Rystil Arden
First Post
(OOC:
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The criticals don't add as much as it might initially seem due to low probability. Let's continue to consider the edge case of 14 strength d6 weapon with 19-20/x2 that hits on a 15 (lower strength and the arrow is always better, higher dice and the weapon is) vs two-handing the silver arrow that hits on a 19 (note that Juliana's flail only crits on a 20, so this is actually being overly optimistic for the d6 weapon). Here is the exact honest-to-goodness expected value, including criticals, as best as I can do based on my 6.041 class (MIT's Probability Course).
Two-handed d6 weapon with 19-20/x2: E[Damage from 18 or below] = 4/20 * 10 / 6 = .3333 damage per round, E[Damage from 19 and 20] = 1 / 10 * 6 / 20 * 8 + 1 / 10 * 14 / 20 * 10 / 6 = .24 + .11666666666 Total Expected Value =.69
Two-handed d6 weapon with 20/x2: .41666666 + .12 + .0583333333 = .5949999
Silvery arrow: E[Damage] = 1/10 * 9/10 * 5.5 + 1/10 * 1/10 * 11 = .605
So...the arrow beats a d6 /x2 and loses to a d6 19-20/x2 weapon with a couple of important observations:
#1: A huge amount of the average damage comes from criticals considering how infrequent they are. This should be pretty upsetting, as it indicates that without crits, expected damage is pretty dismal.
#2: Expected damage is really awful even with crits. Based on that expected damage, loss was pretty much assured--and we did worse than the expected damage too thanks to IC's hatred
To see just how bad our expected damage is, compare it to the wererats' expected damage and they should be mowing through us unopposed exactly as they are.
#3: It is very close here, and with the scarcity in difference (.1 per round at most), it isn't worth the action to switch weapons between any of these three)
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[SBLOCK]
The criticals don't add as much as it might initially seem due to low probability. Let's continue to consider the edge case of 14 strength d6 weapon with 19-20/x2 that hits on a 15 (lower strength and the arrow is always better, higher dice and the weapon is) vs two-handing the silver arrow that hits on a 19 (note that Juliana's flail only crits on a 20, so this is actually being overly optimistic for the d6 weapon). Here is the exact honest-to-goodness expected value, including criticals, as best as I can do based on my 6.041 class (MIT's Probability Course).
Two-handed d6 weapon with 19-20/x2: E[Damage from 18 or below] = 4/20 * 10 / 6 = .3333 damage per round, E[Damage from 19 and 20] = 1 / 10 * 6 / 20 * 8 + 1 / 10 * 14 / 20 * 10 / 6 = .24 + .11666666666 Total Expected Value =.69
Two-handed d6 weapon with 20/x2: .41666666 + .12 + .0583333333 = .5949999
Silvery arrow: E[Damage] = 1/10 * 9/10 * 5.5 + 1/10 * 1/10 * 11 = .605
So...the arrow beats a d6 /x2 and loses to a d6 19-20/x2 weapon with a couple of important observations:
#1: A huge amount of the average damage comes from criticals considering how infrequent they are. This should be pretty upsetting, as it indicates that without crits, expected damage is pretty dismal.
#2: Expected damage is really awful even with crits. Based on that expected damage, loss was pretty much assured--and we did worse than the expected damage too thanks to IC's hatred

#3: It is very close here, and with the scarcity in difference (.1 per round at most), it isn't worth the action to switch weapons between any of these three)
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