First let’s set the input sequence to be very malevolent toward Omega: it will always say the reverse of what Omega is projected to say based on the previous bits.
This is probably a very uninformed question, but couldn’t Omega break even vs. a intended-to-be malevolent bit stream by choosing a random sequence?
In the post I wasn’t talking about any possible Omega, but about one specific Omega that has a mathematical definition. But I wouldn’t call your question uninformed, because it might be the correct question to ask here: paulfchristiano has already suggested that Solomonoff induction augmented with randomizing has the potential to win more games than the regular kind.
This is probably a very uninformed question, but couldn’t Omega break even vs. a intended-to-be malevolent bit stream by choosing a random sequence?
In the post I wasn’t talking about any possible Omega, but about one specific Omega that has a mathematical definition. But I wouldn’t call your question uninformed, because it might be the correct question to ask here: paulfchristiano has already suggested that Solomonoff induction augmented with randomizing has the potential to win more games than the regular kind.