Highest Possible Crit Range?

[sofawall]

Because if I only hit on 11s, and you're blinking, I only hit 1/4 of the time.

And yes, the build can go infinite, I spent a while writing out some of the maths to prove it. the 7-20 threat range which can hit on a 2 has a 60/133 chance to never run out of attacks, with each attack it makes. It doesn't hit with every attack, and it's not a guarantee that it'll go infinite....but if you get 3 attacks, and you hit with a 2 on all of them (Blood on the Water, hit rats. a lot.) then you get an 83.5% chance to go infinite that turn.

@aethernox is that the d2 trick? I love that trick, it's just funny.

Halfling: I poke him with my tiny dagger (basically a letter opener

DM: The impact completely destroys him, and nothing is left.

You do not understand math. EDIT:Or at least that math.

As people have said, if there is any chance, any chance of not going infinite, if there is any chance of rolling enough natural ones to break the chain, as you get closer and closer to infinity, the chance of you failing to hit infinity approaches one. Therefore, as you hit infinity, you screw up and miss, thus resulting in a non-infinite result.

Yay high-school math.

[SparkMandriller]

Watch out dude, he's gonna use his Cambridge maths powers on you. They take hours to power up, they must be hugely destructive. Like Goku.

[AirGuitarGod32]

Has anyone thought of using a Disciple of Dispater with an Iron Aptitude Kopesh?

[ghashxx]

Because if I only hit on 11s, and you're blinking, I only hit 1/4 of the time.

And yes, the build can go infinite, I spent a while writing out some of the maths to prove it. the 7-20 threat range which can hit on a 2 has a 60/133 chance to never run out of attacks, with each attack it makes. It doesn't hit with every attack, and it's not a guarantee that it'll go infinite....but if you get 3 attacks, and you hit with a 2 on all of them (Blood on the Water, hit rats. a lot.) then you get an 83.5% chance to go infinite that turn.

@aethernox is that the d2 trick? I love that trick, it's just funny.

Halfling: I poke him with my tiny dagger (basically a letter opener

DM: The impact completely destroys him, and nothing is left.

Unless there's something terribly going wrong here in the real world then you're eventually going to roll a one, missing completely and not even threatening to crit, thereby ending the chain. If there is even the ittiest bittiest tiniest chance of ever failing then it's not infinite. What you're claiming is like saying that every time I successfully throw a basketball through a hoop that my chances of succeeding next time increases exponentially. But so long as I ever at any point in time eternal have a chance of not hitting, then eventually I will miss meaning that my chain of hits will end.

[ex cathedra]

I think the part that people are having trouble grasping is that, as the chain goes on, it progressively becomes more likely to generate attacks to what seems like an infinite amount. However, any amount that is infinite must go through an infinite set of numbers. This includes natural 1s. This loop is not literally infinite, but it's near enough as to not matter.

[SparkMandriller]

I don't think that anyone's arguing that. They're just arguing that it's not infinite. Because it's not.

[ex cathedra]

@aethernox is that the d2 trick? I love that trick, it's just funny.

Halfling: I poke him with my tiny dagger (basically a letter opener

DM: The impact completely destroys him, and nothing is left.

Indeed it is.

Any 1d2 weapon + Aura of Chaos + something like Imbued Healing: Luck.

[Set]

So the build is defeated by a smokestick?

Or DR equal to your weapons max critical damage.

Ping, pah-ping-ping, pingity-ping!

[ex cathedra]

Or DR equal to your weapons max critical damage.

Ping, pah-ping-ping, pingity-ping!

Blood in the Water has already been mentioned; it grants you a cumulative +1 attack and damage each time you crit. So your weapon's base damage quickly becomes moot.

[lvl 1 sharnian]

Doesn't Dragon Ascendant from Draconomicon give 1 divine rank?

Just play a Dragonwrought Kobold and at epic levels, they'll be able to get infinite

[Zeful]

Indeed it is.

Any 1d2 weapon + Aura of Chaos + something like Imbued Healing: Luck.

