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| #1Batla76Nov 02, 2014 15:12:55 | I am trying to figure out the % chance of a 20 in a given round with multiple attack rolls. Example: A fighter attacks 4 times each round, what is the % chance roll a single 20?
1 attack = 5% chance 2 attacks = ?% 3 attacks = ?% 4 attacks = 17% chance ??
Any help would be appreciated!
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| #2FrogReaverNov 02, 2014 17:02:20 | Easy can I ask why?
Simply take 1 - chance to "not crit" to the power of the number of attacks
So at 5% crit and 3 attacks you would do:
1 - (.95)^3 = .14265 |
| #3AnsbachNov 02, 2014 17:17:56 | When you are talking about getting "at least one" of something, then the easiest way to do it is to find out the chance of it not happening at all and then subtract that from 100%.
So for example, if you are rolling two dice it would be...
95% (1-19) x 95% (1-19) = .95 x .95 = .9025
The chance of not rolling a 20 on either die is 90.25%. Therefore, the chance of getting at least one 20 when rolling two dice is...
100% - 90.25% = 9.75%
So 3 dice would be .95 x .95 x .95, etc.
Edit: this is just a detailed explanation of FrogReaver's formula.
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| (Reply to #2)Coredump00 |
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| (Reply to #3)Coredump00 |
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| (Reply to #4)FrogReaver |
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| (Reply to #5)FrogReaver | It is not correct. It would be .95*.05 + .05*.95 = .0475 + .0475 = .095
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| #8FrogReaverNov 02, 2014 17:17:49 | For 3 attack a rolling exactly 1 20 it would be:
3*.95*.95*.05
for 4 attacks: 4*.95*.95*.95*.05
And so on... |
| #9AnsbachNov 02, 2014 17:19:38 |
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| #10Batla76Nov 02, 2014 18:37:35 | Thanks! I guess I should have stated, the chance of rolling (A) 20, not exactly (1) 20. As far as why this is important, I am trying to figure out % chances of a Vorpal sword hitting and doing 6D8 on a 20 used by a fighter attacking with it several times each round. I am trying to estimate damage probability per round with that sword vs the same fighter using a sword with a +1d6 enchantment to Dmg (fire,ice,etc) |
| (Reply to #6)Coredump00 |
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| (Reply to #10)Coredump00 |
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| #13Batla76Nov 02, 2014 18:49:00 | Thanks Core! That helped a lot! This is a copy of my edited post above regarding where I am headed with this:
I am trying to figure out % chances of a Vorpal sword hitting and doing (6D8 on a 20 beta rules) used by a fighter attacking with it several times each round. I am trying to estimate damage probability per round with that sword vs the same fighter using a sword with a +1d6.
Basically, what does more Dmg a 1d8 sword with a potential to vorpal 6D8 on 20, or a sword doing 2d8 each hit? |
| (Reply to #13)bid |
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| (Reply to #13)FrogReaver |
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| #16FrogReaverNov 02, 2014 19:34:51 | Does the 6d8 damage of a vorpale get upped to 12d6 on a crit? |
| #17FrogReaverNov 02, 2014 19:37:58 | Also, Should I assume advantage or not? |
| (Reply to #17)Batla76 |
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| #19FrogReaverNov 02, 2014 20:12:57 | im pretty sure the vorpal sword is better than the regular at 75% hit and below (assuming 15% crit) also assuming 4 attacks.
However assuming a 5% crit and 4 attacks the voorpal will only be better when your chance to hit is 30% and below.
I'll post calculations In a couple of hours. |
| (Reply to #14)FrogReaver | Double check ur work. Voorpal will work similar to sneak attack and champion can get extra crit chance.
Vorpal should do better than the regular attack against high ac values just like sneak attack does (with multi attacks)
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| #21Batla76Nov 02, 2014 20:50:32 | Non-Champion Spec:
Without figuring any damage bonuses and assuming an average of 4 on a D8, a fighter with 4 attacks that hit would do 16DMG. If the sword were enchanted with +1d6 extra damage per hit (average 3), the damage would be 24 after the 4 attacks.
