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Declarations that start combat vs. initiative
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<blockquote data-quote="Dausuul" data-source="post: 8605349" data-attributes="member: 58197"><p>Assuming rational behavior from all parties, the least accurate gunslinger--call him Eddie--always has the highest chance to survive. Exactly how high depends on how the scenario is set up.</p><p></p><p>If the gunslingers are allowed to hold their fire, but there is some time limit which will force them into combat eventually, then the two best gunslingers go after each other, and Eddie holds his fire until one of them falls. If the middle gunslinger--call her Susannah--survives, then Eddie gets the first shot on her and has a 50% chance to win right there, <em>plus</em> a nonzero chance that Susannah could miss her return shot and he could get her with his second.</p><p></p><p>If the best gunslinger, Roland, survives, then Eddie's chances are exactly even. Either he hits with his first shot, or he misses and Roland, who never misses, kills him. Even odds against Roland, better than even against Susannah, means a combined chance over 50% for Eddie.</p><p></p><p>If gunslingers are not allowed to hold their fire, Eddie still has the best chance to survive out of the three, but it's a shade <em>under</em> 50%, because he might go before Roland and hit him; which means Susannah is likely to kill him before he can shoot again.</p><p></p><p>If holding fire is allowed and there is no time limit... then it becomes a question of how confident the gunslingers are in each other's intentions. If they are fully confident that the others are behaving rationally and are interested only in survival, they all simply holster their guns. This results in a 100% chance for <em>everybody</em> to survive, which is better than anyone would have in a shootout. But if they suspect the others are <em>not </em>rational, or have some motive other than survival, then there is a strong incentive for both Roland and Susannah to shoot each other before the other can fire back. Eddie <em>probably</em> holds his fire... but if he's worried that Roland and/or Susannah are not rational, he has to weigh the risk that one of them shoots at him while the other is still alive.</p></blockquote><p></p>
[QUOTE="Dausuul, post: 8605349, member: 58197"] Assuming rational behavior from all parties, the least accurate gunslinger--call him Eddie--always has the highest chance to survive. Exactly how high depends on how the scenario is set up. If the gunslingers are allowed to hold their fire, but there is some time limit which will force them into combat eventually, then the two best gunslingers go after each other, and Eddie holds his fire until one of them falls. If the middle gunslinger--call her Susannah--survives, then Eddie gets the first shot on her and has a 50% chance to win right there, [I]plus[/I] a nonzero chance that Susannah could miss her return shot and he could get her with his second. If the best gunslinger, Roland, survives, then Eddie's chances are exactly even. Either he hits with his first shot, or he misses and Roland, who never misses, kills him. Even odds against Roland, better than even against Susannah, means a combined chance over 50% for Eddie. If gunslingers are not allowed to hold their fire, Eddie still has the best chance to survive out of the three, but it's a shade [I]under[/I] 50%, because he might go before Roland and hit him; which means Susannah is likely to kill him before he can shoot again. If holding fire is allowed and there is no time limit... then it becomes a question of how confident the gunslingers are in each other's intentions. If they are fully confident that the others are behaving rationally and are interested only in survival, they all simply holster their guns. This results in a 100% chance for [I]everybody[/I] to survive, which is better than anyone would have in a shootout. But if they suspect the others are [I]not [/I]rational, or have some motive other than survival, then there is a strong incentive for both Roland and Susannah to shoot each other before the other can fire back. Eddie [I]probably[/I] holds his fire... but if he's worried that Roland and/or Susannah are not rational, he has to weigh the risk that one of them shoots at him while the other is still alive. [/QUOTE]
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