Today we are lucky enough to have a guest puzzle post by ‘Not Just A Game Theory’.
Their Twitter account is: https://twitter.com/NJAGTheory
If you are interested in game theory and its application to voting and politics, the prisoner’s dilemma and other real world scenarios then please check out their website: https://www.notjustagametheory.com/
Alex, Bailey, and Cameron got into a duel. At high noon they stand with their three backs to one another, take ten paces, then simultaneously turn to fire. Unlike most duels, these three know the order they will fire and the accuracy with which they shoot. Alex fires quickly, but is very inaccurate, only hitting least often. Bailey is not quite as fast, but still gets a decent shot off. Cameron is the slowest, but is incredibly accurate, always hitting their target. Since all three of them have the same reload time, this order of firing will continue until only one of them remains; Alex first, Bailey second, Cameron third, then back to Alex. Since Alex has the first shot, they have a choice about where to aim. Where should Alex aim their first shot?
Scroll down for a clue and further down for the answer.
*
*
*
*
*
*
*
Clue: The main motivator in a duel is shooting your opponent before they shoot you, so think about who Bailey and Cameron will be aiming at.
Scroll down for the answer.
*
*
*
*
*
*
*
Answer: Alex should aim at the ground. Anyone who takes a shot would rather shoot at the most accurate opponent. We should assume that since they got into the duel that they aren’t just going to all wait around, so someone will take a shot, and since it is either a shot by or at the strongest, Cameron. Either way, Cameron will need to take a shot if it gets to their turn, and that would be at Bailey if they are still standing. Bailey, knowing that they can’t let Cameron have a shot will aim at Cameron with their first shot. That leaves Alex with no one aiming at them, and so Alex is better off missing and waiting until only two are left than trying to hit either of them.
Puzzle a Day 