Hypothetically,

If I (or one) were to "solve" chess, I.e. come up with an algorithm that always results in a check mate and has an induction proof to prove it, what would this be worth? What would be the "best" way to use it? What would it mean for chess?

Any input serious or not so serious is very much appreciated

It's worthless. Such an algorithm already exists -- actually many such algorithms exist, e.g., backwards induction, exhaustive search, etc.

An algorithm that one could implement to run on a personal computer? Probably just a few times more than whatever the current market is for chess engines.

As for the impact on chess itself, I'm not sure it would be that great. Computers are already better than almost all humans at almost all time controls. Yet many amateurs (let alone professionals) continue to play the game...

there might be a million or so in it if you could sell it to a world championship contender, it would be of serious use in opening preparation (assuming like Sholar says the algorithm runs quickly on a normal computer).

I don't see how you could get $10m out of it directly, the people who would be most impressed are academics and chessplayers who just don't have a load of money to throw at you.

The only way you could make serious money out of it is to start your own software business on the back of your transient fame, even in bad economic times lots of venture capitalists would be happy to invest in a programming genius such as yourself. Then take the money and run.

If there was a solution the popularity of chess would probably decline, because people don't want to play clearvoyant opponents.

A: "You played that move because you memorized the solution"
B: "No, I did not!"
A: "Yes, you did!"
B: "1.e4 is the winning move. Play 1.d4 instead!"
A: "No, I don't want to play 1.d4. I want to play 1.e4. Now make a move!"
B: "Let me see, I play 1...e5"
A: "HAHA, that's a mistake!"
B: "How do you know?"
A: "I don't know it, I just have a feeling"
B: "Dude, I told you: YOU KNOW THE SOLUTION"
A: "NO, I DON'T!"

....and so on....

I doubt it would be of much serious use or interest to anybody. Imagine how strange some endgame solutions look when you are playing for zugzwang and other such themes. Now imagine the same type of moves, but with 32 pieces on the board. Many of the moves and their best responses are going to be completely nonsensical.

As for the OP itself, I hope you don't just mean coming up with the algorithm. There are already very trivial algorithms to solve chess. A simple depth first search of every single move with a table ensuring you don't reprocess the same game state (game state = position/repetition status/side to move) twice would be just fine and trivial to program. The only problem is it, like any other solution, would take a few eternities to finish.

that, and there isn't enough space in the observable universe to store the data.

to strongly solve chess you'd need a perfect position-evaluating function.
a weaker solution could be discovered at any time, if white has a forced win.

You don't need that much space for data because you cut off every branch once the position is a trivial technical win, similar to evaluations in an opening book. The most likely result is that chess is a draw though, pretty much like complex version of tic-tac-toe.

I solved chess but I can never fit the whole post in the reply box.

Huh, thanks for the responses. I'm not terribly chess fluent so I appreciate the insight from your actual experience.

$1mill is a lot... lol
Just to add more details to the hypothesis:

It's a computable finite process that would be easy to use dynamically--ie you put in the board position and it gives you the "analytically best" move. It would generate both the optimal white solution, and the black one at once. It would resolve the question of final result: white, black, draw, and would also generate the number of turns required--so it could be that white has a guaranteed solution if it follows the "optimal path" but if black is using optimal black strategy it could take 300 turns or something for white to win. It would not need a super computer, just a PC. It could be somewhat learnable without a computer. Furthermore it could be generalizable to chess-like games maybe including go and checkers.

so it's this
But needing the universe ceases to be an issue, for similiar reasons as Shandrax pointed out. Furthermore this would be the strong solution, and with it would come any weak solution you wanted.
Thanks again!

Such databases exist for chess positions with 6 pieces and even these databases are of almost 0 use for practical chess players.

And the opening position in chess has 32 pieces, so it's not possible to achieve what you are talking about.

these two statements go pretty well together.

and by pretty well I mean they're 100% inextricably linked

Hypothetically, it is.

@Dire: maybe not 100% inextricably linked, because they depend on definition of learnable. To be honest I consider a lot of things learnable that most people do not--like Quantum Field Theory.

Also, I don't really get your point, I could write:

I'm not terribly fluent in French,
The french language could be somewhat learnable without a computer/instructor/book.

So I don't see how that weakens the hypothesis tbh.

Cofeeyay I don't think you get it. The solution would not be learn able because no one could ever remember all the lines. Lets say you can remember every possible permutation following 1.e4 (which is impossible but nevermind) boom I play 1.d4 and you are lost. I hate to be the one to say it again but there are more possible lines in chess then there are atoms in the universe. Maybe someone could remember the best first 10 moves or so for all possible openings if they discount all the trivial obvious opening erorrs and can just play vs those off of natural ability? But idk what do others think of that?

