Rhadamanthus says... #2
As a supplement to Epochalyptik's response, see Lord of the Pit for an example of a creature that specifically says you have to sacrifice something else. Doomgape doesn't say that, so he'll eat himself if he has to (or if you want him to).
Epochalyptik says... Accepted answer #1
Doomgape itself is a creature, so you will never "not have any creatures to sacrifice" if you control it. If Doomgape is your only remaining creature, it must be sacrificed to its own ability.
If Doomgape could not be sacrificed to its own ability, that ability would be worded "At the beginning of your upkeep, sacrifice a creature other than Doomgape. You gain life equal to that creature's toughness."
Also, Doomgape 's flavor text kind of hints at the answer.
July 19, 2012 4:10 p.m.