Stubbazubba
2015-04-13, 09:21 PM
I'm tinkering with a loosely d20-based fantasy system that is level-less. So to handle fighting hordes of weaker enemies I have created a mechanic, but I wanted to see if it's actually any better than simply using the base iterative attack scheme I have. The maths get a little complicated, and I am not a maths person, so I wanted to let you fine number-crunching eggheads help me out, and hopefully have fun solving a quick little optimization problem:
Iterative attacks: Attacks are simply d20+modifiers vs. defense TN, and if you beat the enemy's attack by 10 or more you get to make another attack at full attack bonus, regardless of how many enemies you have targeted. There is no cap on the number of successive attacks you can make this way. E.g., Aragorn has a +12 attack bonus against an Orc with a defense of 11, so if he rolls a 21 or better (60% chance), he gets to make another attack, which also has a 60% chance of giving him yet another attack, and so on.
Attacking multiple targets: You can take a -3 penalty to attack an additional target with the same attack roll, e.g., Aragorn takes a -3 penalty to target 2 Orcs (net +9 bonus), a -6 penalty to attack 3 Orcs (net +6 bonus), a -9 penalty to attack 4 Orcs (net +3 bonus), etc. If you fail to hit the DC, you can still hit a number of targets equal to the number of targets you tried to hit subtract how much you missed by, e.g. if you targeted 4 opponents with a defense TN of 14 but only roll a 13 you still hit (4 [# tried for] - (14 [TN] - 13 [result])) = 4 - 1 = 3 targets. IOW, if Aragorn targets 3 Uruks (defense TN 15), he takes a -6 penalty (net +6 bonus), and on a 15 he would hit all 3 (60% chance), on a 14 he would hit 2 (5% chance), on a 13 he would hit 1 (5% chance), and on a 0 or below he would hit nothing. And if he rolled 25 or more (10% chance), he would hit 3 and make an iterative attack.
Variables: I'm looking at these three variables - attack bonus, defense TN (and, by implication, the delta between these two), and number of enemies targeted. Assume for now that any hit will kill a target.
The Question: Under what conditions, in terms of those three variables, are you statistically better off taking your full attack bonus and hoping for successive iterative attacks than attacking multiple targets with a single attack? IOW, Aragorn is facing hordes of Orcs, and he has the option of attacking 1 with his full +12 bonus (60% chance of iterative attack) or attacking some number of them with a single attack. Aragorn's player is a first-rate min-maxer, so how many Orcs does he decide to attack to maximize the number of Orcs hit/killed?
Thank you! I hope someone has fun with this.
Iterative attacks: Attacks are simply d20+modifiers vs. defense TN, and if you beat the enemy's attack by 10 or more you get to make another attack at full attack bonus, regardless of how many enemies you have targeted. There is no cap on the number of successive attacks you can make this way. E.g., Aragorn has a +12 attack bonus against an Orc with a defense of 11, so if he rolls a 21 or better (60% chance), he gets to make another attack, which also has a 60% chance of giving him yet another attack, and so on.
Attacking multiple targets: You can take a -3 penalty to attack an additional target with the same attack roll, e.g., Aragorn takes a -3 penalty to target 2 Orcs (net +9 bonus), a -6 penalty to attack 3 Orcs (net +6 bonus), a -9 penalty to attack 4 Orcs (net +3 bonus), etc. If you fail to hit the DC, you can still hit a number of targets equal to the number of targets you tried to hit subtract how much you missed by, e.g. if you targeted 4 opponents with a defense TN of 14 but only roll a 13 you still hit (4 [# tried for] - (14 [TN] - 13 [result])) = 4 - 1 = 3 targets. IOW, if Aragorn targets 3 Uruks (defense TN 15), he takes a -6 penalty (net +6 bonus), and on a 15 he would hit all 3 (60% chance), on a 14 he would hit 2 (5% chance), on a 13 he would hit 1 (5% chance), and on a 0 or below he would hit nothing. And if he rolled 25 or more (10% chance), he would hit 3 and make an iterative attack.
Variables: I'm looking at these three variables - attack bonus, defense TN (and, by implication, the delta between these two), and number of enemies targeted. Assume for now that any hit will kill a target.
The Question: Under what conditions, in terms of those three variables, are you statistically better off taking your full attack bonus and hoping for successive iterative attacks than attacking multiple targets with a single attack? IOW, Aragorn is facing hordes of Orcs, and he has the option of attacking 1 with his full +12 bonus (60% chance of iterative attack) or attacking some number of them with a single attack. Aragorn's player is a first-rate min-maxer, so how many Orcs does he decide to attack to maximize the number of Orcs hit/killed?
Thank you! I hope someone has fun with this.