Algorithms to Live By

By Brian Christian & Tom Griffiths

16 min read

Why does it matter? Because the rational ideal — survey all options, pick the best — is computationally impossible in the real world.

You're standing in a San Francisco apartment, checkbook in hand, and you have thirty seconds to decide. Walk away and you might spend months regretting the one that got away. Sign and you might spend years regretting the stone left unturned. The cruel part: every minute you spend gathering information to make a better decision is a minute the apartment is still on the market. This isn't a quirk of San Francisco real estate — it's the shape of an entire class of decisions, and it's genuinely hard. And computer science has known the mathematically optimal solution for fifty years. The answer turns out to be a number: 37%. But that's just the beginning. Once you see how the algorithms computers use to handle limited time, imperfect information, and finite memory map onto human life, your own so-called cognitive failures start looking less like bugs and more like reasonable engineering under impossible constraints.

The 37% Rule: There's a Provably Optimal Way to Stop Searching

You've found the apartment. The light is good, the commute is manageable, the price is almost right. The landlord is standing in front of you with a lease. Do you sign?

This is the trap. You've only visited three places. Maybe something better is out there. But if you walk away to keep looking, this one is gone — the San Francisco rental market doesn't do callbacks. Every apartment is a one-way door.

Here's what makes this genuinely hard: to know whether an apartment is the best available, you need a baseline. To build a baseline, you need to look at apartments. But looking at apartments means passing on apartments. The very act of gathering information destroys the opportunities you're trying to evaluate. It's not a personality flaw or a failure of nerve — it's a structural paradox built into the problem itself.

Most people sense that the answer involves some balance between exploring and committing. They're right. What they don't know is that mathematics has worked out exactly what that balance is. The answer is 37%.

If you have 30 days to find an apartment, spend the first 11 just looking. No checkbook, no commitments — you're calibrating. Then, starting on day 12, take the first place that beats everything you've seen so far. This is called the Look-Then-Leap Rule, and it's not a heuristic or a rule of thumb. It's the mathematically proven best answer to a problem type called optimal stopping.

The result has a striking property: the strategy's success rate matches the threshold itself. Look at 37% of candidates, get a 37% chance of landing the best one. That might sound discouraging — the best possible approach still fails nearly two-thirds of the time. But here's the part that should stop you: this success rate holds regardless of how large the pool is. Whether you're choosing among 100 apartments or a million, optimal stopping delivers the same 37% odds. Without the algorithm, your chances collapse toward zero as options multiply. With it, they stay constant. The bigger the haystack, the more valuable knowing where to look.

To see what this looks like in practice, consider Michael Trick, an operations researcher at Carnegie Mellon who ran these numbers on his own love life. Assuming his search would run from age 18 to 40, the 37% threshold pointed to age 26.1 as the moment to stop exploring and start committing. Right on schedule, he met someone better than everyone he'd dated before, and he proposed. She said no. This is the part the algorithm can't fix — it optimizes your strategy, not your outcome. The math gives you the best possible odds. What happens next is not in its hands.

What the 37% rule does clarify is that hesitation and commitment are no longer matters of temperament or courage. They're a math problem, and now it has a solution.

Thinking More Isn't Always Better — Sometimes It's the Problem

More analysis feels like more control. List every pro and con, identify every relevant factor, run every scenario — surely the decision improves as the inputs multiply. It seems obviously correct. Machine learning research suggests it is often catastrophically wrong.

The demonstration comes from a German study tracking life satisfaction through the first decade of marriage. You have ten data points and want a formula that can predict beyond them. A one-factor model — just time since marriage — draws a straight line, captures the general dip after the honeymoon, but forecasts that unhappiness will compound forever toward infinite misery. A two-factor model curves back up and levels off, which is actually what long marriages look like. Then there's the nine-factor model, which threads through every single data point with perfect precision — not one miss.

