Math of Blade Cascade

[comrade raoul]

Blade Cascade, of course, is a cool ranger Daily 15th power that lets you keep attacking a target, with alternating weapons, until you miss.

My question is: given some n-out-of-20 chance of missing (assuming n is the same for either weapon), how many Blade Cascade attacks can a ranger statistically expect? In particular, how many can he expect if he has only a 1-out-of-20 chance of missing--he misses only on a "1"?

(My statistically-naive guess is that a ranger could expect 20/n attacks--so a ranger who missed half the time could expect two attacks; a ranger who only missed on a one could expect 20. But that seems pretty high.)

 

[Andur]

I think it is 20-n, but iirc someone did the calcs and it came to 14 attacks was the "stat average".

 

[quill18]

My question is: given some n-out-of-20 chance of missing (assuming n is the same for either weapon), how many Blade Cascade attacks can a ranger statistically expect? In particular, how many can he expect if he has only a 1-out-of-20 chance of missing--he misses only on a "1"?

.95 ^ 13 = 0.51334208328

If he only misses on a one, the ranger will get in 13 hits (or more) 51% of the time.

 

[JGulick]

The expected number of tests until failure is 1/p(failure).

In this case, p(failure) = (AC - Attack Bonus - 1) / 20, with an upper limit of 95% and a lower limit of 5% because 1's always miss and 20's always hit.

So, if AC and Attack Bonus are reasonably related (that is, not 20 or further apart), expected number of attacks until a success is 20 / ( AC - Attack Bonus - 1 )

(sorry... originally got it backwards... this is corrected, I think...)

 

[comrade raoul]

Awesome, thanks--that makes sense.

Let's take it up a notch, then. What if he's epic, has Deadly Trickster, and is willing to spend all three rerolls keeping Blade Cascade going as long as possible?

(Edited--or, more generally, how does having one or more reroll affect the math?)

 

[quill18]

I think it is 20-n, but iirc someone did the calcs and it came to 14 attacks was the "stat average".

Definitely not 20-n. The math is 95% x 95% x 95% etc...

And my results indicates 13+ *hits* on average, which would translate to 14+ *attacks* on average, so we're in agreement there.

 

[Giryan]

Lots.
there's another thread somewhere, that goes into in in great detail.
With a party backing him up, to give other rerolls etc..., it's insane

 

[quill18]

Awesome, thanks--that makes sense.

Let's take it up a notch, then. What if he's epic, has Deadly Trickster, and is willing to spend all three rerolls keeping Blade Cascade going as long as possible?

(Edited--or, more generally, how does having one or more reroll affect the math?)

There's already a full thread analyzing this, if you're willing to look around for it.

The answer is: Orcus dies.

 

[JGulick]

Let's take it up a notch, then. What if he's epic, has Deadly Trickster, and is willing to spend all three rerolls keeping Blade Cascade going as long as possible?

(Edited--or, more generally, how does having one or more reroll affect the math?)

That's a bit more difficult and I can't quite get to it now. And would very much depend on the chance of success on the re-roll. In other words, this strategy makes very little since if you need 19s or 20s to hit and a lot more if you hit rather often.

 

[essenbee]

... because 1's always miss and 20's always hit...

20 is not always a hit, it is just a critical if you do hit.