Update Beliefs with New Evidence (Bayesian Thinking)

You're frozen. The deadline's approaching. You don't have all the data. Everyone wants certainty. You can't give it. Sound familiar?

Maybe it's a hiring decision with three qualified candidates and red flags on each one. Or a product launch where the market research is mixed. Or a career pivot where you can't predict which path leads where. You want more information. More time. More certainty. But you're not going to get it.

Meanwhile, a small group of professionals—poker players, venture capitalists, military strategists—consistently make better decisions than the rest of us in exactly these situations. Not because they have more information, but because they've mastered something fundamentally different: they think in probabilities, not certainties. I learned this the hard way—I once created a biometric security algorithm that the NSA reverse-engineered, where I mastered probabilistic thinking perfectly in the technology, then made every wrong bet with the business around it.

By the end of this episode, you'll possess a powerful mental toolkit that transforms how you approach uncertainty. You'll learn to estimate likelihoods without perfect data, update your beliefs as new information emerges, make confident decisions when multiple uncertain factors collide, and act decisively even when you can't guarantee the outcome. This is the difference between paralysis and power, between gambling recklessly and betting wisely.

What Is Probabilistic Thinking?

But what does probabilistic thinking actually entail? At its core, it's the practice of reasoning in terms of likelihoods rather than absolutes—thinking in percentages instead of yes-or-no answers. Instead of asking “Will this work?” you ask “What are the odds this will work, and what are the consequences if it doesn't?” This approach acknowledges that the future is uncertain and that every decision carries risk. By quantifying that uncertainty and weighing it against potential outcomes, you make smarter choices even when you can't eliminate the unknown.

The Cost of Demanding Certainty

Today's world punishes those who demand certainty before acting. Research from Oracle's 2023 Decision Dilemma study—which surveyed over 14,000 employees and business leaders across 17 countries—found that 86% feel overwhelmed by the amount of data available to them. Rather than clarity, all that information creates decision paralysis.

And the paralysis has real consequences. When we can't be certain, we freeze. We endlessly research options, seeking that final piece of data that will guarantee success. We postpone critical decisions, waiting for perfect information that never arrives. Meanwhile, opportunities pass us by, problems grow worse, and competitors who are comfortable with uncertainty move forward.

This demand for certainty doesn't just slow us down—it exhausts us. Decision fatigue sets in as we agonize over choices, draining our mental resources until we either make impulsive decisions or avoid deciding altogether. Neither outcome serves us well.

What Certainty-Seeking Actually Costs You

Here's what it looks like in real life: You're the VP of Marketing. Your CMO wants a decision on next quarter's campaign budget by Friday. You have three agencies to choose from, each with strengths and weaknesses. So you ask for more data. Customer focus groups. Competitive analysis. Agency references. By Wednesday you're drowning in spreadsheets and conflicting opinions.

Friday arrives. You still can't be certain which choice is right, so you ask for an extension. Two weeks later, you finally pick one—not because you're confident, but because you're exhausted and the CMO is furious about the delay. The campaign launches late. You've burned political capital. And you still have no idea if you made the right choice.

Meanwhile, your competitor's marketing VP looked at the same decision, spent two hours assessing the probabilities, and launched on time. If it works, great. If it doesn't, they'll pivot. They didn't need certainty. They needed enough information to make a good bet.

That's the tax you pay for demanding certainty: missed timing, exhausted teams, and decisions made from fatigue rather than judgment.

Meanwhile, a small group of professionals thrives in these exact conditions. Professional poker players like Annie Duke understand that good decisions sometimes lead to bad outcomes and bad decisions sometimes get lucky—so they judge their choices by process, not results. Venture capitalists often see that most of their investments will fail, but they bet anyway because one success out of twenty can return the entire fund. Military strategists make life-and-death decisions with incomplete intelligence, not because they're reckless, but because waiting for perfect information means defeat.

The difference isn't access to better information. It's the willingness to act on probabilities rather than certainties.

How To Make Better Decisions When Nothing Is Certain

So how do you actually develop this skill? It's more accessible than you might think. Here are clear strategies to transform how you process uncertainty and make decisions.

Think in Ranges, Not Points

The first shift in probabilistic thinking is abandoning single-number estimates for ranges of possibility. When most people predict an outcome, they pick one number: “Sales will be $500,000 next quarter” or “This project will take three months.” But the world doesn't work that way. Every estimate carries uncertainty, and pretending otherwise sets you up for failure.

Professional forecasters think differently. They don't ask “What will happen?” They ask “What's the range of plausible outcomes, and how likely is each?” This approach forces you to acknowledge what you don't know while still making useful predictions.

