Over the past 6 months I’ve played about 100 hours of the 4X game “The Battle of Polytopia.” Mostly playing on “crazy” difficulty, against 3 or 4 other tribes.
This is more than I’ve played any video game since I was 15 or so. I wanted to write up some of my thoughts, especially those that generalize.
Momentum
Polytopia is a game of momentum or compounding advantage. If I’m in the lead by turn 10 or so, I know that I am basically guaranteed to win eventually. [Edit 2024-09-12: after playing for another 30 hours, and focusing on the early game, I can now almost always win eventually, regardless of whether I have an early lead]. I can turn a current resource advantage into an overwhelming military advantage for a particular city, and seizing that city, get more of a lead. After another 10 turns, I’ll have compounded that until my tribe is an inexorable force moving across the square.
I think the number one thing that I took away from this game is the feeling of compounding momentum. Life should have that flavor.
And, in particular, the compounding loops through the world. In polytopia, you generally want to spend down your resources to 0 or close to 0, every turn, unless there’s a specific thing that you’re aiming to buy that requires more than one maringal-turn of resource. “Saving up” is usually going to be a losing proposition, because the return on investment of seizing a city or building the population of an existing city sooner is exponential.
This also generalizes. I’m very financially conservative, by nature. I tend to earn money and save it / invest it. There’s a kind of compounding to that, but it isn’t active. There’s a different attitude one could have, where they’re investing in the market some amount every year, and putting aside some money for emergencies, but most of their investment loops through the world. Every year, they spend down most of the money they own, and invest it in ways to go faster.
I think most people, in practice, don’t do this very well: they spend their salary on a nice apartment, instead of the cheapest apartment they can afford and tutoring, personal assistants, and plane flights to one-on-one longshot bet meetings. At a personal (instead of organizational) level, I think the returns to spending additional money saturate fast, and after that point you get better returns investing in the market. But I think there might be something analogous to the “spend down your whole budget, every turn” heuristic.
I’ve thought in the past that I should try aggressively spending more money. But maybe I should really commit to trying it. I have a full time salary for the first time in my life. Maybe this year, I should experiment with trying to find ways to spend 90% of that salary (not my investment returns, which I’ll reinvest), and see what the returns to that are.
This overall dynamic of compounding advantages is more concerning that I, personally, haven’t built up much of an advantage yet. Mediocre accumulation of money, connections, and skills seems “medium” good. But because of the exponential, mediocre is actually quite far down a power law. This prompts me to reflect on what I can do this year to compound my existing resources (particularly with regards to personal connections, since I realized late in life that who you know who knows what you can do, is a constraint on what you can do).
Geography
Because of this momentum effect, the geography of the square dominates all other considerations in the question of which tribe will eventually win. In particular, if I start out isolated, far from any other tribes, with several easily accessible settlements available to convert, winning is going to be easy. I can spend the first ten turns capturing those settlements and building up their population without needing to expend resources on military units for defense.
In contrast, if I start out sandwiched between two other tribes with all settlements that are within my reach also within theirs, the struggle is apt to be brutal. It’s still possible to win starting from this position: The key is to seize, and build up at least two cities, and create enough units defensively that the other tribes attack each other instead of you. (That’s one thing that I learned: you sometimes need to build units to stand near your cities, even when you’re not planning an attack, because a density of units discourages other tribes from attacking you, in the first place).
From there, depending on how dire the straights are, and if I’m on the coast, I’ll want to either
- Train defenders to garrison my cities, and then quickly send out scouts to convert nonaffiliated settlements, and build up an advantage that way, or
- Train an attack force (of mostly archers, most likely, because a mass of archers can attack from a distance with minimal risk) target a city that the other two tribes are fighting over. I can sweep in and seize it after they’ve exhausted themselves.
