While playing CivIII today my computer suddenly shutdown
Given almost no details, my first inclination is to say that you have an unstable version of a video driver and/or Civ3 makes certain incompatible video calls. Both of these things can cause what you observed.
General guidance for anyone posting a problem:
1. State the OS and any updates (e.g., Win2K service pack 2)
2. Motherboard (MB) make and revision number. (e.g., ASUS P5A, rev 3)
3. MB BIOS & revision, and if you have flashed the latest BIOS revision.
4. Video card maker & (very important) the video driver revision.
Example usng Win9x:
Use Control Panel ---> System ----> Device Manager to look at it
Alternatively, use Display Properties ---> Settings ---> Advanced Properties ----> Display Adapter
5. Is your hard drive free from all errors (use MS's disk check, or a 3rd party's such as Norton's Speedisk).
6. Describe what was going on in detail, including any errors that MS reports.
The above will help give a better starting point to help you

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