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@@ -16,8 +16,8 @@ Here's the problem from Wikipedia ([CC BY-SA 3.0](https://creativecommons.org/li
> There is an infallible predictor, a player, and two boxes designated A and B. The player is given a choice between taking only box B, or taking both boxes A and B. The player knows the following:
> Box A is clear, and always contains a visible $1,000.
> Box B is opaque, and its content has already been set by the predictor: If the predictor has predicted the player will take both boxes A and B, then box B contains nothing. If the predictor has predicted that the player will take only box B, then box B contains $1,000,000.
->
->
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> The player does not know what the predictor predicted or what box B contains while making the choice.
## The Paradox
@@ -36,13 +36,13 @@ As I suggested in the "telescoping method", we're going to break down the abstra
> Let p be the probability that the predictor is correct. Then:
> 1000000p is the expected value if you choose only box B.
> 1000000(1-p) + 1000 is the expected value if you choose both boxes.
->
+>
> 1000000p > 1000000(1-p) + 1000
> -> 1000p > 1000(1-p) + 1
> -> 1000p > 1000 - 1000p + 1
> -> 2000p > 1001
> -> p > 0.5005
->
+>
> Therefore the expected value if you choose only box B is greater than the expected value if you choose both boxes so long as the predictor is over 50.05% accurate, slightly better than a coin toss.
An AI system that can predict slightly better than a fair coin toss could create the Newcomb Paradox. Given what AI is already capable of, this is a realistic scenario. It also shows that the infallible predictor isn't the root cause of the paradox.