This can work, but it still depends on luck. If you can’t get to your first settlement(s) fast enough, or another tribe captures one of your cities before you’ve had time to build up a detering defense force, there’s not really a way to recover. I’ll be fighting against better resourced adversaries for the rest of the game, until they overwhelm me. Usually I’ll just start the game over when I get unlucky this early.
This overwhelming importance of initial conditions sure seems like it generalizes to life, but mostly as a dower reminder that life is unfair. Insofar as you can change your initial conditions, they weren’t actually initial.
Thresholds, springs, and concentration of force
There are units of progress in polytopia that are composed of smaller components, but which don’t provide any value until all components are completed.
For instance, it’s tempting to harvest a fruit or hunt an animal to move the resource counter of a city up by one tick. But if you don’t have the stars to capture enough resources to reach the next population-increase threshold for that city (or there just aren’t other accessible resources nearby), it doesn’t actually help to collect that one resource. You get no benefit for marginal ticks on the resource counter, you only get benefit from increases in city population.
Even if collecting the resource is the most valuable thing to do this turn, you’re still better off holding off and waiting a turn (one exception to the “spend down your resources every turn” heuristic). Waiting gives you optionality in how you spend those resources—you might have even better options in the next turn, including training units that were occupied last turn, or researching technologies
Similarly, capturing a city entails killing the unit that is stationed there, and moving one of your units into its place, with few enough enemy units nearby that your unit isn’t killed before the next turn. Killing just the central stationed enemy unit, without having one of your units nearby to capture the city, is close to useless (not entirely useless, because it costs the enemy tribe one unit). Moving a unit into the city, only for it to be killed before the next turn, is similarly close to useless.
So in most cases, capturing a city is a multi-turn campaign of continually training and/or moving enough units into position to have a relative military advantage, killing enough of the enemy units, and moving one of your units (typically a defender or a giant, if you can manage it) into position in the city.
Crucially, partially succeeding at a campaign—killing most of the units, but not getting all the way to capturing the city, it buys you effectively nothing. You don’t win in polytopia by killing units, except insofar as that is instrumental to capturing cities.
More than that, if you break off a campaign part way through, your progress is not preserved. When you back your units out, that gives the enemy city slack to recover and replenish their units. So if you go back to capture that city later, you’ll have to more or less start over from scratch with wearing down their nearby military.
That is to say, capturing a city in polytopia is spring-like: if you don’t push it all the way to completion, it bounces back, and you need to start over again. It’s not just that marginal progress doesn’t provide marginal value until you reach a threshold point. Marginal progress decays over time.
I can notice plenty of things that are spring-like in this way, once I start thinking in those terms.
Some technical learning, for instance. If I study something for a bit, and then leave it for too long (I’m not sure what “too long” is—maybe more than two weeks?) I don’t remember the material enough for my prior studying to help me much. If I want to continue, I basically have to start over.
But on the other hand, I read and studied the first few chapters of a Linear Algebra textbook in 2019, and that’s served me pretty well: I can rely on at least some of those concepts in my thinking. I think this differences is partly due to the material (some subjects just stick for me better, or are more conceptually useful for me compared to others). But largely, I think this is a threshold effect: if I study the content enough to chunk and consolidate the concepts, it sticks with me and I can build on it. But if I read some of a textbook, but don’t get to the point of consolidating the concepts, it just gets loaded into my short term memory, to decay on the order of weeks.
Writing projects definitely have the threshold-dynamic—they don’t provide any value until I ship them—and they’re partially but not fully spring-like. When I’ve left a writing project for too long, it’s hard to come back to it: the motivating energy is gone. And sometimes I do end up, when I’m inspired again, rewriting essentially the same text (though often with a different structure). But sometimes I am able to use partial writing from previous attempts.
Generalizing, one reason why things are springs, is because short term memories and representations decay, and you need to pass the threshold of consolidating into long term representations.
