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*Dungeons & Dragons
The mathematics of D&D–Damage and HP
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<blockquote data-quote="Asisreo" data-source="post: 8221083" data-attributes="member: 7019027"><p>Immediate kills are more valuable than consistent kills for a particular reason: a dead enemy can't kill your teammates. </p><p></p><p>If you have an attack that guarantees a kill but it has a 50% chance to-hit (We'll call it attack A), you'd have a higher variance than an attack that guarantees a hit but takes 2 rounds to kill(which we'll call attack B). Which is better? Does it matter? </p><p></p><p>Yes, it does matter which one you choose. If we look at it with a sufficiently large number of trials, the percent misses to hits will equal about 50% and it will <em>average</em> to 2 rounds to kill on each, but we want an enemy dead as soon as it can be. With B, there's a 0% chance it will die round 1, a 100% chance it dies on round 2 and no more rounds have to be considered. But if you attack with A, you'd have a 50% chance to kill on round 1, a 25% chance to kill round 2, a 12.5% chance to kill round 3, etc. </p><p></p><p>What does this mean in terms of damage mitigated? Well, lets say the order is you first, monster second. The monster averages 100% of the damage round 1 and 0% damage round 2 for B. A has an average damage reduction of 50% for round 1 and 25% round 2, etc. </p><p></p><p>The significance is that depending on your own current survivability, you should choose one over the other. </p><p></p><p>If you can survive 2 rounds before resetting to full HP, you should do the second attack. But if you die as soon as the creature gets to attack, you should choose the first attack. </p><p></p><p>So now we can have our own survivability married to our decision of what is a good or bad attack. The average told us nothing, but the probabilities helped us understand the differences between A&B and which attack is best for which situation. </p><p></p><p>In general, if you're on your last ropes, you'll want to break out attacks with high variance. If you're certain that you won't be felled anytime soon, you'll want attacks with low variance. </p><p></p><p>And the application can now inform us that when your barbarian has high HP in a fight, he'll want to use his Greatsword. At low HP, however, he'll want to start swinging his Greataxe to increases the odds that he kills before he gets killed.</p></blockquote><p></p>
[QUOTE="Asisreo, post: 8221083, member: 7019027"] Immediate kills are more valuable than consistent kills for a particular reason: a dead enemy can't kill your teammates. If you have an attack that guarantees a kill but it has a 50% chance to-hit (We'll call it attack A), you'd have a higher variance than an attack that guarantees a hit but takes 2 rounds to kill(which we'll call attack B). Which is better? Does it matter? Yes, it does matter which one you choose. If we look at it with a sufficiently large number of trials, the percent misses to hits will equal about 50% and it will [I]average[/I] to 2 rounds to kill on each, but we want an enemy dead as soon as it can be. With B, there's a 0% chance it will die round 1, a 100% chance it dies on round 2 and no more rounds have to be considered. But if you attack with A, you'd have a 50% chance to kill on round 1, a 25% chance to kill round 2, a 12.5% chance to kill round 3, etc. What does this mean in terms of damage mitigated? Well, lets say the order is you first, monster second. The monster averages 100% of the damage round 1 and 0% damage round 2 for B. A has an average damage reduction of 50% for round 1 and 25% round 2, etc. The significance is that depending on your own current survivability, you should choose one over the other. If you can survive 2 rounds before resetting to full HP, you should do the second attack. But if you die as soon as the creature gets to attack, you should choose the first attack. So now we can have our own survivability married to our decision of what is a good or bad attack. The average told us nothing, but the probabilities helped us understand the differences between A&B and which attack is best for which situation. In general, if you're on your last ropes, you'll want to break out attacks with high variance. If you're certain that you won't be felled anytime soon, you'll want attacks with low variance. And the application can now inform us that when your barbarian has high HP in a fight, he'll want to use his Greatsword. At low HP, however, he'll want to start swinging his Greataxe to increases the odds that he kills before he gets killed. [/QUOTE]
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