There are problems that can't be solved simply by publicly throwing hundreds of millions of dollars at them. For example, an agent probably could swing the elections for Mayor of London between the two candidates running with that kind of money, but probably could not get a person of their choice chosen if they weren't already a fairly plausible candidate. And I don't think total control of the US nuclear arsenal is susceptible to lead-pipe cryptanalysis.
In short, world takeover is filled with hard problems that a pre-FOOM AGI probably would not be smart enough to solve. Going FOOM implies that the AGI will path through the period of vulnerability to human institutions (like the US military) faster than those institutions will realize that there is a threat and organize to act against the threat. Achieving that invulnerability seems to require solving problems that an AGI without massive resources would not be smart enough to solve.
It all depends on whether an AGI can start out significantly past human intelligence. If the answer is no, then it's really not a significant danger. If the answer is yes, then it will be able to determine alternatives we can't.
Also, even a small group of humans could swing the election for Mayor of London. An AGI with a few million dollars at its disposal might be able to hire such a group.
I was very interested in the discussions and opinions that grew out of the last time this was played, but find digging through 800+ comments for a new game to start on the same thread annoying. I also don't want this game ruined by a potential sock puppet (whom ever it may be). So here's a non-sockpuppetiered Irrationality Game, if there's still interest. If there isn't, downvote to oblivion!
The original rules:
Enjoy!