Newcomb's Problem, explained.
Newcomb’s problem is a choice between a sealed predicted prize and that prize plus a visible smaller reward, used to examine competing principles of decision.
Why it happens
Conditional reasoning asks what contents tend to accompany each choice under the prediction rule. Causal reasoning asks what taking an additional box changes when those contents have already been fixed. The comparisons need not give the same recommendation.
Newcomb’s problem puts evidential reasoning about a reliable prediction alongside causal reasoning about boxes whose contents are already fixed.
Read the result
Change the stipulated accuracy and compare the conditional means. A sampled outcome illustrates that model only. Also read the fixed-contents comparison: adding the open box always adds ten to whatever is already there.
A worked example
A 90% accurate stipulated predictor
With one-box predictions rewarded by 1,000, taking one box has conditional mean 900.
Taking both has conditional mean 100+10=110 under the same predictive convention.
Holding the sealed contents fixed instead makes the second box add ten; distinguish these questions before interpreting the choice.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The sealed box holds 1,000 tokens if the prediction was one box, otherwise zero. The open box holds 10. A stipulated predictor accuracy yields conditional expected payoffs; the realized teaching outcome is sampled after a choice, without implying backward causation.
Where this idea is useful
A practical use
A predictive association may help estimate outcomes while leaving a separate question about what an intervention actually changes.
A common misconception
“The game proves that a present choice changes the past.”
The conditional prediction model does not imply backward causation and cannot settle the philosophical dispute.
What this explanation leaves out
- This is a disputed philosophical thought experiment. The probability model stipulates the predictor and does not settle which decision theory is correct.
Why are two expected comparisons shown?
They make their assumptions explicit: predictive association is different from a causal intervention holding prior events fixed.
Are you using a prediction to describe outcomes, or a causal claim to decide what changing an action does?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.