Some games feel like tiny universes we almost understand: in tic-tac-toe, perfect play guarantees a draw, while in chess we sense there must be a right move even if we can’t see it. Life, on the other hand, looks a lot more like poker: we act on incomplete information, the deck shuffles against us, and “good” decisions can still lead to bad outcomes. In this post, I will use familiar games to explore how information, randomness, and sheer complexity shape what can be known, what can be “solved”, and why a choice can be reasonable even when the result hurts. Later, I will zoom out to careers, physics and relationships to ask what it really means to play well in an uncertain world.
Tiny universes: games as labs for uncertainty
Let’s think about games like toy universes: tiny, self-contained worlds where the rules are simple, the pieces are few, and everything that can ever happen is, at least in principle, laid out in front of us. Tic-tac-toe is one of these: two players, nine squares, a handful of possible positions, and a well-known verdict. If both players known what they are doing, nobody ever wins. Chess lives in a much bigger universe, with more possible positions than there are atoms in the observable cosmos, yet it still has the same feeling of order: no hidden cards, no dice, just two minds and a shared board. Poker, by contrast, feels messy from the start. There are secret hands, shuffled decks, and probabilities instead of certainties. You can make the right call and still lose, or a terrible call and get rewarded.
Follow me to explore those tiny universes and think more clearly about the big one we actually live in. By looking at games, we can tease apart different kinds of uncertainty: not knowing what others know, not knowing how the world will evolve, and not being able to compute everything even when, technically, the rules are fixed. We will wander from tic-tac-toe to chess to poker; from small, “solved” worlds to vast, effectively unsolvable ones; and then out into real life. You can think of careers, physics, relationships, where decisions are rarely black and white and where “playing well” often matters more than winning any single hand.
Seeing the board: perfect vs imperfect information
In some worlds, everyone can literally see everything that has ever happened. In others, key facts are hidden just out of sight. That’s the difference between perfect and imperfect information, and once you notice it, you can’t unsee it.
In tic-tac-toe and chess, every move is made on a shared board, fully visible to both players. There are no secret pieces, no face-down tiles, no surprise dice rolls. If you blundered three moves ago, your opponent can point to the exact square where it happened. These are games of perfect information: at any moment, the entire history of the game and the current position are common knowledge. In theory, nothing is “hidden” from anyone; the only mystery is whether you can think far enough ahead.
Poker lives on the other side. Your cards are private, the deck is unknown, and you never see the full state of the game while you are playing. Even if you replay a hand later, you only reconstruct what was there by revealing what used to be hidden. This is imperfect information: some relevant facts exist right now but are invisible to at least one player. You are not just thinking; you are guessing, inferring, reading people, trying to update your beliefs as new clues trickle in.
That one shift, from “we both see everything” to “someone is in the dark”, changes almost everything about how you play. In perfect-information games, strategy is about calculation and pattern recognition: if you think harder, you can, in principle, see deeper. In imperfect-information games, strategy is also about managing uncertainty: you are not just choosing moves, you are choosing how much to reveal, how much to conceal, and how to act when the picture will never be complete. Life tends to look a lot mire like poker than chess: you rarely have the full board in view, yet you have to move anyway.
Knowing the payoffs: complete vs incomplete information
Even when everyone sees the same board, they might not be playing the same game in their heads. That’s the twist behind complete and incomplete information: it’s not about what moves have been played, but about whether you understand what everyone wants and what the underlying “rules of reward” are.
In a clean, classroom version of chess, we quietly assume complete information. Both players know the rules, the possible outcomes, and the basic ranking of preferences: a win is better than a draw, which is better than a loss. You don’t have to wonder whether your opponent secretly prefers stalemates for aesthetic reasons or gets a bonus for losing their queen. The structure of the game and everyone’s goals are common knowledge. Even in tic-tac-toe, this assumption is baked in: nobody is deliberately trying to lose; X and O both want three in a row.
Poker already broke perfect information with hidden cards, but it also breaks complete information. You might know the official rules and payout structure, but you don’t know how risk-loving your opponent is, how they value money, or whether they’re the kind of maniac who will happily go all-in on a weak hand just for the thrill. Two players can look at the same pot and the same odds and “see” very different payoffs in their minds. The same goes for real-world situations like salary negotiations or auctions: the other side’s budget, urgency, and private goals are part of the game, but you only ever see shadows of them.
This shift from complete to incomplete information changes the nature of strategy. When payoffs and preferences are common knowledge, you can reason directly about “if I do X, they’ll respond with Y because they also want to maximize the same kind of payoff.” When you’re unsure what others value, you’re no longer solving a single, crisp game. Instad, you’re juggling a whole family of possible games and trying to guess which one you’re actually in. In that sense, life rarely offers us pure complete‑information situations. Other people’s motives, constraints, and private rewards are always a bit opaque, so we learn to think in probabilities and stories rather than in exact trees and tables.
