RE: generally speaking, how far will a deer run...
In my experience, a good double lung/ heart shot, deer seldom go past 75 yards. Therewere a few that went past 100yards. Then again I've seen them drop with in 20 or 30 yds.
I've noticed that deer that are calm and relaxed, such as a feeding, they seem to go down much quicker than a deer that sees you or knows something is up, before you shoot. Must be the dose of adrenaline they got running through them at the time of the shot.
Liver shot deer will usually lay down quickly but won't die for quite a while. It is best to give them a few hours before tracking.I've seen livershots throw a good bit of blood making one thinkthe deer is down for good. Just give the liver shot some extra time.
Gut shot I'd let go all nite or all day depending on when the hit was made.