Mr. Smith

Smith, Brown and Jones are to fight a three-cornered pistol duel. All know that Smith's chance of hitting his target is 50%, Brown's is 80% and Jones never misses. They are to fire at their choice of target in succession in the order Smith-Jones-Brown (50%, 100% 80%) cyclically (but a hit man loses further turns and is no longer shot at) until only one man is left. What should Smith's strategy be? What is her probability of survival?