Random walks only apply if you have an equal chance of going both directions. You don't know what you're talking about.
Wow, did you just fail even harder? Amazing. Go back to the part where I specifically stated that it's a random walk if the average number of attacks generated per attack is 1. It's almost like I already stated this a long time ago, and do know what I'm talking about. Interesting.
Here's the quote by the way, a while back:
(Critical Threat Chance/10)+(Critical Threat Chance * 19/5) = X. Now, sum X^i for i=1 to infinite. Multiply that sum by the base number of attacks to yield average number of attacks. If that sum is infinite, the average is infinite, if it's not, the whole thing can never go infinite, and the project breaks down at X=1 and requires higher math due to the Random Walk issue. In the old TO post, X was higher than 1, hence the issue.
See? X=1 is a random walk, and X is the average number of attacks generated. And here's another:
It most certainly CANNOT go infinite as long as the amount of attacks generated per attack is no higher than 1. I reviewed this a good bit since last time... at 1 it's a random walk, and CANNOT go infinite. At less than 1 it doesn't either. At more than 1 it can, and often will, which is what happened last time.
It's almost like I said it twice already, and like you completely failed to read yet again. Once again, I know what I'm talking about. I was just a little sleepy in the first post (which I said!) and made one numerical error. Everything else is just you failing... HARD.
@Judging: I gave you the complete formula, do you really need me to spell it out for you? It still doesn't justify your post of bitching at me for not doing the math when I clearly did, and you just came in here and whined at me without reading past the first post.
But here you go. The number of attacks generated per attack is equal to the chance of a new attack being generated times the number of attacks generated. If P is the probability of a non confirmed critical threat and Q is the probability of a confirmed critical threat, and on non confirmed critical threats you get 2 more attacks while on confirmed threats you get 4, and X is the number of attacks generated per attack, then you get this formula:
X = P(2)+Q(4).
Now, assuming we're confirming on a 2+ (which is believable on a build that gets this many critical hits with Blood in the Water, and requires only Dex and Int, and gets Int to confirm critical hits), and we're threatening on a 15-20 as per the first build, P = .3*1/20, and Q = .3*19/20. This yields an X of 1.17, which goes infinite due to being greater than 1. Using heavy crossbows instead, we get X=.73, which does not go infinite, which we'll work with for a bit.
Now from here, the expected number of attacks added per base attack is the sum of X^i, where i goes from 1 to infinity. You can see now why if this goes over 1 you get infinite attacks, and if it's less than 1 you get finite attacks. This formula has a problem where X=1, but it can then be modeled as a random walk. Now, to spell out why this is the sum we use, the each individual attack will generate, in the current example, .73 new attacks, so now it has turned into 1.73 attacks. However, the new attack will also generate .73 new attacks, and the chance that two attacks are generated is .73*.73, or .73^2. And so on. Got that?
So now you take the initial number of base attacks, multiply it by that sum, and you've got the number of generated attacks. Now add that back to the base number and you've got the total attacks. If you prefer, you could have just done the sum from 0 to infinity, and not added the base attacks the second time... you get the same number.
Okay, still with me? I assume I've shown my work enough, professor Eagle?
Okay, so now that sum is 39 if the X value is .975, which it is when you have a 25% chance to critically hit (16-20 critical threat range). This means every base attack yields 39 new attacks on average, or a X40 multiplier on the total number of attacks. Nifty. And this is where Woodenbandman's contribution becomes quite useful. Sadly, we lose TSS and Raging Mongoose, but at least we've got Dancing Mongoose, and we get our feats earlier.
Okay, so we'll change the build around, to Feat Rogue 4/Fighter 4/Barbarian 7 (Cityscape and Whirling Frenzy)/Warblade 5, with the same basic feat load out, plus Extra Rage, and we'll use Heavy Crossbows to avoid the whole infinite issue.
Okay, so this gives us a base of 9 attacks (Rapid Shot, Whirling Frenzy, TWF), and Dancing Mongoose makes it 11. Splitting brings that to 22. And now the extra attacks kick in, bringing us to 880 shots. Neat. On rounds where you don't use Dancing Mongoose, you're sadly lowered to only 720 attacks. But hey, it's not like you're often getting to a second round of combat with damage like this, right?
Now, to answer your damage question, that's going to be very tricky. Your base damage is going to be the damage of your heavy crossbows, which if huge is 3d6 (Permanent Enlarge Person, Strongarm Bracers... note that this adds 50% to the range, and I don't think hitting will be a big issue). They're enchanted as +5, and assuming a Dex of 30 (at level 20) we've got another +5 due to Crossbow Sniper. So your base damage here is 3d6+10 per shot, with 880 shots, which if hitting on a 2+ (VERY likely when Blood in the Water is kicking in) is 836 hits for a base of 17138 damage, not counting criticals. This alone of course is enough to wipe out nearly any encounter.
Now, here's the tough part. You're going to, on average, confirm about 209 critical hits, meaning by the end you're getting +209 to hit and damage with every shot (you can see why I'm talking about hitting on a 2+). The exact damage is hard to do, but let's say for the sake of arguement that we critically threaten every fourth shot, starting with the third shot (which is pretty reasonable when we have a 25% chance to critically hit). If we fail to confirm every 20th critical threat, starting at the 11th critical threat, then that's roughly average behavior, right?
And at this point it's 2am, so I'll work out the rest in the morning, but suffice to say this build is just about the best non infinite archer you can possibly get... thanks to Woodenbandman for his very useful contribution. I'm not sure we can still get to TSS even with Bloodline abuse due to need for feats, but I'll consider that later. Still, we're well past the point of "Everything's dead!" so that's good, and if the DM throws another encounter at you while you're still charged up, that's awesome.
JaronK
