Highest Possible Crit Range?

[SparkMandriller]

Will you please learn what the word infinite means?

[term1nally s1ck]

Infinity (symbolically represented by ∞) is a concept in mathematics and philosophy that refers to a quantity without bound or end.

The attacks have a chance of having no end.

[OracleofWuffing]

Psychic weapon master and disciple of dispater can't ever stack by the books- one requires a crystal weapon, and the other an iron/steel one.

Well... Iron crystals do exist in catgirl-killing land... I'd imagine such a weapon wouldn't last that long, though.

[Signmaker]

Infinity (symbolically represented by ∞) is a concept in mathematics and philosophy that refers to a quantity without bound or end.

The attacks have a chance of having no end.

Put it this way:

For any given interval of attacks, there is a probability associated with it of the attack stream ending right then and there. Maybe you have it absurdedly low.

As the limit tends to an infinite number of attacks, the probability of a long enough stream of '1's tends to 1. Which means that it is, in fact, NOT an infinite amount of attacks. Just an arbitrarily high amount. Therein lies the difference between finite and infinite.

[Claudius Maximus]

Also, if 3.0 stuff is allowed, I believe that bladed gauntlets exist which have a base crit range of 17-20.

An Erratum changed this to 19-20.

[term1nally s1ck]

Put it this way:

For any given interval of attacks, there is a probability associated with it of the attack stream ending right then and there. Maybe you have it absurdedly low.

As the limit tends to an infinite number of attacks, the probability of a long enough stream of '1's tends to 1. Which means that it is, in fact, NOT an infinite amount of attacks. Just an arbitrarily high amount. Therein lies the difference between finite and infinite.

There's a chance that I hit with exactly 0 attacks.
There's a chance that I hit with exactly 1 attack.
There's a chance that I hit with exactly 2 attacks.
There's a chance that I hit with exactly 5 attacks.
There's a chance that I hit with exactly 34676456 attacks.

If you add all those chances together for every number that exists, you get a number which is LESS than 1, for the best builds. Meaning there is a positive chance for me to attack a number of times that is not any writeable number, and exceeds any number you care to name. What do you call that, except an infinite number of attacks?

[Signmaker]

There's a chance that I hit with exactly 0 attacks.
There's a chance that I hit with exactly 1 attack.
There's a chance that I hit with exactly 2 attacks.
There's a chance that I hit with exactly 5 attacks.
There's a chance that I hit with exactly 34676456 attacks.

If you add all those chances together for every number that exists, you get a number which is LESS than 1, for the best builds. Meaning there is a positive chance for me to attack a number of times that is not any writeable number, and exceeds any number you care to name. What do you call that, except an infinite number of attacks?

Partially incorrect. For the natural numbers, the sum of the probabilities adds to one if there exists a chance of failure (fumbling), and zero if there does not exist a chance of failure (removing the ability to fumble, while recieving more attacks = an attack stream that doesn't stop).

[SparkMandriller]

A very high number, but still not infinite. If there's even the smallest chance that your attacks will stop at some point, then your attacks will stop at some point. Guaranteed.

[Fiery Diamond]

Remember, for example, that 1/3 = .33333333333333333333333333333333333...,
2/3 = .66666666666666666666666666666666666666...,
and 3/3 = .99999999999999999999999999999999999999999..., which means that since 3/3 = 1, .99999999999999999999999999999999999999999... = 1. This is why if there is a chance of failure the probability of failure will reach 1 as the number of times reaches infinity - because math is confusing like that.

[quiet1mi]

all that work... then the Dm throws nothing but crit immune zombies.... this would not be funny except that it is true that this would happen...

[Zeful]

What do you call that, except an infinite number of attacks?

Arbitrarily high. There are legitimate inifinite loops in D&D, but since the game deals with real numbers, the loop has to be non-terminating. Pun-pun, the greatest rules abuse in the game, does not have infinite ability scores.

Even if you have only a 5% (20/100=5) chance of any attack not generating another attack, eventually you will run out of attacks because 1/20 attacks will fail statistically. Eventually a long string of 1s will occur, whether this is part of the third iteration or after Graham's Number of iterations is irrelevant. Statistically you will roll 1 enough times to end the sequence, eventually. Therefore it's not infinite.

[Eldariel]

all that work... then the Dm throws nothing but crit immune zombies.... this would not be funny except that it is true that this would happen...