Except when you ask it to predict the future. The nine-factor model says you should expect misery at the altar, a giddy recovery after a few months, a roller-coaster through the middle years, and a cliff-drop after year ten. Vary the data slightly — run the survey again with a different group — and the model gyrates into completely different absurdities, while the simpler models stay roughly stable. The nine-factor formula doesn't understand the underlying pattern; it has memorized the noise. This is overfitting: a model so perfectly tuned to the specific data it has seen that it loses all grip on the world that data was sampled from.

The lesson cuts deep. Adding factors to a model will always improve how well it matches existing data — mathematically, this is guaranteed, the same way a line through two points fits perfectly but a line through one point can point anywhere. But matching existing data and predicting new outcomes are different things, and past some point they actively trade off against each other. The most sophisticated model available is not the most accurate model available.

Harry Markowitz discovered this from an uncomfortable angle. He won the Nobel Prize in Economics for inventing mean-variance portfolio optimization, the mathematical framework for allocating investments to maximize returns at a given risk level. When it came time to invest his own retirement savings, he didn't use it. Instead he split his money evenly between stocks and bonds. His reasoning: the formula requires accurate estimates of how different assets will behave, and errors in those estimates can push the optimization in wildly wrong directions. A simple fifty-fifty split doesn't try to fit the historical data at all — which means it can't overfit it either. The man who built the most sophisticated investment algorithm available concluded that, under realistic conditions of uncertainty, ignoring the data was the smarter bet.

The principle generalizes. When the gap between what you can measure and what actually matters is large — when your data is noisy, your inputs uncertain, your proxy metrics imperfect — complexity becomes a liability. The right move is to stop early, use fewer factors, paint with a broader brush. Not because rigor is overrated, but because in an uncertain world, a simpler model fails more gracefully when reality doesn't match the data you fed it.

Your Brain Doesn't Forget — It Prioritizes, and It's Doing It Optimally

Overfitting is what happens when analysis drowns in its own detail. But the brain faces a different problem with information: not too much analysis, but retrieval under load — which is why you forget names.

The intuitive answer is that your brain ran out of room, or that memory deteriorates with age — some kind of storage failure, a hard drive filling up or wearing out. Carnegie Mellon psychologist John Anderson spent years believing something similar. Then, in 1987, he read about library information retrieval systems and saw the problem completely differently.

Anderson realized the brain's challenge isn't storage at all. It's organization. You can't hold everything at the front of your mind simultaneously — there's only so much cognitive workspace — so the brain has to decide, constantly, what to surface. The question becomes: is it making those decisions well?

To find out, Anderson and his collaborator Lael Schooler did something unusual. Instead of studying forgetting in the lab, they studied the world. They analyzed word frequency in years of New York Times headlines, in recordings of parents talking to their children, in Anderson's own email archive. The question was simple: once a word or topic appears, how quickly does it stop appearing? What they found was striking. The rate at which subjects fade from the world's attention follows almost exactly the same curve as the rate at which things fade from human memory — the Ebbinghaus forgetting curve, the reliable arc of how fast memories fade, that psychologists had been puzzling over for a century.

We forget at the same rate the environment stops talking about things. That's not a flaw in the design. That's the design. Human memory is tuned, with remarkable precision, to the statistical structure of the world around it — surfacing what the environment is currently referencing, quietly deprioritizing what it's stopped mentioning. A cache, not a hard drive.

That reframes cognitive decline. Michael Ramscar at the University of Tübingen showed that retrieving information takes longer when you have more of it — not because the search process slows down, but because the archive genuinely grows. A 65-year-old navigating decades of names, places, and experiences isn't failing at an easy problem. They're running a harder search than they've ever run before, on a larger dataset than most computers are asked to manage. What looks like a stumble is often just load. A brain fart, properly understood, is a cache miss — and the delay is partly a measure of how much you know.

