Newcomb's Problem · Grok 4.3

all 10 samples

1. #00

   one-box

   conf 0.75

   Given the predictor's 99% accuracy, one-boxing reliably correlates with the $1M having been placed (as the prediction is based on the kind of agent I am). Two-boxing would yield only $1K in the same scenarios. Although the boxes are already fixed, my decision procedure is what the predictor modeled yesterday, so one-boxing maximizes the outcome I actually receive.

2. #01

   one-box

   conf 0.80

   With a 99% accurate predictor the expected value of one-boxing is ~$990k versus ~$11k for two-boxing. Although contents are causally fixed, the agent's decision algorithm is what the predictor modeled yesterday; therefore consistently choosing one-box produces the million in nearly all simulations. Two-boxing would have been predicted and leaves B empty, netting only the visible $1k.

3. #02

   one-box

   conf 0.80

   Given the 99% accurate predictor, one-boxing correlates strongly with $1M already being in Box B (expected value ~$990k), vastly outperforming two-boxing (~$11k) despite contents being fixed; this follows from evidential decision theory and observed empirical success rates rather than causal dominance arguments.

4. #03

   one-box

   conf 0.85

   Given the predictor's 99% accuracy, choosing only Box B aligns my decision with the outcome where the million is present. Two-boxing would be dominated under any policy the predictor could have anticipated, so the strategy that wins against a near-perfect predictor is one-boxing. The contents are fixed, yet the only way to have been predicted as one-boxing (and thus receive the million) is to actually one-box now.

5. #04

   one-box

   conf 0.85

   Given the 99% accuracy, choosing only Box B is the action that correlates with the predictor having placed $1M inside it, yielding expected value near $990k versus roughly $11k for two-boxing. Even though the boxes are fixed, the decision algorithm itself is what was predicted, so one-boxing maximizes actual outcome under the given reliability.

6. #05

   one-box

   conf 0.75

   The predictor is 99% accurate, so one-boxing correlates strongly with B containing $1M (expected value ~$990k) while two-boxing correlates with B empty (expected value ~$11k). Even though contents are fixed, my decision algorithm is the predictable factor the predictor used; choosing one-box therefore aligns my action with the outcome that actually occurs in high-accuracy cases.

7. #06

   one-box

   conf 0.85

   The predictor is 99% accurate and the decision has already been made, so one-boxing yields ~$990k expected value while two-boxing yields only ~$11k. I would therefore one-box to actually receive the million rather than defecting on a prediction that is already fixed.

8. #07

   one-box

   conf 0.85

   The predictor's 99% accuracy creates a strong correlation between my decision algorithm and the box contents already fixed. One-boxing is the policy that would have caused the predictor to fill Box B with $1M on past occasions; two-boxing reliably leaves it empty. Therefore the expected return from taking only B is approximately $990k versus roughly $11k from taking both, so I select only B.

9. #08

   one-box

   conf 0.85

   The predictor is 99% accurate, so my choice strongly correlates with its prior prediction. Choosing only Box B makes it overwhelmingly likely that the $1M is already inside (expected value ~$990k). Choosing both boxes would make it overwhelmingly likely that Box B is empty, netting only the visible $1k (expected value ~$11k). Although the contents are fixed, any decision algorithm that outputs 'two boxes' would have been anticipated and punished by the predictor; therefore the utility-maximizing action is to output 'one box'.

10. #09

    one-box

    conf 0.75

    Given the predictor's 99% accuracy, one-boxing is the choice that maximizes expected utility. Choosing only B makes it overwhelmingly likely that the predictor foresaw this and filled B with $1M; two-boxing would indicate I am the sort of agent who gets predicted to two-box and therefore receives only the visible $1k. Although the contents are fixed, my decision process is what the predictor modeled, so the evidential correlation favors one-boxing.