to be true is an assertion. I could use my philosophical expertise and make a counter-claim. It's called an "argument from authority" and it's almost worthless.
I don't accept it's known to be true, anyhow. You would have to prove it. That is impossible, in my opinion. It's just a claim.
Nice to see that you agree that "argument from authority" is virtually worthless. I hope that means that we will see no more claims that we know chess is a draw, we know black cannot have a forced win, and other opinions you dismiss without proof because you understand everything better than anyone else does.
Chess is just too hard man
The entire claim you made.
Honestly, Megache3se, there are plenty of clever and competent people who comment on this site but there is quite a lot of people who have some mental problem or inability and you don't want to be looking like them. Sure, that kind of person will befriend you. Very often, due to age, people's mental abilities decline and they cover it up by becoming cynical and trolling defensively. Don't take their word for anything. You have to be able to tell who is honest and who is intelligent and knowledgeable ... or you just become like the trolls.
Always the aspersions about people collaborating clandestinely to take you down...
I doubt anyone has "befriended' anyone here. This is just the status quo...you make claims, and the nature of your erroneous claims draws more and more opposition from more and more people over time 
. It's really pretty simple.
To say what I did was an argument from authority would be a strawman. I was speaking in the terms of that it is known that 1+1=2its an axiom (technically 1+1=2 isn’t an axiom but that is a technicality)
The mirror move plausibility is directly derived from the rules of chess
It can likely be 'solved," as the possible positions and games are finite.
It's also worth noting that, while computers seem to have clearly surpassed humans in terms of play*, they are (afaik), programmed by humans; and thus the determinations of optimal play could still be flawed, even for computing power (until you can map every possible game and analyze that data set).
Even moves that are seemingly obvious (eg - taking a free piece with no obvious giveback in material or position) doesn't necessarily mean the play is optimal, or that taking the piece is correct, as you'd need to examine ever branch to know that for certain (I would think).
* not sure if this is correct but I thought I read that no human has beaten the top computers in more than a decade or something (though I don't know how many games that encompasses or if the top computers are free to play against). It's a little surprising if true, as you'd think that by analyzing computer games you could see what was happening enough to actually compete.
Has chess been solved? No
Can chess be solved? Yes, it takes 5 years on cloud engines.
Will chess be solved? Maybe, it depends on somebody paying 5 million $ for the cloud engines and the human assistants during 5 years.
Have humans walked on Mars? No
Can humans walk on Mars? Yes
Will humans walk on Mars? Maybe, it depends on somebody paying billions of $ to build and launch a spacecraft.
You are wrong. And if do not believe so, then I would love for you to prove that your postulate is not wrong. Take quantum computing, which is by far the fastest type of computing available right now, with approximately a trillion calculations per second. If we just assume the first answer on Google is correct, then we need to calculate some ~10^40 moves.
Computational speed = 10^12*s^-1
Moves to be calculated = ~10^-40
I want to leave it as an exercise to you to figure out how many years that would take. Sure, there might exist certain algorithms, which have a great efficiency in terms of solving this issue, but I don't think anything that we know and possess right now will be able to solve chess in 5 years.
@8731
"love for you to prove"
"Take quantum computing" ++ Not even necessary: existing engines can do it.
Computational speed = 10^9*s^-1
Positions to be calculated = 10^17 = Sqrt (10^37 *10 / 10^4) for weakly solving Chess
"how many years that would take" = 5
3 engines * 10^9 nodes/s/engine * 3600 s/h * 24 h/d * 365.25 d/a * 5 a = 4.7 * 10^17
Computational speed = 10^12*s^-1
Just to clarify, is this a single top computer, or all of the world's computers. If the latter, couldn't you start chopping away by using multiple devices?
@8731
"love for you to prove"
"Take quantum computing" ++ Not even necessary: existing engines can do it.
Computational speed = 10^9*s^-1
Positions to be calculated = 10^17 = Sqrt (10^37 *10 / 10^4) for weakly solving Chess
"how many years that would take" = 5
3 engines * 10^9 nodes/s/engine * 3600 s/h * 24 h/d * 365.25 d/a * 5 a = 4.7 * 10^17
Is this just to map positions/games, or does it include some sort of analysis?
@8731
"love for you to prove"
"Take quantum computing" ++ Not even necessary: existing engines can do it.
Computational speed = 10^9*s^-1
Positions to be calculated = 10^17 = Sqrt (10^37 *10 / 10^4) for weakly solving Chess
"how many years that would take" = 5
3 engines * 10^9 nodes/s/engine * 3600 s/h * 24 h/d * 365.25 d/a * 5 a = 4.7 * 10^17
Bad info in Red. Bad calculations derived from bad info in Orange. There is no credible source for 10^17, this is the personal opinion of Tygxc...and nobody else. Repeating it 500 times doesn't change that.