The Explore-Exploit Tradeoff Explains Why Your Habits Change as You Age

Imagine you're spending a year living in a new city. In the first few months, you eat everywhere — the sketchy noodle stall, the Brazilian place no one has reviewed yet, the third Thai restaurant on the same block. Then, as your departure date approaches, you stop experimenting. You spend your last weeks at the five places you love most. This isn't neurosis or nostalgia. It's optimal strategy.

Data scientist Chris Stucchio described exactly this pattern from his own life: adventurous eating across Pune, India when he arrived, then a strict return to favorites as he was leaving New York. The math behind his instinct is clean. The value of exploring — finding something new and wonderful — comes entirely from what you do with that discovery afterward. Find the best restaurant in town on your last night, and you've wasted the information. The longer your remaining time, the more exploration pays. The shorter it is, the more ruthlessly you should exploit what you already know.

Psychologist Laura Carstensen found the same logic buried inside something that looked like decline. Older people have smaller social networks than younger people, and the standard explanation is diminished capacity: less energy, less reach. Carstensen found something else entirely. When young people were asked to imagine they were about to move away, they immediately preferred spending time with close family over meeting interesting strangers. When older people imagined receiving twenty additional years of life, their preferences shifted back toward novelty. The variable driving behavior wasn't age — it was perceived time remaining. Shrinking social networks in old age aren't deterioration. They're rational pruning: cutting the exploration budget because the exploitation window has grown short, and reinvesting in the relationships most worth savoring. What looks like withdrawal is actually a portfolio rebalancing toward known returns.

The Scheduling Mistake That Nearly Wrecked a Mars Rover

In the summer of 1997, a $150 million rover was navigating the Martian surface for the first time in human history — and silently ignoring its most important job. The Mars Pathfinder had crossed 309 million miles of empty space, bounced to a landing on airbags, and was now mysteriously neglecting the task of shuttling data through its information bus. Instead, it idled on medium-priority busywork. Eventually the onboard system noticed the neglect, panicked, and rebooted entirely — wiping out a full day's work. Then it happened again.

JPL engineers, working furiously from Earth, eventually diagnosed the problem: priority inversion. A low-priority task had locked a shared resource, then been interrupted before finishing. The scheduler, doing its job, tried to run the high-priority data task — but couldn't, because that resource was occupied. So it moved down the list and ran medium-priority tasks instead. The high-priority work sat blocked indefinitely, starved by work that mattered less, held hostage by work that mattered least. The fix, beamed across millions of miles of space, was called priority inheritance: if a low-priority task is blocking something critical, it temporarily becomes the most urgent thing in the system until it finishes and releases the lock.

Conventional productivity advice breaks down here. Doing the most important thing available sounds like wisdom. But "available" is doing serious work in that sentence. Sometimes your highest priority genuinely cannot proceed until something trivial gets finished first — a precedence constraint, in scheduling terms. Treating the trivial blocker as low-priority doesn't defend your priorities. It defeats them. The unimportant task is what matters most right now, because everything downstream is waiting on it.

The broader picture is more humbling still. The vast majority of scheduling problems — 84%, by one survey — have no efficient solution; no algorithm exists or is likely to exist. Only 9% can be cracked cleanly. The sensation of calendar overwhelm isn't a discipline problem. It's an encounter with genuine computational hardness. The chaos is built into the structure of the problem itself, not into you.

What scheduling theory does offer is a cleaner metric for the tractable cases. Rather than ranking tasks by importance alone, divide each task's importance by how long it will take. Work the highest-ratio item first — this is called Weighted Shortest Job First. You only bump a longer task up the list if it's proportionally more valuable: twice as long only jumps the queue if it's twice as important. The answer isn't always to do the hard thing first, or the urgent thing, or even the important thing. It's whichever task gives you the most value per unit of your finite time.

Your Hunches Are Actually Bayesian Inference — And the Marshmallow Test Was Wrong

How reliable are your gut feelings? The standard advice says not very — trust data, not instinct, be systematic, be rigorous. But there's a compelling case that your instincts are already doing something close to rigorous, just invisibly.