Watch a professional poker player deciding whether to call a bet. They're not thinking “Do I have the best hand?” They're thinking “Given what I've seen, maybe 35% chance I have the best hand, 20% chance my opponent is bluffing, 45% chance they've got me beat.” They act on probabilities, not certainties.

Steps to implement range thinking:

1. Replace point estimates with probability ranges. When making any prediction, state a range instead of a single number. Instead of “We'll close 50 deals,” say “We'll likely close 40-60 deals, with a small chance of 30-70.”
2. Assign rough percentages to your ranges. You don't need mathematical precision—just honest self-assessment. Estimate: “60% chance of 40-50 deals, 30% chance of 50-60, 10% chance outside that range.” This forces you to think about likelihood, not just possibility.
3. Track your estimates against actual outcomes. Keep a simple log of your predictions and what actually happened. Over time, you'll discover if you're consistently over-optimistic, over-cautious, or actually well-calibrated. This feedback loop is how you improve.

Update Your Beliefs with New Evidence

One of the most powerful aspects of probabilistic thinking is treating your beliefs as hypotheses, not conclusions. When new information emerges, skilled thinkers update their probability estimates rather than clinging to their original position. This practice—called Bayesian updating after the mathematician Thomas Bayes—is how professionals stay accurate in changing environments.

Consider a doctor diagnosing a patient with intermittent chest pain. Initially, based on the patient's age and health history, she estimates a 15% probability of heart disease. Then the EKG comes back with minor abnormalities—not definitive, but concerning. She updates her estimate to 35%. Blood work shows elevated cardiac markers. Now she's at 65%. Each piece of evidence shifts the probability, but none gives absolute certainty. She doesn't wait for 100% certainty to act—she orders more tests and starts precautionary treatment based on her updated 65% estimate. That's Bayesian thinking in action.

Financial firms continuously adjust their models as new data arrives. Weather forecasters update storm predictions hourly. In my own work building biometric security systems, we updated our false acceptance and rejection rates constantly—but I failed to apply that same updating framework to the business model itself.

The enemy of updating is confirmation bias—our tendency to accept information that supports our existing beliefs and dismiss information that contradicts them. When you're emotionally invested in being right, you'll unconsciously filter evidence to protect your original view.

Steps to update your thinking:

1. Start with a baseline probability before you have strong evidence. If you're launching a new product, estimate: “Based on what I know about similar products, there's maybe a 40% chance this succeeds.” That's your prior—your starting point before specific evidence comes in.
2. When new information arrives, ask: “How much should this change my estimate?” Not all evidence is equal. Strong evidence—like actual customer purchases—should move your probability significantly. Weak evidence—like one person's opinion—should barely budge it.
3. Separate the quality of a decision from the quality of the outcome. This is crucial. A good decision based on sound probabilities can still result in a bad outcome due to chance. Conversely, a terrible decision can get lucky. Judge yourself on whether you correctly assessed the probabilities and acted accordingly, not on whether you “got it right” this time.
4. Actively seek disconfirming evidence. Force yourself to look for information that contradicts your current view. If you think your strategy will work, deliberately search for reasons it might fail. This counteracts confirmation bias and gives you a more accurate probability estimate.

Make Decisions by Expected Value

Probabilistic thinking isn't just about estimating odds—it's about acting on them. The concept of expected value gives you a framework for making decisions when outcomes are uncertain. Expected value multiplies each possible outcome by its probability, then adds them together. It's how professionals decide whether a bet is worth taking.

Here's why it matters: sometimes a decision with a low probability of success is still the right choice if the potential payoff is enormous. Venture capitalists know that perhaps 18 out of 20 startups in their portfolio will fail or return little money. But that one company that becomes the next Airbnb or Uber can return 100x their investment—more than covering all the losses. That's positive expected value thinking.

Conversely, decisions that seem “safe” can be terrible bets. Playing it safe might give you a 90% chance of mediocre success, but if that 10% downside risk includes catastrophic consequences, the expected value might be negative. This is why you buy insurance: the probability of your house burning down is low, but the cost if it happens is devastating.

Think about a parent choosing between schools for their child. Public school is free but overcrowded. Private school costs $20K/year with smaller classes but adds an hour of family stress daily. Charter school is free with innovative curriculum but it's a first-year program with unknowns. There's no guarantee. The better question is expected value: “Given the probabilities and what matters most to us—academic success, family time, financial stability—which bet has the best expected outcome?”