Does Imbued Healing: Luck work on attack rolls or just damage rolls*? Cause if it's possible to get at least a 2-20 critical, then it's possible to go infinite by simply ignoring 1s.

*I'm pretty sure it works only on damage rolls, but it's nice to be sure.

[Jack Mann]

@aethernox is that the d2 trick? I love that trick, it's just funny.

Halfling: I poke him with my tiny dagger (basically a letter opener

DM: The impact completely destroys him, and nothing is left.

Essentially, you can now make a tonberry in D&D.

"DOINK!"

[ex cathedra]

I do not believe so, no.

[term1nally s1ck]

Aether has it.

The basic reason the build tends to go infinite is that it generates attacks faster than basic probability can generate nat 1s (or merely non-crits) to stop the trick. The chances that the build stops are actually higher EARLIER in the attack chain, just because by the 9th-10th attack, you're likely to have 3-4 attacks to use, and as you get further and further through the attack sequence, you'll have more and more attacks.


As an example, lets use the simpler crits and hits on 6+ to have a look.

If I want to get 10 nat 1s in a row, the expected number of rolls I need to make are 20^10, or 1.02400 * 10^13. Meanwhile, after that many attacks, I expect to have 4.16737342 * 10^23 attacks....which is so far above 10 I can't even explain that. Nearly all the chances for the attack loop to stop happen early on....there's a 1/4 chance of the first attack missing, but only about a .2 chance of it stopping ever if the first attack crits, more than halving the miss chance.

Of course, having thought about it, I found a very pretty and simple way to calculate the probability of a given build going infinite, but it requires you to know that it's infinite in the first place. I rigorously proved this by looking at the chances of failure, but you seem to not want to accept this.

How about this one.

The infinite sum 1/2 + 1/4 + 1/8 + 1/16 + 1/32 ........ is precisely equal to 1. It is a geometric series with a constant factor of 1/2.

The series of 'miss chances' I calculated earlier ((1/4)^((21/16)^n))

starts at 0 with 1/4. When n increases by 1, you multiply the 'miss chance' by (1/4)^(21/16), which is smaller than 1/2.

The miss chances at each step then, not only start smaller than the first infinite sum, term-by-term, but get smaller faster. The infinite sum of the 'miss chances', therefore, is AT LEAST 1/4 below 1. (The first two terms are 1/4 apart)
I'm taking miss chances here to mean if I use every attack I have currently generated, and miss with every single one.

This means that there is a finite chance that the number of attacks I make is NOT A FINITE NUMBER. Non-finite is pretty much the definition of infinity mathematically.


EDIT: Oh, and Sofawall...High school math teaches you precisely NOTHING about dealing with infinities. I couldn't do it til I took Further Maths at A-Level, and even then I was only looking at very specific cases, and without any real understanding. Yes the amount of numbers and chains of nat 1s I go through gets arbitrarily high as you approach infinity, but the number of attacks I make gets MUCH MUCH higher, much much faster, so I can weather them easily.

Here's another trick that might help....If I get to the point where it's likely for me to roll n 1s in a row, it's also equally likely I roll the same number of nat 20s in a row, which would completely cancel the 1s out.

[sofawall]

Infinity does not work like normal numbers, though...

If something can happen, in an infinite series of probabilities, it will. Is it possible to roll enough ones to end the chain? Yes. It will, therefore, happen.

True, it becomes less and less likely it will happen as time goes on. However, all that does is make the chain more and more likely to be really really mind-bogglingly large before it ends.

Watch out dude, he's gonna use his Cambridge maths powers on you. They take hours to power up, they must be hugely destructive. Like Goku.

I bow to Paul Muad'dib.

[term1nally s1ck]

No, it doesn't, which is why it's so hard to deal with. In fact, you cannot consider what happens at infinity, but what happens as things approach infinity. In my case, I've proven that through all the numbers on the number line, there is only a finite chance of me attacking a certain number of times.