With insane numbers of attacks (that doesn't depend on opps being Crittable), it doesn't really matter what opponents the DM throws.

[Saintheart]

With insane numbers of attacks (that doesn't depend on opps being Crittable), it doesn't really matter what opponents the DM throws.

It does if the DM gives your enemy appallingly high Concealment chances, á la the way a lot of optimised wizards create their armor. I'd understood (and someone can correct me if I've got it wrong) that Concealment chance cuts across everything bar a natural 20, including critical hit damage. Assuming the insane number of attacks depends on a continual chain of guaranteed hits, I would've thought most decent Concealment applications have a 40% chance of shutting down this build.

[term1nally s1ck]

I'm going to avoid typing out the full calculation I used, because it's hellish. If you want to continue arguing, I'll type it up, but tbh, you do not want to try and wrap you're brain around it. I'm in my second year studying maths at Cambridge uni, and it took a lot of tricks I've learned and a coupla hours of calculation. (Yes, I've seen the build before, it's on WotC optimisation board, and there's one on this board too...both use TWF kukris though.)

Here's a slightly simpler way of explaining it.

Every time you make an attack, if there's a 3/4 chance of critting and hitting, (hit+crit on a 6) you (on average) spawn 21/16 attacks.

Then, when you make your 21/16 attacks, you multiply the expected number of attacks by 21/16 to get the new number.

The expected number of attacks on your nth 'round' of attacks is (21/16)^n

And the chance of all of them missing is (1/4)^((21/16)^n)

We have to multiply by the probability that the solution hasn't failed yet

And then the sum of those is equal to just under 1/2, nowhere near 1.

The full solution relies on no less than 4 partial sums and 1 sum to infinity. You REALLY don't want to see this. I can provide it if you wish, but I suggest you don't.


EDIT: @Zeful,

The build I'm considering not only continues to generate attacks, but generates MORE attacks as time goes by. It becomes less and less probable for the sequence to end faster than we gain in chances due to sheer numbers of attacks.

[SartheKobold]

With insane numbers of attacks (that doesn't depend on opps being Crittable), it doesn't really matter what opponents the DM throws.

He's got a good point. You can still Crit against things immune to Critical Hits/Percision Damage. You still Crit, and can still confirm that it Crits, it just doesn't take the extra damage...

I seem to recall, probabbly from 3.0, of the psionic powers Embed Weapon which would let you graft two weapons onto your hands. Then manifest Duodimensional Hands to cheese the Crit-Range of whatever you're using... Forgive me if it goes pear-shaped, but I remember it working as such. No idea how it stacks...

[quiet1mi]

So the build is defeated by a smokestick?

[term1nally s1ck]

Yeah, concealment tends to shut down the build, but it'll still get a fair few atttacks off against anything with concealment.

Interesting question....if you crit against a mirror image (as the spell), would you get an extra attack?

And since nobody answered, I'll ask again, do you roll once or twice to attack with a weapon with the splitting property?

[Jack Mann]

There's actually another reason it doesn't give you truly infinite attacks. Let's say you average 15 points of damage per hit (not real high, but you've sunk your resources into an absurdly large crit range). You're fighting a Cauchemar. The Cauchemar has 172 hit points. After around twelve hits, you're probably going to stop.

Unless you want to keep beating a dead horse, of course.

[sofawall]

Wouldn't Aptitude get past this?

No, actually. Aptitude is feats, and those are classes.

I know it was a page back, but many folk don't seem to know that. Just wanted to get it out there.

[term1nally s1ck]

There's actually another reason it doesn't give you truly infinite attacks. Let's say you average 15 points of damage per hit (not real high, but you've sunk your resources into an absurdly large crit range). You're fighting a Cauchemar. The Cauchemar has 172 hit points. After around twelve hits, you're probably going to stop.

Unless you want to keep beating a dead horse, of course.

Well, I can think of a couple of scenarios it would be effective.

You have a weapon which deals negative levels somehow and want to buff an undead to ridiculous levels. (you need neg energy damage, or the undead to have DR high enough to not take much damage from normal attacks.)

The Tarrasque. This build can literally put the Tarrasque down, to the extent that it won't get back up for BILLIONS of years.

Can you crit when attacking an object? If so, this build can break the earth with enough time

[sofawall]

Well, I can think of a couple of scenarios it would be effective.

