Author Topic: Calculating the attacks of this archer...  (Read 9891 times)

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JaronK

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Calculating the attacks of this archer...
« on: December 05, 2008, 01:29:23 AM »
I think I'm a bit sleepy, but I'm having trouble figuring out how many attacks this archer has.  Assume this is a game played by strict RAW, so Aptitude Great Crossbows work fine with Hand Crossbow Mastery, Lightning Mace, and Roundabout Kick.  Also, the archer is using Time Stands Still with Raging Mongoose, TWF, ITWF, GTWF, and Rapid Shot, and his crossbows are both Splitting, so he's got a base of 48 attacks.  He also has Blood in the Water and Int to confirm critical hits, so let's assume he's confirming criticals on a 2+.  So... how many attacks does he actually have, on average?

Feat Rogue 2/Fighter 2/Warblade 16, Human, 1 Flaw (Vulnerable).
Hand Crossbow Mastery,  TWF, Improved Unarmed Strike, Power Attack, Weapon Focus (Light Mace), Point Blank Shot, Roundabout Kick, Rapid Shot,Combat Reflexes, Improved Critical (Hand Crossbow), Lightning Mace, Improved Two Weapon Fighting, Improved Initiative, Greater Two Weapon Fighting, Blind Fighting, Crossbow Sniper

He's weilding two Aptitude Splitting Great Crossbows, one of which is +5, the other +1, but with a Tooth of Leraje so they're both effectively +5.  He has a 25% chance to threaten a critical hit with every attack, and every threatened critical generates 2 extra attacks (due to Splitting and Lightning Mace) while every confirmed critical generates 4 attacks (Splitting, Lightning Mace, Roundabout Kick).

At least this time I'm sure he doesn't go infinite, nor can he, but how many shots is this?

JaronK

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Re: Calculating the attacks of this archer...
« Reply #1 on: December 05, 2008, 03:42:21 AM »
You've got a 30% chance to threaten a crit.  Per the infinity math I explained to you waaaay back on that TO thread we get infinite on average.
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X-Codes

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Re: Calculating the attacks of this archer...
« Reply #2 on: December 05, 2008, 04:29:59 AM »
I thought that infinite didn't count because the chance to attack an infinite number of times was infinitely small?

JaronK

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Re: Calculating the attacks of this archer...
« Reply #3 on: December 05, 2008, 05:21:31 AM »
You've got a 30% chance to threaten a crit.  Per the infinity math I explained to you waaaay back on that TO thread we get infinite on average.

Yeah... that one someone else (not you) explained way back was for a 55% chance to threaten crit, though it is true that I accidentally went to 30% instead of 25.  If needed, I can drop Roundabout Kick so it's only +2 attacks generated.  Easily solvable.  The idea here, obviously, is to avoid going infinite, but to make sure it's easy to calculate this time.

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JaronK

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Re: Calculating the attacks of this archer...
« Reply #4 on: December 05, 2008, 05:49:56 AM »
Okay, fixed the feats by dropping the flaw and going with this:

Hand Crossbow Mastery,  TWF, Point Blank Shot, Weapon Focus (Light Mace), Rapid Shot, Precise Shot, Combat Reflexes, Woodland Archery, Improved Critical (Hand Crossbow), Lightning Mace, Improved Two Weapon Fighting, Improved Initiative, Greater Two Weapon Fighting, Blind Fighting, Crossbow Sniper

Okay, so that's a 30% chance to threaten, causing 2 extra attacks (but not any chance of 4 anymore).  If I've got this right, each attack generates .6 new attacks, meaning the base attacks each generate .6+.6^2+.6^3... new attacks with no chance of going infinite, or roughly 1.5 extra attacks.  Thus, with 48 base attacks we're looking at about 120 attacks, with roughly 34 confirmed critical hits, so by the end each shot is at +34 to hit and damage.  Not bad.

Really, the trick here seems to be to get an attack routine that generates .99 attacks per attack, thus yielding a very long chain without going infinite.  The original build was at 1.17, a bit too high because I somehow decided that 15-20 critical was 25%.  The fixed build works, but it's lower than I wanted, so some work is needed.

