In many (probably most?) games we consider the opponents strategy, not simply their next move. Making moves in an attempt to confuse your opponent’s estimation of your own strategy is a common tactic in many games.
Your “modified Newcomb” doesn’t allow the chooser to have a strategy- they aren’t allowed to say “if I predict Omega did X, I’ll do Y.” Its a weird sort of game where my opponent takes my strategy into account, but something keeps me from considering my opponents.
In many (probably most?) games we consider the opponents strategy, not simply their next move. Making moves in an attempt to confuse your opponent’s estimation of your own strategy is a common tactic in many games.
Your “modified Newcomb” doesn’t allow the chooser to have a strategy- they aren’t allowed to say “if I predict Omega did X, I’ll do Y.” Its a weird sort of game where my opponent takes my strategy into account, but something keeps me from considering my opponents.