What is the red-eye effect? The following is an example:
Red-eye is caused by light reflected off the subject's retina, and, as a result, a trace of red appears in the eyes of your subject as shown above. If the angle of reflection is less than 2.5 degree, red eye will occur. See the figure below. One way to overcome the red-eye effect is to move closer to your subject so that the angle of reflection will be larger than 2.5 degree.
Or, you can press the flash setting button until the red-eye reduction icon appears. When red-eye reduction is in effect, do not move the camera immediately after the shutter release button is pressed to take a photograph. The camera will fire a red-eye reduction light for about one second, and then fire the flash to actually take the photograph you want. Therefore, after pressing the shutter release button, hold the camera steady for more than one second until the built-in flash fires. Without doing so, the photograph you will get may not be the one you originally planned because the composition has changed. Note that even with this red-eye reduction capability activated, the red-eye effect may not be gone completely. This situation could even be worse when you take photographs of your pets, especially your cats. The best way is to recompose so that the subject's eyes are not looking at the camera lens directly. Or, consider to use an external flash.
To eliminate red-eye, a has to be greater than 2.5 degree. Since tan(2.5 degree) = 0.04, X = 40cm. Since the larger the X the smaller the a, to have a > 2.5 degree X < 40cm! In other words, the distance between the eyes of your subject and your camera must be less than 40cm. Forty centimeters is too short for a shoulder shot! Moreover, you perhaps do not want to ruin your subject's eyes! This is why 950's red-eye reduction almost does not work.