I set the ISO on my Canon 6D to 200: 1081 estimated shots remaining.
I set the ISO to "auto": 728 estimated shots remaining.
I'm shooting in RAW, if that makes a difference.
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Digital cameras, to save space, compress the data. Think of storing a book after it has been converted to a digital file. One could devise a scheme to cast out all entries of the word like “the” or “and”, replacing these with a single symbol. When the data is called and the words are shown on a screen, the omitted letters are restored for easy reading. Such schemes of different complexities are used, some are lossless some not. All of these various schemes have rules that are strictly followed. Even raw files are compress using a lossless routine.
As you turn up the ISO, perhaps unknown to you, some of the image signal will be corrupted by static. This is because, the higher the ISO the more amplification. In other words, the image capturing sites are caused to become more sensitive to light. This is somewhat like turning up the volume of your TV set. What happens is, the music and voce become louder but the cost is induced static. In digital imaging we call this static “noise”.
Now the higher the ISO, the more “noise”, and this corrupt the signal. Noise thus adds additional data to the image file forcing it expand. When your camera is on auto, the camera logic chooses what ISO to use based on the ambient light playing on the subject. In daylight, the ambient light is high, so a low ISO is chosen. The number of remaining images you can make and store on a memory chip is a variable. The camera logic is attempting to estimate how many pictures can be stored. Higher ISO requires more storage space. What you have discovered is high ISO induces more noise and thus more storage space will be required for each image stowed away.
Most cameras use lossless compression to store raw image files. The more uniformity an image has, the easier it is to compress. The more diversity an image has, the harder it is to compress. This is due to the way the types of file compression used for images works. Rather than describing the individual values of each pixel, a compressed image file either describes which pixels have each of a range of values, it describes where the differences in value from one pixel to the next occur and how much those difference are, or it uses a combination of both methods. (These descriptions are gross oversimplifications of how raw compression works, but the basic concepts are correct).
Imagine an entire image that is the same brightness and color from one side to the other and from top to bottom. It will compress to a very small size because the compressed file need only describe one color at one brightness level and then list zero changes between any adjacent pixels. On the other hand, a 14-bit raw file can express 16,384 different brightness values. If each pixel of an image is a different brightness value than the pixels around it and all 16,834 values are used somewhere in the image, the file cannot be compressed very much at all because it must describe every single brightness value between 0 and 16,383 and record a change in brightness between every pixel in the entire image.
In reality most images are somewhere near the middle of these two extremes. But all else being equal, the more "noise" an image has, the greater the variety of total brightness values in the image and the greater variation in brightness between adjacent pixels within the image.
In general, low ISO images of a scene have more uniformity that high ISO images of the same scene. This is mostly due to what we call the signal-to-noise ratio, also known as the S/N ratio or SNR. Assuming the same scene, lighting conditions, lens, focal length, and aperture: when we raise the ISO it is so we can shorten the exposure time. Thus less total light is being allowed into the camera. The noise the camera generates regardless of how much light enters the camera remains fairly constant. So as the signal (light energy) is reduced and the camera's read noise and dark current noise remain fairly constant, the S/N ratio is reduced. This leads to less uniformity on the image. A properly exposed image of a grey-white wall at low ISO and a longer shutter time has pixels that are mostly the same color. A properly exposed image of a grey-white wall at high ISO and a shorter shutter time tend to show much more luminance and chrominance noise. The luminance noise creates more variations in brightness from one pixel to the next. The chrominance noise creates more variations in color from one pixel to the next. The more variations in brightness and in color that an image has, the less it can be compressed losslessly.
High ISO images often have more noise not because they have more "static." They don't. It is because they have much less signal to overcome the constant noise that is always there. When the signal is strong enough there is more uniformity in the image and thus the contents can be compressed more efficiently. When there is less signal in the image the noise leads to less uniformity and thus less compressibility. So the compressed file containing the image data is larger with a lower S/N ratio than the compressed file containing the image data with a higher S/N ratio.