Angela Stockdale runs very successful livestock classes
http://www.dog-partnership.co.uk/sheepintro.htmEvery time your dog DOES escape and chase will reinforce this behaviour and make it more likely to happen again as it is so obviously rewarding to her so prevention and/or proper training is essential.
I am afraid whether she is motivated to chase to play or to kill is immaterial; your dog could be shot just for being loose in field of sheep for example as the mere sight of dogs may cause sheep to abort; cows with calves are extremely dangerous to dogs and their owners and steers will chase and of course cattle and sheep may be injured by being caught in barbed wire, drowning etc etc.
Dogs do not "grow out of" this type of behaviour; they can be "trained out" however; you MUST keep your dog on a lead at all times if your dog is not 100% reliable around livestock.