Rivals A, B and C want to settle a quarrel by shooting at each other with guns. The rules of the truel (3 person duel) are:
- They draw lots to determine who fires first, second and third.
- Each turn, they can choose to fire at a specific person, or not at all.
- A kills in 100% of his shots, B kills in 80% of his shots and C kills in 50% of his shots. No one is killed by a stray bullet.
- The truel continues until only 1 person is left alive
Assuming that everyone chooses their ideal strategy, who has the largest chance of surviving the truel? Is this chance greater than or less than 50%?