Q: macbook shuts down without reason or warning

Also download and run Etrecheck.  Copy and paste the results into your reply. Etrecheck is a diagnostic tool that was developed by one of the most respected users here (and recommended by Apple Support personnel) in the ASC to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

Another thing to consider - even if it is not that likely - is that your mac is overheating (this can cause an abrupt shutdown).  Videos tend to heat things up; if your fan is not keeping pace with the heat you could get into an overheat situation. If you think this could be the case, you could get a temperature/fan monitoring utility (e.g., some of this) and keep an eye on the temperatures and fan behavior as you watch a video.  

Yet another thing to try is to look at system logs (via Console in the Utilities folder) just in case there is some message there which is related to your problem.

This procedure is a diagnostic test. It makes no changes to your data. The instructions must be carried out as an administrator. If you have only one user account, you are the administrator.

I've tested these instructions only with the Safari web browser. That's what I suggest you use, even if your preferred browser is something else.

Please triple-click anywhere in the line below on this page to select it:

syslog -k Sender kernel -k Message CSeq 'n Cause: -' | tail | awk '/:/{$4=""; print}' | pbcopy

Copy the selected text to the Clipboard by pressing the key combination command-C.

Launch the built-in Terminal application in any one of the following ways:

☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)

☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.

☞ Open LaunchPad and start typing the name.

Paste into the Terminal window by pressing the key combination command-V. If you use another browser, you may have to press the return key after pasting.

Wait for a new line ending in a dollar sign ($) to appear below what you entered.

The output of the command will be automatically copied to the Clipboard. If the command produced no output, the Clipboard will be empty. Paste into a reply to this message.

The Terminal window doesn't show the output. Please don't copy anything from there.