I see a similar question in Russian roulette. Now if instead of two bullets being placed side by side, two bullets are randomly put in the chamber. Your opponent played the first and he was alive after the first trigger pull. You are given the option whether to spin the barrel. Should you spin the barrel?
My approach: I felt this would be case dependent. As in first if they are side by side, then it is 1/4 probability of losing in not spinning the barrel vs 1/3 in spinning the barrel, so I go for not spinning the barrel. If not, if one space between them, then I have 1/2 p of losing which is bad so I go for spinning the barrel, now the answer given is 2/5. And I have no idea why. Help please!
My idea of russian roulette: When we don't spin the barrel and we have pulled the trigger, every piece moves clockwise. As in if we number the pieces, where bullet was in 1 and 3, rest 2,3,4,5,6 are all empty, then after first trigger pull (trigger was at position 1), bullet in 3rd position moves to 4th position. Am I right?
(6/15*3/4) + (6/15*2/4) + (3/15*2/4)= 60% chance of surviving the next round. Spinning just gives you the "standard" 66.7% (4/6) chance of surviving, so you should spin. $\endgroup$