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I don't understand what mouse sensor DPI has to do with speed

I keep seeing stuff about mice with adjustable DPI that adjusts speed--- I don't get it. Isn't DPI the number of pixels per inch the camera sees on the surface? What does that have to do with speed?
 
If your screen resolution is 1600 pixels wide, and your mouse is 1600 dpi, then moving the mouse 1 inch will cause the pointer to move all the way across the screen. If the mouse is 3200 dpi, then you only have to move the mouse 1/2 an inch to move the pointer all the way across the screen.
 
Yeah, traditional optical mice have been 400dpi, newer ones up to 800dpi. Even higher end mice (usually marketed as gaming mice) offer 1600dpi and higher.

Of course higher dpi mice can be just as useful to workstation users operating with super high resolution monitors. I can imagine how annoying it would be trying to fumble around on a 30" LCD (2560x1600) with an old 400dpi mouse. Sure, you could turn up sensitivity and even use acceleration but then you run into software interpolation problems and thus lose precision and accuracy.

For gamers, dpi comes in handy as a hardware sensitivity adjustment (avoiding the software interpolation problems I mentioned be for) that can also be very fast to adjust (jumping from 400 to 800 to 1600 dpi by simply pressing a button). Operating at a higher dpi for general movement and then quickly dialing it down for precision movements.
 
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