Edit:  Okay, if we use the original build, but just use regular Heavy Crossbows instead of Great Crossbows, and thus lower our critical chance to 20%, the magic number we hit is .78.  This isn't perfect, but it's a lot better, yielding roughly 3.5 new attacks per base attack, or 214 attacks and roughly 41 confirmed critical hits.  If we could somehow get a critical on a 16-20, yielding a 25% chance to critical as I originally thought, our magic number would be .975, which is as good as it gets.  So the question is... how can we get a 16-20 critical threat range?  And is it possible while still getting Time Stands Still and Raging Mongoose?  If so, the number of shots would be insanely high without ever going infinite, which is my goal here.

JaronK
« Last Edit: December 05, 2008, 06:03:27 AM by JaronK »

Callix

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Re: Calculating the attacks of this archer...
« Reply #5 on: December 05, 2008, 05:56:45 AM »
Wouldn't Roundabout Kick make this a 30% chance to generate 3 attacks, or 0.9 per swing? This would end up with 10 extra swings per base swing, for 528 attacks, and approximately 150 confirmed crits.

EDIT: I'm sure I've seen something that gives +1 to threat range after multipliers. Whatever that is on your heavy crossbow should work. If only I could remember what it was...
« Last Edit: December 05, 2008, 05:59:01 AM by Callix »
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JaronK

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Re: Calculating the attacks of this archer...
« Reply #6 on: December 05, 2008, 06:26:28 AM »
In the first build, Lightning Mace triggers 30% of the time, generating 2 new attacks (1 base, doubled by Splitting).  Roundabout Kick triggers 28.5% of the time (overlapping with Lighting Mace), generating 2 more attacks (again, 1 base, doubled by Splitting).  So our final probabilities are 28.5% chance of 4 new attacks, 1.5% chance of 2 new attacks.  The problem is that results in 1.17 new attacks per attack, and it seems likely that anything over 1 new attack per attack will yield infinite results.

So yeah, a 16-20 critical threat range is the target here, using the original build.  That gives us .975 new attacks per attack, which should result in huge numbers.

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Re: Calculating the attacks of this archer...
« Reply #7 on: December 05, 2008, 06:50:32 AM »
You're talking statistics. It still CAN go infinite. Even given a 5% to get another attack for free for every attack allows for this.
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woodenbandman

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Re: Calculating the attacks of this archer...
« Reply #8 on: December 05, 2008, 10:25:47 AM »
Use those bludgeoining arrows and make the crossbow an impact crossbow? Or use slashing arrows and make it keen.

EDIT: And that barbarian extra class feature, the one that gives you a +1 critical rating on any weapon you wield in rage. Just snag a few extra rages, somehow... You don't really need crossbow sniper, blind fight, or improved initiative, do you? problem would be getting TSS... You might have to go straight warblade on this one to make IL 17, like Warblade 13/Barbarian 7.

Also, it might not be at 7th level that you get it, in which case you're fucked.

ChristopherGroves

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Re: Calculating the attacks of this archer...
« Reply #9 on: December 05, 2008, 11:19:25 AM »
Hmmm ... no way you can do this with Warblade 20 is there?  With 2 more feats?

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Heliomance

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Re: Calculating the attacks of this archer...
« Reply #10 on: December 05, 2008, 11:31:57 AM »
You're talking statistics. It still CAN go infinite. Even given a 5% to get another attack for free for every attack allows for this.

No it can't. It can go arbitrarily high, but never infinite. The chain of natural 20s would always end eventually.

The_Mad_Linguist

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Re: Calculating the attacks of this archer...
« Reply #11 on: December 05, 2008, 11:38:13 AM »
You're talking statistics. It still CAN go infinite. Even given a 5% to get another attack for free for every attack allows for this.

No it can't. It can go arbitrarily high, but never infinite. The chain of natural 20s would always end eventually.

