I think if i had to choose a genre of games and only be able to play that style it would likely be Real Time Strategy (RTS) games. This love affair began many years ago with Dune and carried on through Command and Conquer, Warcraft, and of course the king of them all - Starcraft. However, the thing that sets Company of Heroes apart is that many aspects of it are based on events that actually happened.
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In a overall sense, i tend to enjoy games centered around WW2 anyway, so when i found out there was an RTS game based on the western invasion of Europe during that time period, i didn't even read reviews, I just bought it.
The game starts out very different than RTS games that you might have grown accustomed to in the past such as Starcraft where you could simply amass an overwhelming force and take out the enemy based on very little other than superior numbers. In this game, you actually need to use your units wisely because although you can replenish them, it does take some time. There are no minerals or vespene gas or anything like that to mine. Your ability to produce units is based entirely on how many checkpoints you control, so obviously time is of the essence and you must also decide how many units you wish to leave behind to defend the checkpoints you currently control. You WILL make mistakes on this.
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Certain units have distinct (and sometimes annoying ) advantages... such as a sniper in a bell-tower. Any attempt to infiltrate this unit with infantry will almost certain fail, but a tank will simply destroy the tower, but you have to find out where the fire is coming from first, which can prove difficult.
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most of your surroundings are destructible, which adds a nice element of realism to the game. Infantry units can use abandoned houses as a stronghold in order to increase their chances of being able to hold and area, but if you see a tank moving in, you better quickly get them out of there!
I think the aspect of this game that I enjoy so much is that it is almost never an option to simply stockpile 10 siege tanks and then overwhelm basically any enemy encampment (this was a strategy almost universally utilized in Starcraft.) You have to really think it through how you are going to approach attacking enemy areas and for further realism certain vehicles have weaker points on them, such as tanks having almost all of their armor focused on the front of it. Sneak attack an enemy tank from the side and you can eliminate it much faster. Your infantry can also outrun the turret of said vehicle and throw a "sticky bomb" on the back or side. Of course this is almost impossible if said tank has a machine gun turret on the top of it :)
The only downside of this game is that it rarely, if ever, goes on special. It has been $20 for about as long as I can remember. that's the price I paid for it in 2007 and that's how much it is now. However, if you like RTS and you also have $20 to spare, this game will not let you down, especially if you are a WW2 history fan like me. Despite the fact that I have completed all the campaign missions at least a dozen times, i continually return to play this game over and over again. Therefore, I recommend this game for really anyone.