How many pictures does a Nikon L830 16MP with 30X Optical Zoom hold?

I'm getting it as a Christmas gift and I'd like to know how many pictures will it hold.

It all depends upon the size of the memory card you use. You should be able to download a.pdf version of the manual, and it will have a chart outlining how many images at particular resolutions for different capacity cards.

The number of photos that will fit on a card will depend on:
1. The resolution that you chosen (good, fine, super fine)
2. The compression that you've chosen (good, better, best)
3. The size of the card that you've purchased.
4. The amount of color and details in the scene.

Therefore there are numerous correct answers for any give size of memory card.
At the best settings, your camera will use anywhere between 5-7MB per image. There's a range because the complexity of the scene will affect the overall image size too. A shot highly detailed with lots of different colors will result in a larger file size than something that was not very colorful or filled with lots of details.

So, with a file size of 7MB on an 8GB card, you'll get 8,000MB/ 7MB = 1,000 images.

Here's a review of the L830 - http://www.photographyblog.com/reviews/nikon_coolpix_l830_review/image_quality/

You should read it before asking for this specific model.