The Game of Death (Part II)

Probability Level 5

Surprisingly, all the five agents have survived from The Game of Death Part I. The gangster leader selects an agent and forces the selected agent to play another Game of Death: Russian Roulette. The gangster leader puts two bullets in consecutive order in an empty six-round revolver, spins it, and points the muzzle at agent's head. The rules of the game are:

• In each chance, the agent can choose either he wants to spin revolving cylinder again or not.
• If the agent can survive from four times chance, he and the other four agents will be released. If not, the rest will be killed.

Assuming that the agent uses the best strategy. What is the probability that the agent will survive?

Note: Your answer must be in the interval $[0,1]$.

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