What distinguishes “early”, “mid” and “end” games?
Recently William_S posted:
In my mental model, we’re still in the mid-game, not yet in the end-game.
I replied:
A thing I’ve been thinking about lately is “what does it mean to shift from the early-to-mid-to-late game”.
In strategy board games, there’s an explicit shift from “early game, it’s worth spending the effort to build a longterm engine. At some point, you want to start spending your resources on victory points.” And a lens I’m thinking through is “how long does it keep making sense to invest in infrastructure, and what else might one do?”
I assume this is a pretty different lens than what you meant to be thinking about right now but I’m kinda curious for whatever-your-own model was of what it means to be in the mid vs late game.
He replied:
Like, in Chess you start off with a state where many pieces can’t move in the early game, in the middle game many pieces are in play moving around and trading, then in the end game it’s only a few pieces, you know what the goal is, roughly how things will play out.
In AI it’s like only a handful of players, then ChatGPT/GPT-4 came out and now everyone is rushing to get in (my mark of the start of the mid-game), but over time probably many players will become irrelevant or fold as the table stakes (training costs) get too high.
In my head the end-game is when the AIs themselves start becoming real players.
This was interesting because yeah, that totally is a different strategic frame for “what’s an early, midgame and endgame?”, and that suggests there’s more strategic frames that might be relevant.
I’m interested in this in the context of AI, but, also in other contexts.
So, prompt for discussion:
a) what are some types of games or other “toy scenarios,” or some ways of looking at those games, that have other strategic lenses that help you decisionmake?
b) what are some situations in real life, other than “AI takeoff”, where the early/mid/late game metaphor seems useful?
One model I have is that when things are exponentials (or S-curves), it’s pretty hard to tell when you’re about to leave the “early” game, because exponentials look the same when scaled. If every year has 2x as much activity as the previous year, then every year feels like the one that was the big transition.
For example, it’s easy to think that AI has “gone mainstream” now. Which is true according to some order of magnitude. But even though a lot of politicians are talking about AI stuff more often, it’s nowhere near the top of the list for most of them. It’s more like just one more special interest to sometimes give lip service too, nowhere near issues like US polarization, China, healthcare and climate change.
Of course, AI isn’t necessarily well-modelled by an S-curve. Depending on what you’re measuring, it could be non-monotonic (with winters and summers). It could also be a hyperbola. And if we all dropped dead in the same minute from nanobots, then there wouldn’t really be a mid- or end-game at all. But I currently hold a decent amount of humility around ideas like “we’re in midgame now”.
You get more discrete transitions when one s-curve process takes the lead from another s-curve process, e.g. deep learning taking over from other AI methods.
I like Buck’s A freshman year during the AI midgame: my approach to the next year post from 2023.
Here’s his taxonomy:
I think games sometimes go through something like a phase transition, where strategy heuristics that serve you well on one side of the border abruptly stop working. I think this is typically because you have multiple priorities whose value changes depending on the circumstances, and the phase transitions are where the values of two priorities cross over; it used to be that X was more important than Y, but now Y is more important than X, and so heuristics along the lines of “favor X over Y” stop working.
I don’t think that these phase transitions can be generalized to anything as useful as the concepts of solid/liquid/gas—or at least, I’m not aware of any powerful generalizations like that. I don’t have a set of heuristics that I deploy “in the mid-game” of most or all games. Nor do I think that most games have exactly 3 phases (or exactly N phases, for any N). I think of phrases like early/mid/late-game as meaning “the phase that this particular game is usually in at time X”.
I do think you can make a general observation that some investments take a while to pay for themselves, and so are worth doing if-and-only-if you have enough time to reap those benefits, and that this leads to a common phase transition from “building up” to “scoring points” in many engine-building games. But I think this particular observation applies to only one genre of game, and explains only a minority of the use of phrases like “early game” and “late game”.
As an example of an unusually sharp phase transition: In Backgammon, if you land on a single enemy piece, it sends that piece back to the start. This is a big deal, so for most of the game, players spend a lot of effort trying to “hit” enemy pieces and defend their own pieces. But players have a fixed number of pieces and they can only move forward, so there comes a point where all your pieces are past all of my pieces, and it’s no longer possible for them to interact. At that point, attack and defense become irrelevant, and the game is just about speed.