Again your analogies show you're missing something here.

In French you could be considered reasonably conversant with a vocabulary of just a few thousand words. Many French dictionaries have less than 40,000 words meaning at 40,000 you'd likely know much more of the language than your average native French speaker. Now let's compare this to chess. There are an average of around 30 legal moves in any given chess position. So in the first 10 moves there's around a possible 30^20 or 348,678,440,000,000,000,000,000,000,000 variations possible.

348,678,440,000,000,000,000,000,000,000 = first 10 moves of chess
40,000 = more fluent in French than most native speakers.

And of course this is kind of a silly comparison since the average chess game lasts about 40 moves. And you can cull out some lines, but many less than you'd think. It's not like 1. d4 a6 is a trivial win for white, to say the least. And even if you can cull out 95% of those variations at some point somehow, let's see what you've accomplished:

1,743,392,200,000,000,000,000,000,000 = first 10 moves in chess, culling out 95% of possible moves

And again, this is only the first 10 moves of chess. I could've done the first 40 but then this post would be filled with nothing but 0's.

And I have no clue what you mean stuff like most people do not consider quantum field theory learnable. It was covered in third year undergrad at my university, and shockingly enough more than a couple of people made it to their fourth year. Either way the analogy again isn't even on close to the same scale when thinking of comparing it to something like learning the 'solution' to chess.

You're absolutely right that the french and field theory were irrelevant--my point was just to bring up common ideas of learnable and to get a sense of yours. Quite the university that covers it 3rd year. It's not an American one is it?

So my point is learnability is part of the hypothesis... so let's make it more definite so that it stops being on these weak relative terms.

The difficulty in work would directly proportional to something I can approximate, so here's my approximations and then I'll give a nice real analogy:

Counting a lot, probably up to a 100.
Adding up to three numbers at a time of sizes of 2 digits each
add them together, so being able to add 23 + 47 + 12 in addition to being able to accurately count to get the numbers in the first place.
Now you also have to be able to multiply and divide 2 digit numbers by each other.
Lastly you have to be able to solve quadratic equations,
Now, here there are tricks to solve them that could let you avoid taking square roots and stuff, but then you have to know the tricks and then still have to be able to use them while doing the counting and multiplying and dividing and playing chess.
You would not have to do all of this every turn, and it's only the middle game that's messy, (which it already is, am I right?), furthermore let's set a firm limit that you only ever need to look 2 moves ahead in terms of board positions.

SO how learnable is this? here's some analogies that I find reasonable, obviously not a complete list: I see it as harder than learning how to count cards and basic strategy for blackjack. harder than remembering all of the muck in double deck bridge. but i see it as easier than basketball or tennis, much easier than piano or violin. I also see it as significantly easier than what it takes to be a grand master chess player right now, but I have very little insight into this directly (hence the questions!).



So it is "learnable" though imo, but the quotes are there because "it depends" ... this is how I hoped to mean it earlier, but it's definitely worth fleshing out the details.

Furthermore, one actually NICE thought I had about this is that there would still be choice and strategy in the game when playing with clocks. As I said before the strategy might guarantee wins at turn 300 if black plays really good defense. So white might try a quicker strategy--which involves study and work to learn even assuming the best learning possible. But suddenly Black has strategies that let him win if white doesn't play the strategy that takes 300 turns, perhaps! Ah but if he tries that, and white is playing optimal, then white gets a QUICK win out of it suddenly! Furthermore, since you have to think between moves and do all that hard stuff I talked about before, it would even more promote skill and strategy in a timed competition. It might encourage lots more people to try to learn the game since they know they CAN at one point play it perfectly if they REALLY apply themselves and commit to it.

I know i know, tl;dr

I sincerely appreciate all the comments here. I know the touchiness of the question I ask, especially with all of the hypothetics, and no track record or history whatsoever. However, I really respect the intelligence and seriousness that you guys have brought to the matter. Any insight and information I get from this matter helps me tremendoulsy--it is insight into something I have loved my entire life and enjoyed since I remember enjoying--GAMES I've been feeling sad and been trying to rethink things in my life. Thanks again, you guys (and the 2p2 forum in general) have been beyond expectation

Does anybody know what he's talking about? Anyone? Coffee, there is no mathematical process that can be solved to give us the best move in a given position. It simply doesn't exist. The only way we generally consider solving chess is with a brute force method of determining the absolute evaluation (via analysis) for every position. Nobody could remember the correct move in every possible position because the number of possible positions is so freaking big. Obviously if we could simply do a minimally difficult math problem in order to find the best move in a given position then solving the game would be trivially simple. Chess is in no way analogous to counting cards.