In the 1970s, Walter Mischel ran his famous marshmallow experiment at a Stanford nursery school. The children who ate immediately were tagged as lacking willpower — and when Mischel followed up decades later, the early-eaters had lower SAT scores, suggesting that impulse control at age four predicted life success.

But researchers at the University of Rochester ran a different version that reframes everything. Before the marshmallow appeared, an experimenter made each child a promise about art supplies — then either kept it or broke it. Then came the marshmallow test. The children who'd been deceived ate the marshmallow early. Not because they lacked willpower. Because they had learned, from fresh experience, that this adult doesn't follow through. Waiting, for them, was a bad bet.

Four-year-olds doing Bayesian reasoning. If adults in your life disappear for unpredictable stretches — if their absence follows what statisticians call a power-law distribution, where a long wait predicts a longer one — then eating the marshmallow early is the correct move. The Multiplicative Rule applies: waiting time compounds, so the longer you've already waited, the longer you should expect to keep waiting. The kids who 'failed' the willpower test may have been applying accurate priors about the adults in their world.

Mischel's finding that early-eaters did worse later in life might not be measuring self-control at all. It might be measuring the trustworthiness of the environments those children grew up in.

Tom Griffiths and Josh Tenenbaum at MIT tested human intuition more broadly and found the same pattern: people's gut predictions about movie grosses, human lifespans, and congressional tenures closely matched what Bayes's Rule — the math of updating beliefs from evidence — would calculate from the actual statistical distributions of those quantities. We absorb accurate priors from experience without knowing it. Small data — a single observation, a gut feeling — isn't thin because it lacks volume. It's dense because it arrives loaded with everything you've already learned about how the world tends to go. In domains you know well, your instincts are already doing the math.

When the Best Algorithm Is to Randomize

The two sections share a premise worth naming: both treat apparent irrationality as engineering. Bayesian updating looks like second-guessing; the marshmallow test looks like impulse control dressed up as wisdom. What follows looks like giving up. It isn't.

In 1946, Stanislaw Ulam was recovering from emergency brain surgery for encephalitis at Los Alamos, worried he'd never think clearly again. To pass the time, he played solitaire. And as he played, he found himself wondering: what fraction of shuffled decks actually produce a winnable game? The naive approach — reason through all the possibilities — was immediately hopeless. A standard deck has more than eighty unvigintillion possible orderings. No one was working through that. So Ulam tried something that felt almost like giving up: just play it out. Deal the cards, see what happens, repeat. Track the wins. The proportion converges to the answer.

The insight sounds obvious until you realize what it replaces. Analysis — the thing we trust — was simply unavailable. The problem wasn't that Ulam lacked mathematical sophistication; it was that the space of possibilities was too large for any mind, human or mechanical, to examine systematically. Sampling didn't produce a worse answer than analysis. It produced an answer when analysis produced nothing at all. Ulam and John von Neumann formalized this into the Monte Carlo Method, which went on to solve nuclear physics problems with the same logic: simulate random interactions, run them many times, let the distribution of outcomes tell you what exhaustive calculation cannot.

This principle reaches further than anyone expected — into problems that seem to have nothing to do with probability. When Michael Rabin needed to test whether a massive number was prime (a yes-or-no question, nothing fuzzy about it), he found that picking random test values and checking them against a set of equations could drive the error rate to effectively zero. Ten random checks: less than one-in-a-million chance of a wrong answer. Forty checks: the odds of a wrong answer are lower than one false prime per grain of sand on Earth. That algorithm still runs behind every credit card transaction you make — not despite its randomness, but because of it. The deterministic alternative doesn't exist.

The Tournament Bracket Is a Lie — And So Is Every Ranking You Trust

The silver medal is a lie. Charles Dodgson — better known as Lewis Carroll — proved this with uncomfortable precision in 1883, when a tennis player's complaint about losing a tournament sent the Oxford mathematician into a formal investigation of bracket formats. His finding: in a single-elimination structure, the second-best competitor in the entire field could be eliminated in the very first round by the eventual winner, and someone substantially weaker would claim the runner-up prize. The probability that the truly second-best player actually wins the silver? Sixteen out of thirty-one. Barely better than a coin flip.