I'm going to ask you a question now. If I add up the probability of attacking n times, for all n that exist on the number line (the infinite sum), I get 4/9 for the total. I'd like you to tell me now, if the build will always finish it's attacking at some point, how many attacks do I make for the remaining 5/9? Every natural number from 1 to 45762342454687564645, (And 0), and every number higher still is included in the 4/9, so your answer cannot be any of those, so how many attacks am I making?

[lvl 1 sharnian]

Theorectical optimization turns to theorectical mathmatics? I'm dreadin college now

[tcrudisi]

Theorectical optimization turns to theorectical mathmatics? I'm dreadin college now

Meh, just avoid Calculus and Advanced Mythology and you should be fine.

[Heliomance]

In simple terms, the reason why this has a chance to go infinite is that it's not a fixed number of natural 1s needed to end the chain. As the number of attacks you make tends to infinity, the number of consecutive natural 1s you need to roll to end it also tends to infinity. Yes, on your way to infinity you will roll every conceivable number of consecutive natural 1s at some point, but the number you need to roll is ever increasing, and so there's a pretty good chance that however many you roll in a row, at the point at which you roll it it won't be enough.

[Fortuna]

Hmmmm. If I'm right (and I am never right), then you need to be able to show a conceptual point of some kind (not neccesarily a point on the number line, just a point) at which the odds of your string of natural ones are infinitesimal. Is that correct? If you can show such a point, then doesn't the whole thing end at infinity (specifically, at aleph-0) when such a ratio loses meaning and the two are equal? And, assuming that we ignore the gross stupidity that this post has no doubt shown so far, does that not mean that it is a terminating sequence which nevertheless sums to infinity?

[Zaq]

Arcane Duelist's False Keen specifically does not stack with either Improved Critical or keen.

Are we reading the same Arcane Duelist?

False Keenness (Ex): To create the idea that she is more effective than she really is, the arcane duelist can make her chosen melee weapon keen once per day per arcane duelist level. To activate the keen effect, she must subtract the weapon's normal threat range for critical hits from her attack bonus. For example, if the arcane duelist wields a rapier, she must subtract 3 from her attack bonus, since the rapier has a threat range of 18-20, to make it keen. The keen effect lasts for 1 round per arcane duelist level, and it does not stack with the keen edge spell or other magical effects that make a weapon keen. The ability does stack with the increased threat range granted by the Improved Critical feat and by a keen magic weapon. If the arcane duelist uses this power in conjunction with the dexterous attack power, the damage dealt by a critical hit is reduced by the weapon's critical multiplier. Thus, the arcane duelist wielding a rapier and using dexterous attack to reduce the damage by 4 on her rapier has it reduced by 12 if she scores a critical hit using this power. The weapon must still do a minimum 1 point of damage.

Emphasis added. It doesn't stack with keen edge, but it DOES stack with Improved Crit and an actual Keen weapon. Confusing, but that's WotC for you.

[lvl 1 sharnian]

Thank you my friend, I believe it's now 3-20 Crit Range for either Psionic or regular version

[Curmudgeon]

Are we reading the same Arcane Duelist?

Yes, we're reading the same class description. What you're not reading are

• the date of the Arcane Duelist (02/24/2003)
• the Primary Sources errata rule

  Errata Rule: Primary Sources
  
  When you find a disagreement between two D&D® rules sources, unless an official errata file says otherwise, the primary source is correct. One example of a primary/secondary source is text taking precedence over a table entry. An individual spell description takes precedence when the short description in the beginning of the spells chapter disagrees.
  
  Another example of primary vs. secondary sources involves book and topic precedence. The Player's Handbook, for example, gives all the rules for playing the game, for playing PC races, and for using base class descriptions. If you find something on one of those topics from the Dungeon Master's Guide or the Monster Manual that disagrees with the Player's Handbook, you should assume the Player's Handbook is the primary source. The Dungeon Master's Guide is the primary source for topics such as magic item descriptions, special material construction rules, and so on. The Monster Manual is the primary source for monster descriptions, templates, and supernatural, extraordinary, and spell-like abilities.

The primary source for the Improved Critical feat is the 3.5 Player's Handbook, which came out in 2003 July, after the Arcane Duelist (a 3.0 prestige class).

