Link to the Problem
Since you as a cyborg are intelligent, assuming the other two cyborgs also to be equally intelligent, Sujit gave the right solution! Here goes my solution assuming the same!
Lets analyze the scenario when both you and the 50% accuracy cyborg miss:
The 100% accuracy cyborg gets the chance now and he surely hits. So he would want the cyborg who would have a lower accuracy of hitting to get the next chance so that he has a higher probability of surviving and hence he would choose to kill the 50% accuracy cyborg.
The 50% accuracy cyborg knows this and hence would never want the 100% accuracy cyborg to get a chance. So in his turn he would want to kill the 100% accuracy cyborg and hence would aim at him.
Now consider your first turn. If you choose to aim at the 50% accuracy cyborg and if you hit then the 100% accuracy cyborg would aim at you and you are sure to be dead and if you miss, the 50% accuracy cyborg would get the next turn and he would aim at the 100% accuracy cyborg for reasons mentioned above. On the other hand if you aim at the 100% accuracy cyborg and if you hit, then the 50% accuracy cyborg would aim at you but this time you have 50% chance of survival. However, if you miss, the 50% accuracy cyborg would again aim at the 100% accuracy cyborg(same as above). Therefore, you have more chances of survival if you aim at the 100% accuracy cyborg than if you aim at the 50% one.
Hence, you aim at the cyborg with 100% accuracy!
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