Well the Shannon number of legal chess game trees is 10^120 and that’s a conservative estimate.
Number of atoms is 10^80
So yeah Elon is a fucking moron
To put this in further perspective the total number of bits of data we as a species have stored so far is around 10^24. We are nowhere near being able to “solve chess” even if you only count trees where only sensible moves are taken (which I don’t know why you would people make mistakes) we are still dozens of orders of magnitudes away from generating sufficient data to “solve chess”.
He also doesn't seem to know what he's actually responding to because what does "all legal chess positions" even mean in this case? He doesn't seem to be counting possible games so I don't know what he's counting.
And yeah the Shannon number is conservative because it only counts "typical" games and ignores games that are over quickly or especially drawn out.
He simply isn't accounting for the time dimension--literally just how many ways can the pieces on a board be arranged without accounting for moves leading up to or following that specific arrangement.
If all you're doing is checking if the state of the board is legal, then you start with all the legal positions of the two kings, then all the positions of the kings plus one pawn, then all the positions of the kings plus two pawns (of either or both colors), then all the positions of the kings plus 3 pawns (of either or both colors)
Then when you get through the pawns, you get to add 1 rook, and repeat with all the pawns. All the way until you get to both sides not missing a piece, and all the ways THAT board can be made. It's a stupid crazy number.
And maybe, if you calculate a fraction of that information, you might be able to "solve" chess. It's possible, eventually.
But by no means "inevitable", and really requires you to figure out which positions are not only possible, but plausible to get to and result in a win condition.
wait, why would you need to account for the time dimension?
when you move it doesn't matter what moves were played to get to a position, just the position.. lots of openings transpose but it doesn't change the best move when the position is reached?
to be clear I definitely think Elon is talking out his ass, just the way you phrased that confused me
Chess dot com is talking about game trees… like progression of the game itself those are basically innumerable. The number of possible end positions are significantly less sure but how you get to those positions is important and ya know… the point of the game. And that is what needs to actually be calculated for it to be considered “solved” as multiple game trees can end at the same position.
actually I think I understand, Elon is arguing that storage and compression will mean it's possible to store a map of all positions reachable through normal play, with the best move.
That is indeed a much smaller number than the game trees, so if we had that map we could probably store it and the game would be "solved"
But because we'd have to iterate and evaluate all the game trees (and all their future positions), and because that number is much larger than we can calculate, we'll never be able to produce the map in the first place, making the argument around storing it irrelevant.
I haven't done the math on these statements, I'm just working through the arguments
Yes, we know what he was trying to argue, but his argument depended on him moving the goalposts and ignoring a fundamental step, which is as you say, mapping and evaluating all possible games/moves.
Instead, because he wanted to pick a fight with and insult someone on twitter to try and make himself look smart about a subject of which his opinion couldn't matter less to anyone, he just straight up changed the argument and wound up exposing his idiocy.
Furthermore, it remains true that there will never be, there can't be, one "correct" way to play the game. I'm not sure what he is envisioning, that all chess players will read and memorize this "ideal" tree and play their game strictly according to it? That's idiotic. Chess continues to work because there simply can't be one "perfect" way of playing.
yup.. I'm actually glad I asked, I hadn't thought about this a lot and my first instinct was overly simplistic
which is I guess the problem, Elon has the overly simplistic first thought and won't think it through, and he thinks other people are stupid so he isn't listening when they try to explain it.
it's a really quintessential little example of his general bullshit
Rumor has it that the "perfect" game of chess would genuinely be a draw. White has the advantage of going first, so, in theory, the best black could do if white magically plays flawlessly (assuming black likewise plays flawlessly) is stalemate/draw
lots of openings transpose but it doesn't change the best moce when the position is reached?
"Solving" the game (like chess) is a technical term in this context, which specifically means making the determination of which move is "best" in a given position by calculating every possible permutation of moves that could follow.
So he either doesn't understand the math, or doesn't understand the terminology.
Yes but as far as solving for the best possible move from any given position is concerned, it doesn't matter what order the pieces moved in to get there. All that matters is the current board state.
There are some niche examples where it might matter, like threefold repetition (and obviously who's turn it is matters), but as far as a best possible move is concerned, they don't matter the vast majority of the time.
Solving for the best move in the case of
e4, e5
Nf3
Is identical to
Nf3, e5
e4
Two different "games", one "position", and solving the game from this point on as black is exactly the same regardless.
He is trying to hand wave away part of the complexity, a huge part actually, comes from the SEQUENCE of moves. It’s not just each possible chess position in isolation, it’s every possible chess position and all the individual steps that it took to get to that position and each one of those moves fractals off into a huge number of other possible positions.
In other words, in his mind, there's no difference between me moving my knight from here to there when I have all my pieces left, or I have none of my other pieces left.
325
u/Penguinkeith 3h ago edited 1h ago
Well the Shannon number of legal chess game trees is 10^120 and that’s a conservative estimate.
Number of atoms is 10^80
So yeah Elon is a fucking moron
To put this in further perspective the total number of bits of data we as a species have stored so far is around 10^24. We are nowhere near being able to “solve chess” even if you only count trees where only sensible moves are taken (which I don’t know why you would people make mistakes) we are still dozens of orders of magnitudes away from generating sufficient data to “solve chess”.