Should video lightbox "remember" the last video position?

There is a promo page that sells some app or game. It has a grid of thumbnails, click on which shows videos about an app. Something like this:

enter image description here

After user clicks on thumbnail, modal (lightbox) appears with YouTube video in it and starts playing immediately:

enter image description here

If user clicks on "Close" icon, or grey area behind modal - it closes.

Now, here is what user does:

  1. User clicks on thumbnail and watches video for some time.
  2. User closes the modal (lightbox), we do not know if it was intentional or accidental.
  3. User clicks on the same thumbnail

So the question is: should the video start from the beginning or from the moment the user closed the modal on the first time? Will your answer change if the user refreshes the page between step #2 and #3?

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