This effect doesn’t stack with any other effect that expands the threat range of a weapon.

The primary source for the keen weapon special ability is the 3.5 Dungeon Master's Guide, which also came out in 2003 July.

This benefit doesn’t stack with any other effect that expands the threat range of a weapon (such as the keen edge spell or the Improved Critical feat).

WotC's official rule is that, since both of these disagree with the Arcane Duelist's False Keenness, and they're from primary sources, they're both right. The Arcane Duelist's False Keen specifically does not stack with either Improved Critical or keen.

[Eldariel]

Except specific trumps general, Arcane Duelist specifically stacks with both so it works. Improved Critical and Keen have just general line "stacks with nothing", so the "except"-abilities function just fine.

It doesn't matter that the said limitations were added in the 3.5 revision, no errata has been applied to Arcane Duelist so its ability still functions as written and thus trumps the limitation on Imp. Crit and Keen (even though there was none by the time of the printing of the class).

[Emmerask]

Not actually important to hit, as Lightning Maces triggers an extra attack everytime it threatens a critical

Sorry but you are wrong there

from the srd:
Critical Hits

Sometimes your threat range is greater than 20. That is, you can score a threat on a lower number. In such cases, a roll of lower than 20 is not an automatic hit. Any attack roll that doesn’t result in a hit is not a threat

So you have to actually hit to threaten a critical... it is important to hit ;)

[lvl 1 sharnian]

Don't even bring in Disciple of Dispater or Weapon Master or Psychic Weapon or Streetfighter Barbarian or anything like that (all 3.0) which all state that they stack with improved critical

[Curmudgeon]

Except specific trumps general ...
It doesn't matter that the said limitations were added in the 3.5 revision

The game is D&D, version 3.5. Wizards of the Coast has set up rules for how material that differs from the 3.5 primary sources is handled. Page 4 of the 3.5 Dungeon Master's Guide says:

This is an upgrade of the d20 System, not a new edition of the game. This revision is compatible with all existing products, and those products can be used with the revision with only minor adjustments.

The core rules say that there will need to be minor adjustments to incorporate 3.0 material. The primary sources errata rule specifies how to make those minor adjustments in the case where there's a disagreement.

This isn't a case of there being a general 3.5 rule and a specific exception to that rule. This is a case where the general rules used to be different and then were changed. (That is, Improved Critical and keen used to stack in 3.0.) Most 3.0 content doesn't have specific update information, so you follow the required 3.5 rules for how to make the necessary adjustments to that older material.

[Eldariel]

The game is D&D, version 3.5. Wizards of the Coast has set up rules for how material that differs from the 3.5 primary sources is handled. Page 4 of the 3.5 Dungeon Master's Guide says: The core rules say that there will need to be minor adjustments to incorporate 3.0 material. The primary sources errata rule specifies how to make those minor adjustments in the case where there's a disagreement.

This isn't a case of there being a general 3.5 rule and a specific exception to that rule. This is a case where the general rules used to be different and then were changed. (That is, Improved Critical and keen used to stack in 3.0.) Most 3.0 content doesn't have specific update information, so you follow the required 3.5 rules for how to make the necessary adjustments to that older material.

Indeed, but since the only necessary adjustments are changing obsolete skills and DR system, Arcane Duelist remains untouched without an update or errata. The critical feats themselves changed, but that system is still identical to the 3.0 system and as such, 3.0 classes utilizing the system work as they used to. Same goes for Weapon Master, Disciple of Dispater and so on. They all have specific exceptions (now with the 3.5 rules) that enables them to function.

[Curmudgeon]

Indeed, but since the only necessary adjustments are changing obsolete skills and DR system

That argument doesn't hold water. It's also necessary to change a bunch of other things to work with 3.5 rules. One example is 3.0 weapon sizes, where the rules are quite different in 3.5. Another example is that things that increase threat range don't stack any more. Those minor adjustment are necessary, too.

[The Random NPC]

Do not argue RAW with Curmudgeon, he is always right.