@8700
"its staggering branching factor" ++ The branching factor of Chess is much smaller than you think. Chess has many transpositions, leading to the same node via different branches.
"This factor creates an exponential number of possible game states"
++ There are no more game states than there are positions.
Legal positions have been counted to be 10^44. Of these only 10^38 result from restricting promotions to either a queen, or a previously captured piece. Of these only 10^34 result from reasonable moves. E.g. 1 e4 e5 2 Ba6? is not a reasonable move.
"making it impossible to solve the game completely" ++ Strongly solving to a 32-men table base is not feasible with present technology. Weakly solving as has been done for Checkers is possible in 5 years, but costs $ 3,000,000 to rent 3 cloud engines and hire 3 grandmasters.
"The number of possible game states is determined by raising the branching factor to the power of the tree's depth, where the branching factor represents the average number of possible legal moves in each position, and the depth is proportional to the average length of the game in half-moves."
++ That is correct: N = w^(2d)
All legal moves: N = 10^44
Promotions restricted to either queen, or previously captured piece: N = 10^38
Moves restricted to reasonable moves: N = 10^34
For weakly solving only: Nweak = w^d = Sqrt (w^(2d)) = Sqrt (N)
"Using Shannon's number" ++ That is outdated and wrong.
"the game tree for chess has approximately 10^120 nodes" ++ No. There are only 10^44 legal positions, 10^38 with restricted promotions, 10^34 from reasonable moves.
"implausible to search through the game tree exhaustively"
++ With present technology it is not feasible to strongly solve the game for all 10^44 legal positions, but existing computers can exhaust all 10^17 positions relevant to weakly solving Chess: showing how black can draw against any white opposition.
"the optimal move may not exist in every case" ++ In most positions there are several optimal moves. In the initial position white has 19 optimal moves that draw and 1 error that loses: 1 g4?
"predicting the ultimate conclusion of a game, even with complete knowledge of the game state and all possible moves, is entirely impossible"
++ It is correct that no algorithm is possible to evaluate any position being a draw / win / loss except for calculating all the way to the 7-men endgame table base.
That is also how Schaeffer weakly solved Checkers.
@8734
"Is this just to map positions/games, or does it include some sort of analysis?"
++ The essence is the roadmap from to initial position to other drawn positions until reaching a 7-men endgame table base draw.
Some imperfect analysis speeds up the process.
Just to clarify, is this a single top computer, or all of the world's computers. If the latter, couldn't you start chopping away by using multiple devices?
1. Quantum computers cannot be used to solve chess as they currently exist, or even as they are predicted to evolve in the foreseeable future.
2. If you spent the entire world's collected wealth (estimated at ~80 trillion dollars) on the fastest supercomputers (over a quarter million of them), the combined petaFLOPS still take more than a million years to solve the 10^44 unique positions.
3. There's no basis for 10^17. It's a made-up number.
1. Quantum computers cannot be used to solve chess as they currently exist, or even as they are predicted to evolve in the foreseeable future.
2. If you spent the entire world's collected wealth (estimated at ~80 trillion dollars) on the fastest supercomputers (over a quarter million of them), the combined petaFLOPS still take more than a million years to solve the 10^44 unique positions.
3. There's no basis for 10^17. It's a made-up number.
Here's some numbers I posted in 2015 and reposted later on...they have not actually changed much for the purposes of this topic. 10^46 is now 10^44, and the supercomputers are faster, but not very much faster:
"100 PetaFLOPS is 10^17 floating point operations/sec. Evaluating a chess position is not 1 operation, mind you, nor is it 10, so let's be kind and say it falls in the 100s order of magnitude, which knocks 10^17 back down to 10^15 positions/second, which is 8.64^19 positions/day, 3.15^22 positions/year.
At that processing rate (assuming infinite memory/storage and ignoring all the issues thereof) you would solve chess in...3.175^24 years. I guess you could amortize a loan for the duration on the $273 million for the supercomputer...
Adding in storage, you solve chess...never (in this scenario).
The fastest supercomputer could solve checkers in a matter of seconds (10^17 FLOPS vs. calculating 10^14 positions), but it will take 3.175^24 years to solve chess. If you spend the entire wealth of the planet (approx. $80 Trillion in currency) to build an array of these supercomputers, approx. 290,000 of them, and use them all for solving chess leaving the human race to starve and die (so we'll also leave as aside the question of who would run the giant computer array), it still would take 3.8 million years to get your answer."
What is important to note is that black does not HAVE to play the mirror move, rather that they COULD choose to do that. If white decides to lose 2 tempo, black does not have to Match that.