Damage = 24
Now, the same fighter chooses a vorpal sword instead:
Damage = 16 + the potential for an extra 6d8 if he roles a 20 (18.5% chance in 4 rolls)
The battle rages on for 4 rounds:
Enchanted Sword After 4 rounds = 96,
Vorpal Sword after 4 rounds = 64 +6D8 for any 20's he may have rolled in 16 attempts, even with 1 20 rolled, the avg DMG in 4 rounds = 88 (56%chance)
He may get lucky and roll a few 20's which would put the DPR higher.
Am I on the right track or totally off base? |
| #22FrogReaverNov 02, 2014 21:16:31 | Off base. I'll explain why later |
| #23FrogReaverNov 03, 2014 3:59:46 | So maybe I'm misunderstanding. Does vorpal blade effect trigger off a crit or a natural 20?
If vorporal blade triggers on a natural 20 then and crit chance is only 5%
Let C = chance to hit but not crit Let X = chance to crit Let V =Average DPR of vorpall blade Let E = Average DPR of extra damage blade Let N = chance for natural 20
For the vorporal blade:
V = X*(6d8 + 2d8) + C*(1d8)
V = X*6d8 + X*2d8 + C*1d8
For the 1d6 extra damage on hit sword
E = X*(2d8 + 2d6) + C*(1d8 + 1d6)
E = X*2d8 + X*2d6 + C*1d8 + C*1d6
-> V-E = X*6d8 - X*2d6 + C*1d6
Let V-E > 0 ->
X*6d8 - X*2d6 + C*1d6 > 0 X*6d8 > X*2d6 + C*1d6
X*(27) > X*7 + C*3.5 X*20 > C*3.5
X/C > 3.5/20 = 5 / 28.57 ->
C < 28.57% for V > E
So at 25% chance to hit but not crit (and values lower than that) or (30% combined chance to hit and lower) you will do better with the vorpal blade.
----------------------------------------------------------------------- If crit is increased to 15% and vorpral blade just triggers on a crit then X/C > 3.5/20 = 15 / 85.714 -> C < 85.714 for V > E.
So for values of C 85% and below you would do more damage with the vorporal blade. *Note that I had assumed up till this post that Vorporal blade trigged on a crit ------------------------------------------------------------------------ If crit is increased to 15% and vorporal blade just triggets on a natural 20 then:
V = .05*27 + X*(9) + C*(4.5) E = X*9 + X*7 + C*4.5 + C*3.5
V-E = .05*27 -X*7 - C*3.5
V-E > 0 1.35 - 7X - 3.5C >0 1.35 > 7x +3.5C
.3857 > 2x + C .0875 > C or C<.0875 for V>E
-> chance to hit but not crit of 5% and lower would cause vorpal blade to do more damage (20% total chance to hit or crit) -------------------------------------------------------------------------------------
Hopefully you can follow the algebra here and pick whichever case is actually supposed to apply to vorporal blade. |
| #24GnarlNov 08, 2014 7:58:10 | This should help: http://en.wikipedia.org/wiki/Binomial_distribution |
| #25GnarlNov 08, 2014 8:18:41 |
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| #26Batla76Nov 08, 2014 20:21:36 | Thanks Gnarl! I ran some numbers with a binomial distribution calculator but wasnt sure if they were correct. As far as the vorpal wording, it would be more appropriate to say "whenever you roll a 20". The math is making my head spin! It has been a while since algebra, probability and statistics, etc. The conclusion that I have come to is; given a certain amount of attacks per round without advantage(4 rolls in this case), the vorpal probably will not do as much damage on average as a sword with an extra D6 enchantment over the course of many rounds of combat. However, it think it would be more fun to wield it to "play the dice" making each roll more exciting hoping that a 20 will show up. With advantage, I think that the probability turns more in favor of the vorpal.
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| #27Coredump00Nov 08, 2014 22:14:46 | So... the harder it is To Hit, the more important the Crit damage becomes. The Vorpal does a lot more crit damage, but a lot less normal damage...
If you need a To Hit of 15 or less, you are better off with the Elemental sword.
It doesn't matter if you have 1 attack per round or 5.
OTOH, there isn't *that* big of a difference anyway....
If the attack has advantage, it gives more crits, which helps the Vorpal, but also more regular hits, which helps the elemental.
Mostly cancels out.... If you need a To Hit of 14 or less, you are better off with the Elemental sword.
NOTE: these calculations based on Elemental, 1D8+1D6.....crit gives 2D8+2D6
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| #28GnarlNov 12, 2014 16:14:50 |
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