In the Wild West, some problems were simply resolved with the weapon. As in the case of the three cowboys, who would like to kill each other immediately.
Now they meet for an extended duel with very special rules. Only one person is allowed to shoot. The right to squeeze off the revolver goes in a row - in the order Cowboy A, Cowboy B, Cowboy C. And then again from the beginning.
Everyone is free to choose their destination. If someone is shot, the next one is in the round. The extended duel ends when there is only one cowboy left.
All three men are very good shooters. What they target, they also meet. Obviously Sagittarius A has an advantage, because he is allowed to start and can thus turn off an opponent.
To make the shootout fairer, the cowboys A and B get manipulated ammunition. In Cowboy A every third cartridge is a blank cartridge. His chance to hit is only 1/3 . For Cowboy B, the hit probability is 1/2 - every second cartridge is a blank cartridge.
The cartridges were mixed well, they can not be distinguished externally. Only Cowboy C has only live ammunition - so his hit probability is 100 percent. Everyone involved knows about their own chances to hit and those of the other cowboys.
Which of the three men has the highest chances of survival?
Note: Each of the cowboys will apply the strategy that gives them the best chance of survival.
