Sherlock Holmes and Moriarty play the game of death with a pistol. Holmes puts exactly 1 bullet in his pistol containing 6 bullet slots, rotates the revolver (so that the bullet takes a random position - this event is completely random and unbiased) and takes a shot at Moriarty. The latter, if alive, picks up the same pistol and shoots Holmes. Holmes, if alive after this shot, picks up the pistol and shoots Moriarty.
Now Moriarty, if alive, rotates the revolver (bullet again takes a random position, as it took before the first shot) and shoots Holmes. Holmes shoots Moriarty back if he survives Moriarty’s shot and Moriarty takes his next shot if he survives Holmes’ shot.
Now, Holmes takes the gun and rotates the revolver (bullet’s position gets randomized again) before shooting Moriarty. In the same way, after every 3 shots, the person whose shot is to be made randomizes the position of the bullet before taking his shot. Shots are taken alternatively by the two combatants with Holmes taking the first shot of the game. If any one of them dies while facing a shot, the other person is considered to have won the game. What is the probability of Holmes winning the game?