Only because we have a metagame constraint of "rerolling the same die over and over" can't be done, along with a filter based on the knowledge that it's far more probable for the die to be imperfect than to roll ten twenties in a roll.
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JaronK

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Re: Calculating the attacks of this archer...
« Reply #12 on: December 05, 2008, 04:15:12 PM »
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.

The Barbarian class feature looks possible... it's at level 7, but it's from Cityscape which I don't have.  Is it melee only, or during rage only, or something like that?   If we do that I can't use TSS or Raging Mongoose, but it might still be worthwhile.

But yeah, 16-20 critical range with Lightning Mace, Roundabout Kick, and Splitting gives us .975, which is as good as we're going to get... the trick is just to get that.

JaronK

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Re: Calculating the attacks of this archer...
« Reply #13 on: December 05, 2008, 04:42:44 PM »
Do I HAVE to explain probability again?  This is the EXACT SAME FUCKING QUESTION you asked way back.  I explained it to you back then with set theory approximations and it was valid then.  Random walks only occur if you're working one dimension of complexity lower (no pool).  Furthermore:

You asked average.  You have a chance of infinity.  I don't give a shit about how small that chance is.  With third grader math I can prove to you that any portion of infinity averaged with real numbers still yields infinity.

Change your question or change your numbers so you don't on average go forever.  Right now you have a very small chance NOT to get infinite attacks.  Drop improved crit and you'll drop into very large, but incalculable number off attacks (because you don't generate more attacks than you use).  Give me numbers to work with so that you won't get infinite attacks on average and ask for a number other than an average because any chance of infinity makes the average infinity.

QED.
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JaronK

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Re: Calculating the attacks of this archer...
« Reply #14 on: December 05, 2008, 05:00:18 PM »
Do I HAVE to explain probability again?  This is the EXACT SAME FUCKING QUESTION you asked way back.  I explained it to you back then with set theory approximations and it was valid then.  Random walks only occur if you're working one dimension of complexity lower (no pool).  Furthermore:

You asked average.  You have a chance of infinity.  I don't give a shit about how small that chance is.  With third grader math I can prove to you that any portion of infinity averaged with real numbers still yields infinity.

Go away.  You don't understand this level of math at all, especially infinity math.  You didn't explain a damn thing last time, other people did and you're trying to copy their work.   The second build I made has NO CHANCE to go to infinity.  Furthermore, as long as the number of attacks generated per attack is 1 or less, there is no chance of ever going infinite, but if it's higher than 1 it's got a very high chance to go infinite (more than average case) so your third grader math doesn't apply.

Quote
Change your question or change your numbers so you don't on average go forever.  Right now you have a very small chance NOT to get infinite attacks.  Drop improved crit and you'll drop into very large, but incalculable number off attacks (because you don't generate more attacks than you use).  Give me numbers to work with so that you won't get infinite attacks on average and ask for a number other than an average because any chance of infinity makes the average infinity.

Interesting note:  The second build, posted about 7 or so hours ago, has NO CHANCE to hit infinity.  Furthermore, dropping improved critical gets a VERY calculable number of extra attacks, and the number is not very large.  It is in fact lower than the second build I listed.  You clearly don't know what you're doing here, and just trying to copy other people's work.  If you'd read the second build I made you'd see that I put in the calculated attacks numbers already... the first post was made when I was quite sleepy and distracted due to a party going on outside. 

We've now moved on, as I've figured out the calculations a while ago.  At this point, the question is this:  how do we get a 16-20 critical threat range with a crossbow of some kind?  This will get a very large number of attacks without ever going infinite, since it actually does the 25% chance to critical that I originally thought I was getting, generating .975 attacks per attack to begin with.  The calculation becomes easy from there... sum .975^i for i=1 to infinite, then multiply that sum by the base number of attacks and there you go.  That was the formula I needed in the first post, including the calculation for how to get the .975 number.

So, to answer my own OP, the formula was this:

(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.

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Re: Calculating the attacks of this archer...
« Reply #15 on: December 05, 2008, 05:04:57 PM »
Go away.

