Just a mild one I got from an old puzzle book:
Once upon a time in the Old West, Alan, Bob and Chuck were 3 outlaws in town with a reputation of great shooting. All 3 of them never missed by more than an inch, and they're renowned for their accuracy when shooting at a vertical string 100 feet away, which they called "cutting with a bullet". Chuck was a respectable 50% shooter and could always cut a string once for every two shots. Bob was an even better 80% shooter who would only miss once for every five shots. However, Alan was the best among the three. Being a pure 100% shooter, he never missed with any shot he fired.
During one failed train-robbing attempt all 3 of them were captured. The Sheriff decided that for their crime two must die, with the remaining one exiled. To decide who was to survive he came up with this cruel plan:
The three were hanged up (tied around the torso, not the neck) very high above the ground by a long string, positioned in the corners of an equilateral triangle so that each was exactly 100 feet away from each of the other two. Each of them was equipped with a gun with only 2 bullets. Then they had to take turn shooting at the string hanging the others, in the following way:
The Sheriff would throw a fair die (dice) to determine the order for them to shoot. Considering there were only 6 possible different orders each of the 6 faces of the die represented a particular order. For example, if a 1 was throwed, the order would go like this: Alan -> Bob -> Chuck.
Then these were the rules:
1. During each turn a criminal must shoot only once. The goal was to "cut" the string hanging on the body of another criminal, so that the victim would immediately fall to the ground and die. If a criminal shot "out of turn", or shot twice instead of once within a turn, the string hanging himself would immediately be set loose and he would fall to the ground and die immediately.
2. The criminals must not shoot a body (of another criminal or any other people). If anybody got hit by a bullet from a gun, the shooter would immediately be dropped to the ground and die. But considering the exceptional shooting accuracy of these three, their bullets would only hit a body if they shot at that person intentionally.
3. If a criminal used up his 2 bullets (in 2 turns) and didn't hit a string at all, he would immediately be dropped to the ground and die.
4. Whenever one of them died (either by having his string cut by a bullet or by violating any of the rules above), the turn would be passed to the next criminal in the order.
5. If two of the criminals died, the remaining one (provided he didn't violate any of the rules above) would not be executed and would be exiled alive.
So these were all the rules. Also, we knew that all 3 of them were very cool-headed in calculations and would always act in ways which would maximise their own chance of survival. Also despite they were tied and hanged high above the ground their shooting abilities weren't affected by a single bit. So their respective accuracy of 100%, 80% and 50% of "cutting a string with a bullet" stayed intact. Lastly, all 3 of them were perfectly aware of each other's shooting accuracy and knew very well their common tendency to do whatever to maximise the chance of own survival.
With these conditions, could you work out who had the best chance to survive, and what was the survival probability for each of them?
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Let me rework]