Steps for expected value decision-making:

1. List all plausible outcomes for your decision, not just the best and worst. For a job offer, don't just think “great career move” versus “terrible mistake.” Consider: “Modest improvement (40%), breakthrough opportunity (20%), lateral move (25%), step backward (10%), complete disaster (5%).”
2. Assign a rough value to each outcome. This doesn't have to be money—it can be career satisfaction, life quality, time saved, or any currency that matters to you. The key is making the values comparable across outcomes.
3. Multiply each outcome's value by its probability, then add them up. This gives you the expected value. If the positive expected value option has meaningful downside risk, ask: “Can I survive the worst case?” If yes, it's usually the right bet.
4. Remember: expected value is about long-term results, not single instances. If you make a high expected value bet and it fails, that doesn't mean you were wrong. Over many decisions, following expected value will outperform any other approach. Trust the math, not the emotional reaction to one outcome.

Practice: The Probability Forecast Journal

A practical way to develop your probabilistic thinking is to keep a Probability Forecast Journal. This exercise builds calibration—your ability to accurately assess how confident you should be in your predictions.

Here's how to implement it:

1. Choose three areas where you regularly make predictions. These could be work-related (project timelines, sales numbers), personal (will your flight be delayed), or current events (election outcomes).
2. Each week, make five specific, testable predictions. Write down the prediction and assign a probability. For example: “70% chance the client approves our proposal by Friday” or “85% chance our website traffic increases this month.”
3. After each prediction resolves, record the actual outcome. Did the thing you said had a 70% chance of happening actually happen? Don't judge yourself harshly on any single prediction—remember that a 70% prediction should fail about 30% of the time.
4. Monthly, analyze your calibration. Look at all predictions where you said “70% confident”—did roughly 70% of them come true? If you're consistently overconfident, you need to adjust. If you're underconfident, you're being too cautious.

The goal isn't perfection—it's calibration. After several months of this practice, you'll notice your ability to assess probabilities improves dramatically. You'll know when you're 60% sure versus 90% sure, and you'll make better decisions as a result.

The Rewards

Mastering probabilistic thinking is a journey, not a destination. It requires practice, humility about what you don't know, and the courage to act despite uncertainty. But the rewards are substantial.

When you think probabilistically, you make faster decisions because you're not paralyzed waiting for certainty that will never come. You become more resilient to failure because you understand that good decisions sometimes have bad outcomes—and that's not a reason to change your approach.

You'll find yourself taking calculated risks that others avoid, capturing opportunities that demand action before perfect information arrives. You'll waste less time second-guessing yourself because you've already thought through the probabilities and made your peace with uncertainty. You'll explain your decisions more clearly to others because you can articulate not just what you think will happen, but how confident you are and why.

Most importantly, you'll stop confusing confidence with correctness. In a world obsessed with appearing certain, probabilistic thinkers have the courage to say “I'm 65% sure, and that's enough to act.” That honesty—with yourself and others—is the foundation of better judgment.

Want to see what happens when you master probabilistic thinking in one domain but fail to apply it in another? I wrote about my experience creating a fingerprint recognition algorithm that the NSA reverse-engineered—where I got the technical probabilities right and the business bets completely wrong. 

Read the full story here

The future will always be uncertain. The question is whether you'll be paralyzed by that uncertainty or empowered by it.

If this helped you think differently about decision-making, I'd really appreciate it if you'd hit the like button and subscribe—it genuinely helps others find this content through the algorithm. And click that notification bell so you don't miss the next episode in this series.

If you want to go deeper, I share the behind-the-scenes thinking, mistakes, and extended stories over on Studio Notes on Substack. Paid subscriptions help cover the costs of the team who makes all of this possible—the editing, research, and production work that gets these episodes to you each week. None of it comes to me; it all goes to supporting them. Without this team, there'd be no podcast, no YouTube channel, no articles. So if you find value in this work, that's a meaningful way to keep it going.

The future will always be uncertain. The question is whether you'll be paralyzed by it or empowered by it.

To learn more about probabilistic thinking, listen to this week's show: How To Make Better Decisions When Nothing Is Certain.

Get the tools to fuel your innovation journey → Innovation.Tools https://innovation.tools

SOURCES CITED IN THIS EPISODE

Oracle Decision Dilemma Study (2023) – Survey of 14,000+ employees and business leaders across 17 countries on data overwhelm and decision paralysis. https://www.oracle.com/uk/cloud/decision-dilemma/

Thinking in Bets – Duke, A. (2018). Portfolio. On judging decisions by process, not outcomes. https://www.penguinrandomhouse.com/books/552885/thinking-in-bets-by-annie-duke/

How to Improve Bayesian Reasoning Without Instruction: Frequency Formats – Gigerenzer, G. & Hoffrage, U. (1995). Psychological Review, 102(4), 684-704. On updating beliefs with evidence.

Prospect Theory: An Analysis of Decision under Risk – Kahneman, D. & Tversky, A. (1979). Econometrica, 47(2), 263-291. Prospect Theory foundations.