In polytopia, because capturing cities is spring-like, succeeding requires having a concentration of force. Splitting your forces to try to take two cities at once, and be worse than useless. And so one of the most important disciplines of playing polytopia is having internal clarity about which city you’re targeting next, so that you can overwhelm that city, capture it, consolidate it and then move on to the next one. Sometimes there are sudden opportunities to capture cities that were not your current target and late in the game, you might have more than one target at a time (usually from different unit-training bases).
Similarly, anything in my life that’s spring-like demands a concentration of force.
If technical learning in my short term memory tends to decay, that means that I need to commit sufficiently to a learning project for long enough to hit the consolidation threshold. I want to concentrate my energies on the project until I get to the point of success, whatever success means.
Same basic principle for writing projects. When writing, I should probably make a point to just keep going until I have a first complete draft.
Video games
Probably the most notable thing I learned was not from the content, but from the format. Video games can work.
I got better at playing polytopia over the period that I was playing it, from mostly losing to mostly winning my games. That getting better was mostly of the form of making mistakes, noticing those mistakes, and then more or less automatically learning the habits to patch those mistakes.
For instance, frustration at losing initiative because I left a city un-garrisoned and an enemy unit came up and took it without a fight while I wasn’t looking, led into a general awareness of all my cities and the quiet units within movement distance of them, so that I could quickly train a unit to garrison them.
Or running into an issue when I ran out of population for a city and couldn’t easily garrison it, and learning to keep a defender within one step of a city, so that I can train units there to send to the front, but move the defender into place when the population is full.
This was not very deliberate or systematic. I just kept playing and gradually learned how to avoid the errors that hobbled me.
And I just kept playing because it was (is) addictive. In particular, when I finished a game, there was an automatic impulse to start another one. I would play for hours at a stretch. At most I think I played for ten hours in a row.
Why was it addictive? I think the main thing is that the dynamic of the game means I never get blocked with no option, or no idea, for what to do next. At every moment there’s an affordance to move the game forward: either something to do or just moving on to the next turn. The skill is in taking actions skillfully, but not in figuring out how to take actions at all. I think this, plus an intermittent reinforcement schedule was crucial to what made it addictive.
Overall, this has been bad for my life, especially after the point when I started mostly winning, and I wasn’t learning as much any more.
But I think I learned something about learning and getting better in that process. I’ve been playing with the idea of intentionally cultivating that kind of addiction for other domains, or pretending as if I’m experiencing that kind of addiction to simulate it.
I bet I could get into a mode like this with programming, where I compulsively keep going for hours over weeks, and in the process learn the habits to counter my mistakes and inefficiencies, less because of anything systematic, and more just because those errors are present to mind in my short term memory by the time I encounter them again. I think I’m probably close to having enough skill in programming that I can figure out how to never be blocked, especially with the help of an LLM, and get into the addictive rhythm.
Further, this makes me more interested in trying to find video games that are both dopamine-addictive and train my intuition for an important domain.
I’ve been playing with Manifold markets, recently, and I feel like I’m getting a better sense of markets in the process. I wonder if there are good video games for getting an intuition for linear algebra, or economics. I have registered that playing 100 hours of factorio is an important training regime. I wonder if there are others.
I haven’t really played video games since I was in middle school (with the exception of some rationality training exercises on snakebird and baba is you). At the time I was playing Knights of the Old Republic, and decided that I would try to become a jedi in real life, instead of in the game. I mostly haven’t played video games since.
I now think that this was maybe a mistake.
It’s hard to know what lessons I would have learned if I had played more video games—when I played Age of Mythology and Age of Empires as a kid, I don’t remember getting better over time, as I did with polytopia. But I do think there are lessons that I could have learned from playing video games that would have helped me in thinking about my life. Notably, getting reps playing through games with early, mid, and late stages, would have given me a model for planning across life stages, which is something that, in retrospect, I was lacking. I didn’t have an intuitive sense of the ways that the shape of my opportunities would be different in my 20s vs. my thirties, for instance. Possibly I would have avoided some life errors if I had spent more time playing and learning to get good at, video games.
musings and rough drafts 