This Paradox Splits Smart People 50/50

You enter a room with a supercomputer and two boxes. One open box contains $1,000. A mystery box's contents depend on the supercomputer's prediction about your choice before you entered.

• Take both boxes or just the mystery box • The supercomputer predicted your choice before you arrived • If it predicted you'd take one box, it put $1 million inside • If it predicted you'd take both boxes, it put nothing inside

The supercomputer has accurately predicted thousands of people in similar situations with nearly perfect accuracy. It is not trying to trick you or deprive you of money.

Do you take both boxes or just the mystery box?

The problem splits people into two roughly equal groups: one-boxers who take only the mystery box, and two-boxers who take both boxes. Philosopher Robert Nozick noted that each camp finds the other's position obviously wrong.

A 2016 Guardian poll of over 31,000 people found 53.5% were one-boxers and 46.5% were two-boxers, nearly perfectly split.

One-boxers argue that since the supercomputer accurately predicted thousands before, it will correctly predict them. Therefore, if they one-box, the $1 million will be there. Their expected utility is higher with one-boxing.

Two-boxers argue that the boxes are already set up and their decision cannot change what's inside. By strategic dominance, taking both boxes always yields $1,000 more than taking one box, regardless of the supercomputer's prediction.

One-boxers use evidential decision theory, basing their calculation on the supercomputer's proven accuracy. Evidence from thousands of correct predictions justifies expecting the $1 million when they one-box.

Two-boxers use causal decision theory, only considering things they can actually cause or influence. Since their current decision cannot change what was already placed in the box, they ignore the supercomputer's prediction and choose both boxes.

Both arguments are mathematically valid. The division comes from different assumptions about what matters: evidential decision theory values the supercomputer's predictive accuracy, while causal decision theory values only causality.

When Veritasium polled its audience with over 24,000 responses, two-thirds answered as one-boxers, showing the theory remains divisive.

The only way to win $1,001,000 is to be a one-boxer mentally but two-box at the last second. However, if the predictor is perfect, this is impossible.

• The rational act is to two-box and take both boxes • Yet in repeated games or society, one-boxers fare better • This shows rationality at the individual level differs from rationality at the societal level

One-boxers end up with more money than two-boxers, leading philosophers Gibbard and Harper to argue the game is rigged. However, this reveals that sometimes acting irrationally is what makes a rational person successful.

Perhaps rationality isn't about choosing optimally in the moment, but about deciding what rules and commitments to live by.

• By the mid-1960s, the US had over 30,000 nuclear warheads and USSR had over 6,000 • Secretary of Defense Robert McNamara advocated for 'assured destruction' strategy • Both sides could destroy each other multiple times over

If either country attacked first, the other would surely retaliate, leading to total annihilation. This commitment to retaliate, even when irrational in the moment, prevents attacks from happening.

A president publicly commits to retaliate against a Soviet attack. When missiles launch, retaliation means nuclear winter killing nearly everyone on Earth. The rational choice in that moment is not to launch.

A good leader maintains the appearance of always retaliating while secretly willing not to. Credibly committing to an irrational action paradoxically produces rational outcomes.

• If choices now can change the past through a wormhole mechanism • If multiple trials occur, building reputation with each game • If you can pre-commit to a choice before the predictor decides

In chicken, the best strategy is to visibly throw your steering wheel out the window, proving you cannot swerve. This commitment to an irrational action forces the opponent to swerve, making you win.

The film depicts a Soviet doomsday device that automatically triggers nuclear annihilation. The tampering kill switch prevents the Soviets themselves from having second thoughts, making the device a credible deterrent.

Rather than deciding what to do in the moment, decide what rules to live by. If you'd committed to one-boxing before learning the problem, you would one-box now because you live up to your pre-commitments.

Life doesn't end after leaving the room. You should always live according to the commitments that would've been good to make before facing any problem.

• In a one-shot game, defecting always gives more personal gain • In repeated games like life, cooperation becomes beneficial • Being a person who sticks to ideal pre-commitments creates better outcomes

By adopting the perspective that you've already made ideal pre-commitments, you reframe yourself as someone who one-boxes. This reframing doesn't require a new decision; it's living consistently with your best self.

You may have been a one-boxer kind of person all along. It took reframing and perspective to see that living by principle is actually the most rational approach.

Newcomb's paradox is fundamentally about deciding if a strong correlation you know isn't causal should matter in your decision.

The supercomputer's predictions are strongly correlated with outcomes, but your present decision does not causally change what was already placed in the box.

• How to determine if a drug really works or if effects are random chance • Distinguishing correlation from causation in real-world scenarios • Understanding what actually drives outcomes versus what merely correlates with them

This thought experiment with Brilliant's interactive courses helps build intuition about probability and reasoning through complex problems, applicable far beyond the paradox itself.