What are you, five?  Get over yourself and go back to school.  Fuck, just wiki it.
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Re: Calculating the attacks of this archer...
« Reply #16 on: December 05, 2008, 05:21:39 PM »
I was wondering if I could get a explanation of the build?  I'm not familiar with how all the feats work with one another or their sources.
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JaronK

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Re: Calculating the attacks of this archer...
« Reply #17 on: December 05, 2008, 05:24:01 PM »
@Ubernoob:  Hey, you're the one who couldn't get the formula because you thought it was "incalculable."  What are you, a college freshman who thinks he knows everything?  Just because you can't figure it out doesn't mean the rest of us can't... and for the record I've already been through Calculus, Statistics, and the rest.  I majored in CS.

So, if you read the rest of this thread, you'd know the that the question is now "how do we get a 16-20 critical threat range."  Your little diatribe about how you'd already explained infinity math and probability and how it was incalculable was both wrong and off topic.

@Cantrip:  5% chance for each attack to generate a new one will never go infinite.  It has to get to the point where the average number of attacks generated by a given attack is greater than 1 for it to go infinite.  My first build sadly did that (1.17 attacks per attack) but as long as we keep the number generated at 1 or less we're fine.

I lack Cityscape though so I'm not sure about the Barbarian thing, but there's potencial there.

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JaronK

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Re: Calculating the attacks of this archer...
« Reply #18 on: December 05, 2008, 05:30:02 PM »
I was wondering if I could get a explanation of the build?  I'm not familiar with how all the feats work with one another or their sources.

First of all, there are some useless feats in there (like Blindfight) because of the Warblade bonus feats.

The main principle is this:  Lightning Mace gives you an extra attack any time you threaten a critical hit with a light mace.  Roundabout Kick gives you an extra attack every time you confirm a critical hit with an unarmed strike.  Splitting makes every attack count as two attacks.  The Aptitude enchantment makes the weapon it's on always count for all feats that work for only one weapon, allowing you to count Great Crossbows as light maces or unarmed strikes for the purpose of those feats, and letting them work with Hand Crossbow Mastery, which lets you reload as a free action.  Meanwhile, Blood in the Water gives you a +1 to hit and +1 to damage for every critical hit, which with this many attacks is awesome.

From there, you just want lots of base attacks, so the TWF line gives 3 attacks, Rapid Shot gives 1, and then Raging Mongoose gives +4 attacks.  Now bust out with Time Stands Still (double attacks) and Splitting (double attacks), and you've got 48 base shots to work with.

The net result of this in the original build is that you get infinite attacks, because I was off on my critical threat chance.  So, if we can get a critical threat range of 16-20, we'll get a huge number of attacks (that I put together a formula for).  That's the basic idea.  If you want something that's workable and non infinite right now, just use the second build, which drops Roundabout Kick, or switch to Heavy Crossbows, which have a worse critical threat range.  Either way just gives you high damage without it being too insane (in the 100-200 attacks range).

JaronK

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Re: Calculating the attacks of this archer...
« Reply #19 on: December 05, 2008, 06:09:15 PM »


At least this time I'm sure he doesn't go infinite, nor can he, but how many shots is this?

JaronK

I can't believe you gave yourself all the necessary information, and then proceeded to not actually do any math to answer your own question.

I mean, what the hell? If you had done the math, and then asked for people to look over it, I would understand a post, but posting to have someone else do the math looks like you either can't, or don't want to, do the work yourself.

If you really wanted to kick Ubernoob, you should have done the actual math. Right now he's telling you that you don't understand it because you can't do it.

Since you're not doing the math, but claiming that you do understand it, you look pretty foolish. You're comitting a logic failure when you say that you can do something, then don't do it. Likewise when someone says "Pics or it didn't happen" and you say "I don't need pics to prove that it happened", you won't look like you're right. You could be right, but it does not look likely.

So just do the math and let the people reading this thread math-check it. It will nip any more pointless back and forth in the bud.
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