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Advantage vs Disadvantage : What's the Math?
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<blockquote data-quote="FormerlyHemlock" data-source="post: 6960671" data-attributes="member: 6787650"><p>The relative difference is actually <em>more </em>important IMO than the absolute difference because in reality the number of rolls you make isn't static. You change your behavior based on risk assessment. If an orc will hit you 10% of the time, then you dare not fight 50 of them head-on in a fight to save the princess. But if you pick up a Cloak of Displacement so that you only get hit 1% of the time, your options change. Maybe you really <em>can</em> fight them head-on. And now because you <em>can</em> fight them head-on, you can risk sneaking in to save her without a fight, because even in a worst case scenario you can still fight your way out.</p><p></p><p>Absolute probabilities only matter when you are faced with an opportunity cost. If you have the choice between spending your concentration to give your ten allies a +20% absolute bump in their to-hit probabilities, then it doesn't matter whether you're raising 40% to 60% or 1% to 21%--either way, that use of your concentration has a specific value. (Total potential damage * 0.2.) You compare that against alternate uses of your concentration (e.g. summoning eight wolves which will do XYZ damage to the enemy and act as meatshields) to decide which is better.</p><p></p><p>Both metrics have their place but knowing the relative probabilities tends to offer more insight into tactical pros and cons.</p></blockquote><p></p>
[QUOTE="FormerlyHemlock, post: 6960671, member: 6787650"] The relative difference is actually [I]more [/I]important IMO than the absolute difference because in reality the number of rolls you make isn't static. You change your behavior based on risk assessment. If an orc will hit you 10% of the time, then you dare not fight 50 of them head-on in a fight to save the princess. But if you pick up a Cloak of Displacement so that you only get hit 1% of the time, your options change. Maybe you really [I]can[/I] fight them head-on. And now because you [I]can[/I] fight them head-on, you can risk sneaking in to save her without a fight, because even in a worst case scenario you can still fight your way out. Absolute probabilities only matter when you are faced with an opportunity cost. If you have the choice between spending your concentration to give your ten allies a +20% absolute bump in their to-hit probabilities, then it doesn't matter whether you're raising 40% to 60% or 1% to 21%--either way, that use of your concentration has a specific value. (Total potential damage * 0.2.) You compare that against alternate uses of your concentration (e.g. summoning eight wolves which will do XYZ damage to the enemy and act as meatshields) to decide which is better. Both metrics have their place but knowing the relative probabilities tends to offer more insight into tactical pros and cons. [/QUOTE]
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