Dice in the machine: deterministic vs stochastic
Some worlds don’t need dice because the rules alone already decide what happens next. Others have randomness wired into their physics. That’s the difference between deterministic and stochastic games, and it’s another way in which chess and poker quietly live on opposite sides of a fence.
Chess and tic‑tac‑toe are deterministic. From any given position, if you know the rules and the players’ moves, the next position is fixed. There is no shuffling, no coin flipping, no cosmic coin toss deciding whether your knight suddenly disappears. In principle, if a super‑intelligence could read both players’ minds and follow the rules, it could trace out the whole game tree with no surprises. The only “uncertainty” is in our heads: we don’t know what the opponent will choose yet, or what we ourselves will notice in time.
Poker, by contrast, is explicitly stochastic. The deck is shuffled, cards are dealt at random, and part of the game is learning to think in probabilities: how often this card comes on the river, how likely your opponent is to have a stronger hand, how frequently a particular line will work if repeated many times. Here, even a perfect strategist cannot know the future with certainty; they can only shape the odds in their favor. The same is true of any game with dice, random events, or “nature” making moves: the rules themselves say, “sometimes, this outcome just happens.”
This distinction matters because it sharpens what we mean by a “good” decision. In deterministic worlds, good play often feels like precise calculation: if you think clearly enough, you can navigate to a guaranteed win or draw. In stochastic worlds, good play is more about managing risk and variance: you choose actions that are right on average, knowing that any single hand, game, or day might go against you. Life leans heavily toward the stochastic side. Weather, markets, health, accidents, serendipity, other people’s choices, all inject dice into the machine. Learning to live with that means judging ourselves less by single outcomes and more by whether we consistently push our probabilities in the right direction.
When the future is pre‑written: solved games
Some games are small enough that, in a sense, the story is already finished. You’re just acting it out. That’s what it means for a game to be solved: from any position, there is a known, provably best way to play, and the final outcome (win, lose, or draw) is fixed if both sides follow those moves. Tic‑tac‑toe is the classic example. With only nine squares and a limited number of possible positions, people and computers have mapped out every line of play. If both players avoid mistakes, the game must end in a draw. There is no secret winning strategy left to discover; the universe of tic‑tac‑toe is completely charted.
Now contrast that with chess. Chess is finite and deterministic just like tic‑tac‑toe: no randomness, no hidden cards, and only a finite (though enormous) number of possible games. In theory, this means chess could be solved: there exists some perfect answer to the question “what happens with best play from both sides?” But in practice, the game tree is so astronomically large that we haven’t come close to fully mapping it. Modern engines play at a superhuman level and can “solve” many endgame positions, yet they are still sampling an ocean rather than draining it. So chess sits in an interesting limbo: mathematically destined to be solvable, practically beyond our reach for now. It might feel mysterious and creative not because the universe is random, but because the space of possibilities is too vast for our limited minds and machines to fully tame.
This contrast between solved and unsolved games loops back to how we see problems in life. Some puzzles really are tic‑tac‑toe‑sized: tax forms, small scheduling problems, tight technical tasks. Given enough time and a clear head, you can in principle find the “perfect” solution. But many of the situations that matter such as careers, relationships, large projects, diplomacy, feel more like chess or beyond: finite in some abstract sense, yet far too complex to ever be fully solved. In those worlds, the game is not about finding the one pre‑written script, but about developing good heuristics, rules of thumb, and styles of play that work well across many possible futures.
How big is a game? Finite vs countably infinite
When we talk about “solving” a game, we’re really bumping into a quieter question: how big is this universe, exactly? That’s where ideas like finite and countably infinite sneak in, not as dry set theory, but as a way of measuring how hard a game is to fully understand.
A finite game universe is one where, if you were absurdly patient, you could in principle list every possible situation and every complete play. Tic‑tac‑toe is like this. There are only so many ways to fill nine squares with Xs and Os, and only so many move sequences before the board is full or someone wins. Chess is also finite: the pieces and board are fixed, rules limit repetition and illegal positions, and any actual game has a bounded length. The universe is enormous, but it has edges; if you had a infinite compute power and time, you could imagine writing down every legal position and every possible full game.
A countably infinite universe is different. Here, there are infinitely many possible states or play histories, but they’re still “listable” in principle: you could number them 1, 2, 3, and so on, even though the list never ends. Some idealized games work like this. Imagine a game that can, in principle, go on forever, players take turns writing digits of a number, or moving a token along an endless track, with no rule that ever forces the game to stop. No matter how far you go, there’s always room for one more move. The space of possible complete plays is infinite but still comes in a neat, countable sequence. You could never finish the list, but you can at least imagine enumerating it.
