Why run a game at faster FPS than the monitor refresh rate?

As far as i'm aware you are correct.

It doesn't matter what your frame rate is, it will be limited to the refresh rate of the monitor.

FPS = Frames per second

Hz = Cycles per second.

FPS and Hz are basically the same thing, In this case they both mean screen updates per second.

The optimum ratio is 1:1, The graphics card sends one frame and that get displayed on screen, then sends a another frame etc. If you have a 90fps and a refresh rate of 60hz, it simply can't display all 90fps. It either drops 30 frames, or combines 1 and half frames and displays it as one frame. Both will result in screen tearing which is pretty annoying.

There's a detailed explanation here on screen tearing http://en.wikipedia.org/wiki/Screen_tearing

There is a method of perfectly syncing the FPS with Hz and it's V-SYNC, most games have it as an option. Si uf your monitor is 60Hz, it will try to run the game at 60fps. Using V-SYNC prevents tearing and so improves quality, but consumes slightly more processing power than if it were off.

There's an explanation of V-SYNC here http://en.wikipedia.org/wiki/Vertical_synchronizat...

There's no difference between DVI and VGA in this respect.

Techno geeks get all over excited with attempting to get a hundred fps. action picture runs at 24 fps, television and complete-action video refresh at 30fps, and your concepts can not technique action lots swifter than that. basically everybody claiming to tell the version between 50 fps and eighty fps is a similar guy or woman who will declare they could tell the version between 24 bit shade and 32 bit shade. the clarification particularly severe fps expenditures count is by way of fact that's the only way for the gfx card makers for example their means and destiny potential for extra stressful video games.

Basically if the game refreshed at only something like 10fps it would not matter if you had a 1000Hz moniter as the game would still lagg.

Fps is how many times the game updates a second.

Hz is how many times the monitor updates a second. (I think)

To get smoothest gameplay your game fps should be sitting around the monitors refresh rate.

Say if the game was 100fps and your monitor was 50Hz the game would play looking as if it was 50fps due to the fact thats all the monitor can do.

Bear in mind i could be completely wrong lol, Its just what i think.