https://simple.wikipedia.org/wiki/Newcomb%27s_paradox

Let's say the Djinn or AI has accuracy a, then the expected value of taking both boxes is:
t+(1-a)*m

where t is the transparent box and m the mystery box.
The expected value of taking only m is:
a*m

So to see at which point is doesn't matter we set it equal:

t+(1-a)*m=a*m | devide by m
t+1-a=a |+a
t+1=2a |devide by 2
a=(t+1)/2

So if you know the Djinns/AIs accuracy, you can make an optimal choice.

Is this correct?

oh, i made a mistake...

t+(1-a)*m=a*m
t+m-am=a*m | +am
t+m=2a*m |devide by 2m
(t+m)/(2*m)=a

So let's say there's 1 million in the mystery box and 1000 in the transparent one:

a=(1000+1000000)/(2000000)=0.5005

So assuming you play that game for more than one round and you don't know if it's the last round, the Djinn has to be only correct about 50%

This post was edited by massmarines on Apr 16 2026 06:13pm

interesting