To win the game, you have to understand how income works. Look at da breakdown often. You'll see two things. First of all, note that the value of your 'hoods goes up each turn you maintain control of them. Second, note that the bonuses for boroughs are what will enable you to win the game. Some boroughs are easier to defend than others. Boroughs that are easier to defend are worth less. Staten Island has only one entrance, but there are five or six ways into Jersey, and many many ways into Manhattan (but hey, Manhattan's the center of the world). Brooklyn is also valuable, in part because it's where the immigrants live. Did you know that about half of the population of the United States has at least one ancestor who lived in Brooklyn?
Bullets can have a large effect on the game, especially the Extra Turn, Lose Turn and Swap 'Hoods bullets. Figure them into your strategy as you can sometimes keep up the momentum of an attack by grabbing bullets along the way.
Combat is pretty even. For each of your guys, there's a 49.5% chance one of your guys will get whacked if you're the defender and a 50.5% chance if you're the attacker. Thus, having more guys increases your odds of taking an enemy hood.
On the default settings it takes two wiseguys to take over a neutral hood. If you click on the question mark next to the Atmosphere pop-up menu in the New Game dialog, it will tell you this, as well as other information.
Avoid getting "dead-ended". Some hoods are adjacent to only one other hood. When you capture these hoods, any troops you move in cannot do anything until you use "fortify" to move the guys out.
The police stations and hospitals will usually not have a large effect on the game, unless you're playing against human opponents. The cops can take away your borough if any hood has just one guy on it. The cops'll come in and take him out! Be careful. You'll find that strategy when playing against the computer is very different from strategy when playing against humans. People can tell who's winning, and people will usually gang up on the winner. The computer can handle tactical details, but is less proficient at overall strategy. You can win if you know what you want starting on the first turn of the game.