I once read about the development of Backgammon AI using early neural nets (I think this was in the 70s and 80s, so the nets were rather weak by today’s standards). They found the strategy changed so much at this point that it was easier to train two completely separate neural nets to play the two phases of the game, rather than training a single net to understand both. (Actually 3 separate nets, with the third being for “bearing off”, the final step of moving your pieces to the exact end point. I think modern Backgammon AIs usually use a look-up table for bearing off, though.)
(Training multiple neural nets then caused some issues with bad moves right around the phase boundary, which they addressed by fuzzing the results of multiple nets when close to the transition.)
I don’t think this story about Backgammon reveals anything about how to play Chess, or StarCraft, or Civilization. Most games have phase transitions, but most games don’t have the particular phase transition from conflict-dominant to conflict-irrelevant.
Another example: I once told someone that, in a certain strategy game, 1 unit of production is much more valuable than 1 unit of food, science, or money, “at least in the early game.” The reason for that caveat was that you can use money to hurry production, and by default this is pretty inefficient, but it’s possible to collect a bunch of stacking bonuses that make it so efficient that it becomes better to focus on money instead of regular production. But it takes time to collect those bonuses, so I know you don’t have them in the early game, so this heuristic will hold for at least a while (and might hold for approximately the whole game, depending on whether you collect those bonuses).
Again, I don’t think this teaches us anything about “early game” in a way that generalizes across games. Probably there are lots of games that have a transition from “X is the most important resource” to “Y is the most important resource”, but those transitions happen at many different points for lots of different reasons, and it’s hard to make a useful heuristic so general that it applies to most or all of them.
A third example: The game of Nim has the interesting property that when you invert the win condition, the optimal strategy remains precisely identical until you reach a specific point. You change only one move in the entire game: Specifically, the move that leaves no piles larger than size 1 (which is the last meaningful decision either player makes). You can think of this as a phase transition, as well (between “at least one large pile” and “only small piles”). And again, I’m not aware of any useful way of generalizing it to other games.
Nod.
I can’t remember if I said this already, but the way I’m looking at this is “take stock of various clusters of strategy heuristics or frameworks, and think about which-if-any apply to stuff that I care about.” So, less looking for universal principles, more “try on different strategic lenses and see what shakes out.”
I keep feeling like I’m on the edge of being able to give you something useful, but can’t quite see what direction to go.
I don’t have an encyclopedia of all my strategic lenses. (That actually sounds like kind of an interesting project, but it would take a very long time.)
I could babble a little?
I guess the closest thing I have to generalized heuristics for early vs late games are: In the early game, desperately scramble for the best ROI, and in the late game, ruthlessly sacrifice your infrastructure for short-term advantage. But I think those are mostly artifacts of the fact that I’m playing a formalized game with a strict beginning and end. Also notable is the fact that most games are specifically designed to prevent players from being eliminated early (for ludic reasons), which often promotes an early strategy of “invest ALL your resources ASAP; hold nothing in reserve” which is probably a terrible plan for most real-life analogs.
If I try to go very general and abstract on my approach for learning new games, I get something like “prioritize efficiency, then flexibility, then reliability” but again this seems like it works mostly because of the ways games are commonly designed (and even a little bit because of the type of player I am) and doesn’t especially apply to real life.
I would say that Civilization, if anything, has the opposite transition, though still less sharp.
Elaborate?
Early on, you’re far enough from your opponents that you can’t really meaningfully compete with them. You’re competing with the environment, and random events. It isn’t until you expand enough to actually run into each other and need to capture resources and territory from each other that conflict becomes significant.
Then again, maybe I’m wrong and this is why I’m not very good at Civ
Thanks for clarifying. I consider the pre-contact period to be a rather small portion of the game, but certainly you can’t attack people on turn 1 or turn 2, so there’s definitely a non-zero time window there.
(This varies somewhat depending on which Civ game, and yeah probably good players expand faster than less-good ones.)
I think that simplest modification is from “game-that-ends” to “eternal game”, which consists of:
Equilibrium—current stable state from which strong players benefit and weak players can’t change
Violation of equilibrium—something happens, players see new opportunities and try to move state of the gameboard to desired direction
New equilibrium—players recognize that new state is stable (moving away is too costly), return to supporting it.
The difference is that usually you can plan for future violations of equilibrium, even if you can’t “win” in current.
That metaphor suddenly slide from chess into poker.
