
I found it a little strange that the only review of Burglary was positive, because I consider this one of the worst cards in the Core Set. In the abstract, spending an action for three resources is sometimes good, because three resources are (very slightly) more valuable than an action. But Burglary brings along with it a host of problems and complications.
Most significantly, there's the up-front 1-action, 1-resource, 1-card cost of playing Burglary. This means the card takes forever to generate a profit. If you successfully Burglarize once, you've swapped 2 actions, 1 card, and 1 resource for 3 resources. Terrible. If you do it twice, you've swapped 3 actions, 1 card, and 1 resource for 6 resources. Still terrible. If you do it three times, you're getting close to breaking even. At 4+ times, you start generating a small profit. For this to really generate enough upside to justify the deck slot, you'd probably need to successfully activate it 5+ times. That is a lot of time to spend Burglarizing--a lot of time in which you're not advancing the Act deck and actually winning the game.
Burglary is even worse than that, of course, when you consider that you might fail the test. The three investigators with in-faction access to Burglary have a base Intellect of 3. That means that unless they're hanging out at a 1-shroud location (which may or may not be there) on Easy, they'll likely fail the test a good chunk of the time. That makes Burglary take even longer to pay for itself, if it ever does. Voluntarily inflicting a ton of skill tests on yourself, by the way, also will expose you to a host of bad special token effects.
Arkham Horror is a rush game. You have limited actions in which to get your objectives done, and you've got to get moving quickly. You simply do not have time to sit around at a low-shroud location for multiple turns doing nothing but amassing resources. And if you play Burglary and only use it a little bit, then you've gotten a terrible deal.
I will grant that Burglary is better for Rex Murphy than it is for other investigators. However, I think it is still not worthwhile even for him. In my opinion, even for Higher Education Rex, picking up 2 clues is slightly better than picking up 1 clue and 3 resources. That means the only real use for Burglary is to clear out locations with 1 clue more efficiently. But Rex has a huge number of ways to get that last clue without sacrificing efficiency (Working a Hunch, Deduction, Seeking Answers, having a teammate do it, etc.) When you consider the up-front cost of Burglary, and the fact that Rex probably has to invest cards and/or resources to succeed by 2+ to get the resources and the clue, I think Burglary is still not paying for itself.
Moreover, Burglary takes up a splash card slot for Rex. That means that instead of a dubious efficiency gain when investigating 1-clue locations, Rex could have had one of the strongest cards in the game: Ward of Protection, Fire Axe, Dynamite Blast, Elusive, etc.