Actually there's a simple way to explain this even more so to him.

Coffee, please go develop a 'learnable' method to solve KNB vs K (that's a bishop and a knight and king versus a bare king) that doesn't rely on abstract skill (eg - corner color, W/triangle techniques) and could be reasonably extrapolated to solve other endings as well. This should be pretty trivial to do if you're even contemplating the possibility of taking on 32 piece chess. There's only on going to be somewhere around 15 possible moves for the superior side, and obviously a max of 9 for the defending side, and you're only using two pieces!

Have fun!

This is over my head, but there is one chunk that I recognize and that is the "leanable" KNB vs K mating method. Deletang's triangulation comes to my mind:

http://www.youtube.com/watch?v=PWZ7h2yrJME

Edit: Just noticed that you ruled out triangulation. Ok, the video is nice nevertheless

Movie was great, greatly appreciated.
So swingdoc:
I think there are some problems to the applicability of your logic--saying it doesn't exist has nothing to do with the hypothesis or the question that I made using the hypothesis. If you assume the hypothesis is true then a solution does exist, and my further hypothesis was that it ISN"T trivially simple as you said, it's complicated--that triangulation video explained the check mate fully but certainly wasn't trivial so it seems a plausible refinement of the hypothesis. Furthermore it is obvious to me that CHESS is not analogous to counting cards, that wasn't the analogy I was making, i was making an analogy to the difficulty of playing chess (in my example playing according to this hypothetical solution), to the difficulty of counting cards. Difficulties are analogous things IMO.

And Dire: This still doesn't explain the value of a solution.
Obviously if one were to go about creating a solution, check mates would have to be part of it, and it IS a nice thought problem that well states your point that a solution is HARD to obtain. However, this is a whole other question IMO.

To further detail this, my point is that there is was no restriction in the hypothesis on how hard the solution was to obtain or how it was obtained or whatever. Maybe ALIENS invented it and beamed it down from Planet Z and one person found it on a desert island in a bottle with a DJINN protecting it. We can even allow the DJINN to be the solution, make him invisible and he can tell you the best move at all times and since he's a DJINN he can do math and see the future and lots of other things real good using magic and TELL YOU the move to make at every spot. Obvioulsy you could not listen to him, but that would ALWAYS be a mistake since he saw the future and told you the best move (we can allow for him to find more than one that are equally good and let you choose if there exist more than one) Furthermore the DJINN can make a CD with some program that could be used to learn his chess wisdom, or maybe he can call up his sister DJINNI and have her be the solution to chess for someone else, or whatever else your imagination says is imaginable.

The question of WHETHER IT CAN exist is entirely different and obviously much more difficult and sort of a math theory or game theory or some other theory question.

my question was FAR simpler: if a person had a solution WHAT IT WOULD BE WORTH, and what it would be useful for and what it would mean for chess. If there are any answers to this besides the ones given by Sholer and Roundtable I'd appreciate more insight since so far for value for instance i heard: Around a Million, but not more than 10, and worthless (maybe he meant priceless?). Quite a spread!

Since we're in a hypothetical realm:

Let's assume a solution existed on a superdupercomputer some time in the future.

For humans to "learn" (know) the solution, they don't have to do any work except be implanted with a microchip in their brains that communicates with said computer and therefore they would be able to receive the solution to every position in a matter of seconds.
No memorization needed.

Okay, gotcha. We're just talking about how much a magical, alien solution is worth. I'm sure I could personally make at least a million or two per year by keeping the solution to myself and annotating games or winning tournaments and sponsorship. Obviously my rapid rise in strength would be suspicious so hopefully our magical alien friend can't easily be detected. Keeping it in as few hands as possible would make it most profitable. Mass selling would be hugely -ev since nobody would give a **** if it became widely known and the chess profession (playing, writing books, teaching) would be completely wiped out if anyone could simply buy the solution.

Just to nitpick, the question of WHETHER IT CAN exist is actually much simpler. The answer is "no" and that is that. The WHAT IT WOULD BE WORTH question is a lot harder to answer

I think if the person who obtained the solution was charismatic it could be worth tens of millions. I mean perfect play would put Kasparov to shame and he's made a pretty decent chunk of change off this game with his charisma matched with his ability.

But yeah, either way. Give the 'solver' out - and it's worthless and -EV for everybody. Keep it to yourself and it's worth a small fortune.

Interesting take. I guess this seems like the consensus as to what is best is to keep it to yourself if it's easy, and if it is hard to use it makes no difference because chess is hard too and so then software or direct sale to World Champ or something is worth considering.

Thanks for the help!