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Rainbow Six games have always been about squad based combat, and focused more on slow movement and planned stealth tactics more than action.
Rainbow Six 3 is no different. However, it has been slightly scaled down from the computer version.
You play the part of Ding Chavez, one of the more elite members of the very elite squad called Rainbow Six. Instead of outfitting your team and planning the tactics before hand, you instead outfit yourself and lead a team of 3 other soldiers into action and play things by ear. This makes for a little more chaos than you'll find in the computer version.
Most of the guns from the computer version have made it into this game, and most of the maps as well. A lot of the levels you'll see will be modified versions of the computer game's maps, but some new ones have been thrown in there as well. They are slightly smaller, but still big compared to most other games of this nature on a console.
Apart from the Single-player Campaign mode, your choices get kind of thin. There are some Custom missions, where you simply go hunting for terrorists on any of the single player maps you have defeated. You can also link a few Xboxes together and have at it with a few different game types, including team Deathmatch and cooperative missions. Xbox Live is also supported, and allows for more customization when you get online than just linking your Xbox does.