The math gets grimmer when you account for randomness in the games themselves. If any given basketball matchup is won by the stronger team 70% of the time — already a generous assumption — then winning six straight games happens for the best team less than 12% of the time. The format would correctly identify the best team roughly once a decade. What looks like a definitive ranking is mostly noise dressed up in bracket form.

Tournaments aren't unfair so much as optimized for something other than accuracy. Michael Trick, who designs schedules for Major League Baseball, notes that the grueling quadratic regular season — every team playing every other team, repeatedly — isn't inefficient. It's deliberate. The games themselves are the point. But when accuracy does matter, round-robin turns out to be the most noise-robust sorting algorithm known: it maps onto Comparison Counting Sort, which survives unreliable comparisons better than anything faster. If your team fails to make the playoffs, you have no statistical complaint. If your team loses in the first round, you might.

The Kinder Move Is to Make Decisions Easier for Everyone Around You

Picture two versions of the same favor. Someone needs you to show up somewhere on Tuesday. Version one: 'Let me know when you're free this week.' Version two: 'Would 1 p.m. Tuesday work?' The first feels more considerate — you're leaving the choice open, respecting their schedule, not presuming. But the authors discovered the opposite when scheduling their own interviews: researchers were more likely to say yes to a specific time slot than to an open-ended invitation. Strange, until you understand what each request is actually asking the other person to do.

Verification is easy. Search is hard. Checking whether Tuesday at 1 works requires a quick scan of one calendar square. Finding the optimal time across an open week requires generating options, weighing constraints, guessing at the asker's preferences — the mental equivalent of a combinatorial search. 'At a convenient time this week' hands someone a search problem. 'Does Tuesday at 1 work?' hands them a yes-or-no question. The polite move turns out to be the computationally brutal one.

Computational kindness means structuring your requests so the cognitive work they require of others is as light as possible. Computation is inherently costly, and good design minimizes it. When we interact with other people, we're constantly handing them problems. The question is whether we're making those problems easier or harder.

The bullfight in Spain lands the point. Three friends on a trip discovered, only after the event sold out, that none of them had actually wanted to go. Each had read the others' vague enthusiasm and mirrored it back, producing a group consensus that existed nowhere except in the gap between them. 'I'm flexible' sounds accommodating, but it passes the hardest possible task to everyone else: guessing what you actually want is some of the hardest mental work anyone can do for someone else. Asserting a preference — even softly, even tentatively — is often the kinder act. It gives people something to respond to instead of something to construct from scratch.

The same logic scales up. A well-designed parking garage is effortless: one spiral, take the first open spot, no decisions required. A multi-lane maze forces look-then-leap analysis under social pressure. That difference — between a system that absorbs cognitive load and one that distributes it onto every user — is available in the way you schedule a meeting, frame a question, or order at a table. The algorithms don't just belong to you. They belong to every interaction you're part of.

What Good Algorithms Actually Have in Common

The most unsettling thing this book does is make rationality look different than you thought. You probably imagined it as thoroughness — covering every option, minimizing guesswork, resisting shortcuts. But the computers we've built to solve hard problems don't work that way, and neither do the best-performing humans. They apply LRU and forget strategically. They stop at 37% and commit before certainty arrives. They run Monte Carlo and randomize when stuck. Not because they're being lazy. Because those are the genuinely correct moves when time runs out and information stays incomplete. What looks like cutting corners is often just reality-adjusted thinking. And when you recognize that, something quietly shifts in how you treat other people too. Handing someone a specific time instead of an open question, asserting a preference instead of performing flexibility — these stop feeling like impositions and start feeling like gifts. Reducing the cognitive weight you place on others isn't just courtesy. It turns out to be the most human algorithm of all.