I know dots and boxes has a large computation element. If you can read out the whole board before the other player, you can likely manipulate it to your favour and win the game. And basically all the dots and boxes content I can find has to deal with ways that you can compute the board sate more efficiently, to get an edge in this computation battle. What I'm wondering is if there are strategies that apply well before the point that you can solve the board in your head - moves that have no obvious benefit when they're made, but will likely help you out in the future. I find most established competitive games are like this. In the beginning things are way to complex to read, and players rely on making moves that study of the game has shown to be beneficial in the long run.
I think how relevant the computation element is, is more a property of the time-setting than the game. The search-space needs to be in a certain range, if it's too small or doesn't exist like in rock-paper-scissors then you won't spend a lot of time calculating even when given a lot of time, because there is nothing to calculate, if it's too big like in Fortnite then it makes no sense to even try. But in all strategic board games that come to mind I can sit down and spend hours thinking about my next move when given the time.
You can absolutely play Dots and Boxes with only a few minutes on the clock and if you do this the computation aspect completely vanishes and the important thing here is this: the game works just as well on low time, I actually like it even more that way. That being said, Dots and Boxes does have a trait that makes the computation element very present in turn-based play: The game WILL end after around 40 moves and at around move 20 it becomes an extremely significant part of the game to somewhat solve the position.
The answer to your question "if there are strategies that apply well before the point that you can solve the board in your head" is a pretty straightforward "yes". The most fundamental core strategy in Dots and Boxes is the long-chain-rule. I won't explain it here, you can look it up if you don't already know it. This is essentially a game where you try to build the correct amount of areas, inside of which you then build long-chains, and you can very well start working towards this quite early on. I think most games should be fairly "readable" from like move 8 onwards or so.
The very beginning of this game does feel really random to beginners, but there is opening theory even for the first move. The opening theory in this game is very strange though. On the one hand it has been proven that every first move wins so you can objectively say that no move is a mistake. And yet if you ask a top player they will be able to exactly tell you which first moves they think are good and which ones are bad. But the reason for why the moves are good or bad require a longer explanation and may come down to "games have shown that this is how it is". In chess you can logically understand why developing a piece could be a good thing, even as someone who doesn't even play the game, but in Dots and Boxes it's gonna be a lot more work to figure out why for example a lot of good players like to play edge moves early on as player 1.
I am aware of the long chain rule, but what I'm not aware of is how it can be used in a more strategic setting. At the moment, the only way I can really use the long chain rule is when I can see where the chains are going to be - where I need to stop chains if the opponent threatens them, and where I need to try to make some and hope my opponent doesn't stop me. But this still is basically me just computing the whole game when I'm doing this. If I want an odd number of chains, for example, I am not aware of any moves that are likely to help me make an odd number chains later into the game, even though I can't compute it right now. Those are the types of moves I'm wondering about.
Wow, thank you for the demonstration! I was familiar with your guide. I thought I read the whole thing but on a second look I realized I must not have.
Little Golem