In the Wild West, you challenge two cowboys - Hunter Jack and Sharp Shooter Leo into a death match. They being better shooter than you readily accept your challenge. But they don't want to waste bullets and thus lay down a certain rules that are accepted by you as well. Here are the rules:
1) Everyone shoot in a given order till only one is left.
2) Everyone shoot only once when his turn arrive.
3) If any one of you is injured, the other two will finish him off together.
4) The worst shooter gets to shoot first (which is you) and the best one shoots at the last.
Now, what tactics will you use if you know that you hit every third shot of yours, Jack hits every second shot and Leo hits every shot?
Solution:
The best thing for you will be to shoot your first shot in air.
If you try to shoot at Jack and hits him by chance, Leo always hits on the target and you are dead.
If you choose to shoot at Leo and hits him by chance, then there is a fifty percent chance that Jack will hit you.
If you shoot in air, the next turn is of Jack and he knows that Leo is a better shooter which means that he will shoot at him. If he misses, he is definitely dead as Leo will shoot on him coz he shot at him. The next turn will be yours and you stand a 1/3rd chance of hitting him. Also if, he is able to hit Leo. The next chance is yours again and you can try the 1/3rd probability of hitting over Jack.
This is the best situation that you can face. At every other possible way, you will face a worse situation for sure.
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