TheoryMachine: Drago and Critical Amputate

[Cuagau]

I did a search but nothing conclusive came up, so I was wondering if anyone had calculated the probability of Drago's critical amputate under the following conditions;

base 2d6 to hit
2d6 + affinity [Vlad] = 3d6, dropping the lowest.
2d6 + affinity [Vlad] + boost = 4d6, dropping the lowest.
2d6 + affinity [Vlad] + Signs and Portents = 4d6, dropping two lowest.
2d6 + affinity [Vlad] + Signs and Portents + boost = 5d6, dropping two lowest.

(Obviously, there are instances where Drago can have signs and portents and not Affinity, but the probabilities are the same as just having the Affinity, as Affinity and Signs and Portents are the same effect.)

I know its a fairly heady task, but my grasp of statistics is weak at best, and am currently comparing Drago to a Kodiak [with use with Vlad].
Obviously, the dropping the lowest is the major complication (or is it, can you just regard a 3d6, dropping the lowest roll as a 2d6 roll for the purpose of Critical probability?)

e.g.'s
On 3d6, dropping the lowest, a result of 6, 4, 4, means no crit, but 6, 6, 5 is. Or because the 'bonus dice' isn't distinctly observable, its not actually significant? i.e. If the 'bonus dice' in the first roll was the six, it just cost me a critical amputate. On the second roll, if the 'bonus dice' was a 6, it just gained me a critical amputate.

I hope this makes sense to some TheoryMachiners. I have enough knowledge to read Statistics others have written, but when it comes to constructing my own, my knowledge is lacking.

Many Thanks. -=C=-

[Marth]

If you want to really wrap your head around some Mathmachine, try this

2d6 + affinity [Vlad] + Signs and Portents + boost = 5d6, dropping two lowest.

and add Stars Crossed from Calandra the truthsayer. That'd be 6d6, dropping two lowest and one highest.

[PG_vytzka]

Yay post count reset.

As usual, when I can't be arsed to calculate exact probabilities, which is often, a brute simulation (simply going through all combinations - not by hand obviously!) will suffice just as well. This is all assuming that you're attacking DEF10 or less (snake eyes miss, anything else hits), and that I made no errors.

2d6: 13.9% (5/36: 2,2 3,3 4,4 5,5 6,6)
2d6 + affinity [Vlad] = 3d6, dropping the lowest: 23.1% (50/216)
2d6 + boost = 3d6: 44.4% (96/216)
2d6 + affinity [Vlad] + boost = 4d6, dropping the lowest: 53.7% (696/1296)
2d6 + affinity [Vlad] + Signs and Portents = 4d6, dropping two lowest: 30.4% (395/1296)
2d6 + affinity [Vlad] + Signs and Portents + boost = 5d6, dropping two lowest: 60.4% (4856/7776)
Add Stars Crossed from Calandra the truthsayer. That'd be 6d6, dropping two lowest and one highest: 66.6% (31056/46656)

The last is kind of odd but it's an odd situation The rest I'm pretty sure about.

Though, come to think of it, a 6% hike from previous case is not really all that unexpected. You "lose" the cases where you had two matching high dice and roll low, and "win" when you had a bunch of nonmatching mid-values and a single high one, and rolled a match for one of the former. If that's clear enough, I might be rambling a bit!

Rather obvious observation is the more dice you can throw at the problem the greater the likelihood of critical is going to be. You don't even need a math or a compsci degree (*gives a sad look to his diploma*) for that stuff.

[Cuagau]

Rather obvious observation is the more dice you can throw at the problem the greater the likelihood of critical is going to be.

Except when you get probabilities like;
2d6 + affinity [Vlad] + Signs and Portents = 4d6, dropping two lowest: 30.4% (395/1296)
Where more is apparently less.

Of most significance I think is:
2d6 + affinity [Vlad] + Signs and Portents + boost = 5d6, dropping two lowest: 60.4% (4856/7776)
i.e. when things have gone south, and your only option is to cripple a 'jack that for some reason you can't destroy, or there's an arm that really must go (deathjack anyone?), this is seemingly the optimal circumstance.

P.S. <3

[Avecrien]

Vytzka is awesome, nevermind the post count and the dusty parchment he worked so hard to get.