I would point out that these concepts only exist in finite games. Yes, “survive the development of AGI” is very much a finite game we have to win, but “then continue to thrive afterwards” is an infinite game. Life, in general, is an infinite game. For infinite games, these boundaries blur or vanish. In some sense it’s all midgame, however many transitions and phases the midgame includes.
I will speak to the question of “what are some situations in real life, other than “AI takeoff”, where the early/mid/late game metaphor seems useful?”. It seems to me that such a metaphor is useful in any situation with
—two or more competitors,
—who start small and expand,
—in a fixed-size field of contention,
—and such that bigger competitors tend to beat small ones.
The phases in such a competition can be described as
—Early: competitors are building up power and resources more or less independently, because they’re not big enough to run into each other significantly. Important to strategize correctly. You can plan longer term because other players can’t upset your plans yet.
—Mid: what other players do matters very much to what you do. Maximum coupling leads to maximum confusion.
—End: time for the leading player to grind down the smaller players. Becomes easier to understand as hope disappears.
Chess is an example, where there are two competitors, and the resource is “pieces that have been moved and not yet taken”. This also applies to multiplayer tabletop games (which is where I thought of it). It also applies to companies moving into a new product area, like desktop operating systems in the ’80s. It applied to European colonial powers moving into new continents.
I think the most natural definitions are that early game is the part you have memorized, end game is where you can compute to the end (still doing pruning), and mid game is the rest.
So eg in Scrabble the end game is where there are no tiles or few enough tiles in the bag that you can think through all (relevant) combinations of bags.
I think perhaps the phases of a 4X game.
Explore: gain information that is relevant for what plan to execute
Expand: Investment phase, you take actions that maximise your growth
Exploit: You slowly start depriotizing growth as the time remaining grows shorter.
Exterminate: You go for your win condition
The “early game is what you have memorized” makes sense for literal games, but doesn’t actually help much with my current use-case, which is “and this translates into real life.” (when I’m thinking about these in game-form, I’m generally thinking about one-shot gaming, where you’re trying hard to win your first time playing a game, such that figuring out the early game is part of the challenge)
I think you mix up translating into real life with translating into one-shot gaming.
For most real-world problems there’s a series of things people who are good at solving those problems do in the beginning when faced with the problem. If you want to fix a computer issue, “Reboot your computer” is an early game move.
Sure, but those areas aren’t the ones that have me interested in gaming metaphors to figure out how to solve my problems.
‘Found a startup’ is a bit more of an established process that ‘counts’ for my purposes here. There’s a lot of reading and learning I can do before getting started. (Compared to ‘build a functioning alignment community’). But even there I think it’s less like playing a game I’ve already studied such that the early game is memorized, and more like sitting down to play a multiplayer game for the first time, which shares structure with other games but is still involved a lot of learning on the fly. (I bet this is still reasonably true on your second or third startup, though maybe not if you literally are running Y Combinator). though interested in hearing from people who have run multiple to see if they think that tracks.
Sorry I see now that i lost half a sentence in the middle. I agree that the notions of early/mid/late game doesn’t map well to real life, and I don’t think there is a good way to do so. I then (meant to) propose the stages of a 4X game as perhaps mapping more cleanly onto one-shot games
Probably shouldn’t limit oneself from thinking only in terms of 3 game phases or fitting into one specific game, in general can have n-phases where different phrases have different characteristics.
I suspect it’s easy to find games or situations that have nice-ish three phase maps, for example:
Choosing a particular chess move: (I) assess the board, (II) generate some candidates moves, (III) find the best move of the candidates
Getting new work as a contractor: (I) get a rough idea of what the potential client wants, (II) create a detailed specification and work plan, (III) finalize financial, ownership, termination, etc details in a contract
Discovering a mathematical proof: (I) gather some foundational knowledge relevant to the problem/proposition, (II) search for ways to connect knowledge (and tricks) into a proof, (III) having found a good candidate strategy, try to develop a proof
Maybe my examples miss the spirit of the early/mid/late game map. Do you agree that in strategy games the three phases are roughly: (I) develop engine, (II) use engine to create relative advantage, (III) try to win.
IMO one of the most important distinctions between middle and late game in chess is that the number of okay to good moves on any given turn is severely reduced in the late game compared to the middle game.
Yes, that was my original frame. But, the whole point of this post is that the Chess example was noticeably different from that, which suggested there might be other lenses that are useful.