Why does this matter? Because the size of the game’s universe tells you something about what “solving” it might involve. For small, finite games, you can sometimes analyze every possibility and compress the universe into a simple rule such as “perfect play leads to a draw.” For vast but finite games like chess, that’s theoretically possible but currently practically unreachable: the universe is technically bounded but effectively endless for human minds. For truly infinite games, you abandon the idea of checking every path and instead focus on patterns, strategies, and guarantees that hold across an unbounded landscape. In everyday life, most of what we care about behaves like those last two cases. The state space of “your career” or “your relationships” is not literally infinite, but it’s large enough that, for all practical purposes, you’re not going to exhaustively map it; you navigate it with heuristics and values rather than a complete catalogue of futures.
Good play, bad luck: ex ante vs ex post decisions
One of the most misleading stories we tell ourselves is that a good decision must always lead to a good outcome. In messy, stochastic worlds, that’s just not true. Decision theorists draw a clean line here with two Latin labels: ex ante (before the fact) and ex post (after the fact). Ex ante, you choose based on the information and probabilities available at the time; ex post, you judge with full hindsight, knowing exactly how the coin landed. The uncomfortable reality is that in a world with dice in the machine, even the best ex‑ante choice can look terrible ex post if you happen to land in the unlucky tail.
Poker makes this painfully concrete. Imagine calling an all‑in bet with a strong hand that statistically wins 70% of the time. In the long run, that call is profitable; it is the correct play ex ante. But 30% of the time you’ll lose your stack and look like an idiot in the one hand everyone remembers. If you grade yourself only on that single outcome “I lost, so the decision was bad” you’ll start punishing good strategy and rewarding the occasional lucky mistake. The same pattern shows up in investing, product bets, and even everyday choices: a conservative decision can “work” by sheer luck, while a bold, well‑reasoned move can blow up because the 1‑in‑10 scenario happened to be today.
Thinking in ex‑ante terms is a kind of mental hygiene. It asks you to judge yourself and others not just by what happened, but by how the choice was made: what information was gathered, what alternatives were considered, whether the risks were understood, how the trade‑offs matched your values. Ex post, outcomes still matter, they’re the feedback that updates your beliefs about the world, but they are noisy signals, not moral verdicts. Seen this way, “good play, bad luck” stops being an excuse and becomes a sober description of how rational action and random outcomes coexist. The art, in games and in life, is to build a process that you’d be proud of even on the days the river card goes against you.
Life is not tic‑tac‑toe: careers, physics, and relationships under uncertainty
If tic‑tac‑toe is a toy universe we can completely solve, real life is the opposite: a sprawling, partially charted landscape where the rules shift, the payoffs are fuzzy, and the game never really ends. You never get to see the full board. Your information is incomplete, other people’s motives are only partly visible, and randomness slips into everything from job markets to medical diagnoses. The result is that careers, physics, and relationships all end up feeling a lot more like poker or an open‑ended chess game than like a neat puzzle with a single correct answer.
Careers are a good example. You choose a degree (or not), a city, a company based on snapshots: forecasts that might be wrong, managers who might leave, technologies that might boom or vanish. Ex ante, moving to a risky startup, changing fields, or taking a sabbatical can be exactly the right call given what you know and what you value. Ex post, a recession hits or a product fails and the move looks like a blunder.
Physics, at the cutting edge, lives with a different flavor of uncertainty: even when the equations are precise, measurements come with error bars, models compete, and the universe itself, at quantum scales, refuses to let certain quantities be pinned down at the same time.
Relationships blend all of this: imperfect information about who someone really is, incomplete information about how both of you will change, and stochastic shocks from health, family, and circumstance. In none of these domains do you get tic‑tac‑toe style certainty; instead, “playing well” means accepting that you’re acting with partial information, under real randomness, and that a decision can be deeply sound even if the story it leads to is not the one you hoped for.
From chessboards to life choices: living with incomplete information
Chess seduces us with a comforting illusion: if only we could think far enough ahead, we’d always find the right move. Life breaks that illusion early. The board is never fully visible, the rules change mid‑game, and other “players” have private goals and constraints we never quite see. The common thread running through all the ideas in this essay, perfect vs imperfect information, complete vs incomplete information, determinism vs randomness, finite vs effectively infinite games, is that we are almost always choosing under genuine uncertainty. We do not know everything that matters, we cannot compute everything that’s possible, and luck will always have a vote.
Living with incomplete information, then, is less about trying to turn life into chess and more about learning to play well without a solved game tree. It means caring about ex‑ante decision quality instead of worshipping ex‑post outcomes. It means building habits that work across many futures rather than optimizing for a single imagined one. It means staying curious about other people’s hidden payoffs instead of assuming they share ours. And it means forgiving our past selves for not having access to the data, models, and hindsight we enjoy now. If tic‑tac‑toe were a fantasy of total control and poker a nightmare given bad luck, real life sits in the complicated middle: structured enough that our choices matter, uncertain enough that we never get guarantees. The best we can do is to keep updating our beliefs, refine our heuristics, and accept that “playing well” is a way of moving through the world, not a promise of always winning the game.
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