April 9, 2026
I'm not really a chess player. It's not really my type of game, at least to play, for similar reasons to why I don't play fighting games. Something about the skill differential, maybe, I don't know, but that's not why I'm thinking about chess today. Recently I watched a video about Connect 4 being "solved". It got me thinking about a question that's burned in my mind for a while. That question is...
Somehow, I'm convinced that it must be a calculable (albeit very large) and finite number.. But, some caveats, for the sake of clarity: First, it's a distinct question from "number of games" (as far as I have read in the past, this number has been estimated, but never truly calculated), since there are many board states that could be achieved by several different sequences of actions. Second, it doesn't assume "perfect play" by expert chess players trying to win the game, but more along the lines of monkeys at typewriters trying to arrive at every possible point.
I'm far from a math expert, or a programming expert, or anything of the sort. Yet, I feel as if the solution - or at least the path towards it - is on the precipice of my mind. What I know about the problem is as follows.
Conceptually, the board in chess is an 8x8 grid, where each spot on the grid can be represented by 13 different states, one state for each color of each piece, and one more for an empty tile. You could represent this mathematically (though I don't even know how to do that). Of course, this wouldn't solve it by itself. It'd be impossible, for example, to have a full board where all 64 spots are occupied by a white bishop. So it has to be narrowed down - the board starts with only half of its spots occupied, and new pieces can never be added (only promoted, in pawns' case), so the number of blank spaces must always be at least 32. You can't ever have more than 1 of either king. There's only 8 of each color pawns to start, and each can be promoted to any other non-king piece, so you can have at most 8(ish) of any non-king piece (and you would have to also take into account how many pawns would have to have been promoted to arrive at how many of those pieces you have, depending on how many you start with - there's only 8 pawns, but 1 queen, and 2 rooks/bishops, etc.).
So hypothetically, then, the solution could be found in a problem something like this: For an 8x8 grid, where each space can have a value of 0-12 (0 being empty), where at least 32 spaces must be 0, and exactly one space must be 1 (white king) and one must be 2 (black king), where no more than X spaces can share the same value greater than 2, X being variable depending on the type of piece... how many possible states of that grid would there be?
If someone went and figured out how to represent and calculate all those numerical conditions to calculate the total... then what? Is that the answer? No. It's still missing a lot of info accounting for the rules of the game, like pawns only being able to move forward except when taking or en passant, illegal board states where both players are simultaneously in check, things like that. I don't think every caveat like that could be predicted in advance. Maybe you'd have to manually review whether a game of chess even could arrive at that state at all. But the result would be such a large number, doing that by hand, alone, would obviously be impossible. I don't know if such a thing is really feasible, by calculation or otherwise. But I do believe it must be possible.
My train of thought usually stops here. I don't know enough about math or programming or anything to take it further. But it keeps eating at me, and it came to mind again today, so I felt I needed to get it off my chest.
P.S. this is the first time I've updated my website in a long while, like, since before cohost went down (oops. and RIP). My cohost profile is still linked on my homepage... I'll fix that later. I keep waiting for myself to want to overhaul parts of my website, or migrate it, or something, before I commit to updating it... but I think that's a mental pitfall, and I should just update it while I've written this instead of waiting for the perfect opportunity when I suddenly have enough focus to redo everything (which probably won't happen). So, here you go. Things are scary out there right now, so tell your loved ones that you love them and all that jazz.