Newcomb's Paradox Explained: One-Boxing, Two-Boxing, and the Science of Rational Decision

Overview

In this Veritasium video, the famous thought experiment known as Newcomb's paradox is unpacked. A supercomputer predicts your choice before you act, and you must decide whether to take one box or two. The discussion contrasts evidential decision theory with causal decision theory, presents a probabilistic threshold, and uses this setup to probe what it means to be rational. A poll of thousands of viewers shows a split between one-boxers and two-boxers, highlighting that there is no single right answer.

What you’ll learn

How prediction, expected utility, and precommitment influence decision making, the difference between evidential and causal reasoning, and the broader implications for free will and practical rationality in life and policy.

Introduction

Veritasium presents Newcomb's paradox, a thought experiment where a near-perfect predictor has already arranged two boxes. Box A contains $1,000 and is visible; Box B is the mystery box that may contain $1,000,000 or nothing depending on the predictor’s forecast of your action. The predictor’s prediction is made before you learn about the problem and is not a trick. You can take both boxes or only the mystery box. What should you do?

Two Camps and the EU Calculation

The video frames two camps: one-boxers who take only the mystery box and two-boxers who take both boxes. By assigning C as the probability that the predictor is correct about your decision, Veritasium derives the expected utilities: one-box yields approximately $1,000,000 × C, while two-box yields a smaller return since taking both boxes often guarantees only the $1,000 reward plus the possible effect of the predictor’s past decision. Solving for the threshold where these utilities are equal gives about 50.05% (0.5005). If the predictor is better than random at predicting your choice, one-boxing yields a higher expected value.

Decision Theories in Play

The video then contrasts evidential decision theory (EDT) with causal decision theory (CDT). EDT uses information about what your choice implies about the predictor’s accuracy, leading to a guidance toward one-boxing. CDT argues that since the predictor’s prediction is in the past relative to your choice, your current decision cannot causally affect whether the million dollars is in Box B, making the dominant strategy to take both boxes and always gain the extra $1,000.

Dominance and Precommitment

Casper argues for a dominant strategy in the problem, but Veritasium reframes the problem by considering four possible outcomes depending on what is already in the mystery box. The key insight is strategic dominance and the power of precommitment: if you wired yourself to one-box in advance, your future actions would align with that commitment, potentially allowing you to secure the million dollars if your predictor is highly accurate.

Deeper Questions and Real-World Parallels

The discussion broadens to questions of free will, rationality, and the rules by which we live. The Newcomb paradox is linked to the Prisoner’s Dilemma and to the idea that sometimes rational action at the individual level may seem irrational for the broader system. The video emphasizes that there is no universally right answer; instead, the problem reveals how our assumptions about prediction, causality, and precommitment shape our sense of rational behavior.