You have a weapon which deals negative levels somehow and want to buff an undead to ridiculous levels. (you need neg energy damage, or the undead to have DR high enough to not take much damage from normal attacks.)

The Tarrasque. This build can literally put the Tarrasque down, to the extent that it won't get back up for BILLIONS of years.

Can you crit when attacking an object? If so, this build can break the earth with enough time

Negative levels don't do anything to undead. Enervation just so happens to add temporary hitpoints.

[ex cathedra]

It does if the DM gives your enemy appallingly high Concealment chances, á la the way a lot of optimised wizards create their armor. I'd understood (and someone can correct me if I've got it wrong) that Concealment chance cuts across everything bar a natural 20, including critical hit damage. Assuming the insane number of attacks depends on a continual chain of guaranteed hits, I would've thought most decent Concealment applications have a 40% chance of shutting down this build.

I'm fairly sure that concealment negates natural 20s. Additionally, I'm not sure if concealment stops you from rolling a critical threat. This build relies on rolling crit threats, not hitting or critting. It may be entirely possible to effectively ignore concealment, if it's only negating 40% of your nigh-infinite number of attacks.

[sofawall]

I'm fairly sure that concealment negates natural 20s. Additionally, I'm not sure if concealment stops you from rolling a critical threat. This build relies on rolling crit threats, not hitting or critting. It may be entirely possible to effectively ignore concealment, if it's only negating 40% of your nigh-infinite number of attacks.

It still makes it far more likely to end abruptly.

[Roderick_BR]

The paladin spell Bless Weapon makes all threats become auto-crits, but doesn't work with weapons that already have some critical enhancing ability.
But I think that one of the abilities of the Fist of Raziel PrC is to gain this auto confirm against evil creatures when using a smite. Unlike the Bless Weapon spell, it does stack with others critical-enhancing abilities. So, if you can afford a level of paladin and a level of Fist of Raziel, you could at least have an auto crit against some creatures once or twice a day.

edit:

Can you crit when attacking an object? If so, this build can break the earth with enough time

No, because the earth (or whatever planet) is an object, therefore immune to critical hits. There are better ways to destroy the world in D&D, though...

[term1nally s1ck]

Just being immune to crits isn't enough, they still threaten and confirm, just don't do extra damage, so they do proc extra attacks. Personally, I think destroying the planet as a standard action at mid-teens ( I think....we don't need too much warblade to get the stance we want and the feats...how much weaponmaster do we need?) in level seems pretty good tbh.

I don't think our weapons have any crit enhancing ability....Improved critical, DoD and weaponmaster levels are all that are used.

@sofawall: Concealment does indeed cause a problem, but if you have enough + to hits from blood on the water, and if you have a good crit threat range, the build can still go infinite vs concealment. As usual, though, true seeing would be very nice to negate some of that miss chance.

I'm sad I can't have the mega-undead...it looked so fun but guess I forgot to check that one properly, I just went by memory, since enervation is the only time I usually come across neg levels in most games.

[ex cathedra]

Just being immune to crits isn't enough, they still threaten and confirm, just don't do extra damage, so they do proc extra attacks. Personally, I think destroying the planet as a standard action at mid-teens ( I think....we don't need too much warblade to get the stance we want and the feats...how much weaponmaster do we need?) in level seems pretty good tbh.

Strongheart Halfling Crusaders with feycraft daggers and a reroll device do it at eleven, if memory serves.

[sofawall]

@sofawall: Concealment does indeed cause a problem, but if you have enough + to hits from blood on the water, and if you have a good crit threat range, the build can still go infinite vs concealment. As usual, though, true seeing would be very nice to negate some of that miss chance.

This build cannot go infinite even with no concealment, unless I;m missing something.

Is there a way to get infinite rerolls or ways to treat nat 1s as something else, even if just for one round?

Also, why do you even bring up to-hit in a discussion about concealment? +10065 to-hit against -10 AC will still miss 50% of the time if the person with -10 AC is blinking.

[Lord of Syntax]

There is a feat from one of the completes that lets rogues treat nat 1s as nat 20s

[sofawall]

There is a feat from one of the completes that lets rogues treat nat 1s as nat 20s

Is that Better Lucky Than Good? Because I don't think that works.

[term1nally s1ck]

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.