Is there A Critfisher handbook?

[lylsyly]

I am in the process of building a critfisher and my googlefu is not turning one up, but I could have sworn I saw one.

Or maybe a thread someone has a link to?

Thanks in advance because I know I will get an answer ;)

(breaks over, back to the table)

[GilesTheCleric]

I think it boils down to "be evil, play Disciple of Dispater, and get a Kaorti weapon. Pray GM doesn't use their power to update 3.0 materials as they see fit to update DoD's crit rules to the default 3.5 rules".

[Bakkan]

Add Lightning Maces and Aptitude Kukris as desired.

To directly answer the question in the OP, I don't know of any such guide. I think it could be useful as there are lots of ways to add rider effects to cross and improve them in other ways.

[lylsyly]

@Giles: Can't play evil so I will going the Kensai Weapon Master route to get that bonus. DM is going to allow me a scabbard of the paladin spell "bless weapon"(3/day auto confirm crit against evil), an idea I found on stack exchange.

@Bakkan: Probably Kukri but still considering Falchion

I am also looking at "fist of raziel" PRC for auto confirming crits

I will be using Dvati (testing the interesting abilities they have when both are flanking the same opponent) as the race and the DM has agreed to giving me MAX hit points since they have to split them. I have two weeks to put it all together. One thing I have noticed is that both the PRC entries are feat intensive.

I also have to look at Psychic Weapon Master. SO much reading, so little time ;)

Thanks folks

[Thurbane]

Just a side-note: Disciple of Dispater ability won't work with Kaorti weapons, as they are no longer metal/iron.

[lylsyly]

which is okay 'cuz I can't play evil anyhoo.

currently looking at Dvati (Draconic) may buy off +2 LA
THF Falchion
Martial Rogue 2/Fighter 4/Kensai (OA version)10/Fighter +4
(doing 2 levels of Martial rogue before fighter let's me sneak in an extra feet (smelly, I know) and allows me some extra skill point/class skills at the start)

1st: Exotic Weapon Proficiency (Kaorti Falchion)
Flaw (Shaky): Weapon Focus (Kaorti Falchion)
Flaw (Pathetic): Improved Critical (crit range 15-20X2)
Bonus: Power Attack
Bonus: Dodge
3rd: Mobility
Bonus: Combat Expertise
Bonus: Combat Reflexes
6th: Whirlwind Attack
Bonus: Weapon Specialization (Kaorti Falchion)
Kensai Ki Damage (1/day/level)
Kensai Increased Multiplier (1/day) Crit Now 15-20X3
9th: Greater Weapon Focus (Kaorti Falchion)
Kensai Superior Weapon Focus (+1 to hit)
Kensai Increased Multiplier (2/day) Crit Now 15-20X3
Kensai Superior Combat Reflexes (AoO/round = DEX + WIS Mods)
12th: Greater Weapon Specialization (Kaorti Falchion)
Kensai Increased Multiplier (3/day) Crit Now 15-20X3
Kensai Ki Critical (Crit range now 13-20X3)
Kensai Increased Multiplier (4/day) Crit Now 13-20X3K
Kensai Ki Whirlwind Attack (now a standard action)
15th: ?????
Kensai: Increased Multiplier (5/day) Crit Now 13-20X3
18th: ?????
Bonus: ?????
Bonus: ?????

[Quertus]

@Bakkan: Probably Kukri but still considering Falchion



Add Lightning Maces and Aptitude Kukris as desired.

AFB, but, IIRC, there are three magic feats. One says, "with weapon foo, if you threaten a crit, gain an extra attack". The second says, "with weapon bar, if you confirm a crit, take an extra attack". The last says, "for any weapon-specific feat, treat the text of that feat as though it referred to your chosen weapon, sna". With just a few more tricks, one can get of an infinite number of attacks. I believe that is what is being referenced here. yes, I realize most programmers use "baz" instead of "sna" for their third variable. Sue me

[Quertus]

which is okay 'cuz I can't play evil anyhoo.

currently looking at Dvati (Draconic) may buy off +2 LA
THF Falchion
Martial Rogue 2/Fighter 4/Kensai (OA version)10/Fighter +4
(doing 2 levels of Martial rogue before fighter let's me sneak in an extra feet (smelly, I know) and allows me some extra skill point/class skills at the start)

1st: Exotic Weapon Proficiency (Kaorti Falchion)
Flaw (Shaky): Weapon Focus (Kaorti Falchion)
Flaw (Pathetic): Improved Critical (crit range 15-20X4)
Bonus: Power Attack
Bonus: Dodge
3rd: Mobility
Bonus: Combat Expertise
Bonus: Combat Reflexes
6th: Whirlwind Attack
Bonus: Weapon Specialization (Kaorti Falchion)
Kensai Ki Damage (1/day/level)
Kensai Increased Multiplier (1/day) Crit Now 15-20X5
9th: Greater Weapon Focus (Kaorti Falchion)
Kensai Superior Weapon Focus (+1 to hit)
Kensai Increased Multiplier (2/day) Crit Now 15-20X5
Kensai Superior Combat Reflexes (AoO/round = DEX + WIS Mods)
12th: Greater Weapon Specialization (Kaorti Falchion)
Kensai Increased Multiplier (3/day) Crit Now 15-20X3
Kensai Ki Critical (Crit range now 13-20X5)
Kensai Increased Multiplier (4/day) Crit Now 13-20X5
Kensai Ki Whirlwind Attack (now a standard action)
15th: ?????
Kensai: Increased Multiplier (5/day) Crit Now 13-20X5
18th: ?????
Bonus: ?????
Bonus: ?????

AFB, but... FTFY?

EDIT: also, look into those three feats. They're golden.

[Kelb_Panthera]

AFB, but, IIRC, there are three magic feats. One says, "with weapon foo, if you threaten a crit, gain an extra attack". The second says, "with weapon bar, if you confirm a crit, take an extra attack". The last says, "for any weapon-specific feat, treat the text of that feat as though it referred to your chosen weapon, sna". With just a few more tricks, one can get of an infinite number of attacks. I believe that is what is being referenced here. yes, I realize most programmers use "baz" instead of "sna" for their third variable. Sue me

Nigh-infinite. Not quite actually infinite. /pedant

[Dayaz]

AFB, but, IIRC, there are three magic feats. One says, "with weapon foo, if you threaten a crit, gain an extra attack". The second says, "with weapon bar, if you confirm a crit, take an extra attack". The last says, "for any weapon-specific feat, treat the text of that feat as though it referred to your chosen weapon, sna". With just a few more tricks, one can get of an infinite number of attacks. I believe that is what is being referenced here. yes, I realize most programmers use "baz" instead of "sna" for their third variable. Sue me

if you can find those feat when you get the books, I'd also like to know them. I might be playing a Kukri fighter soon so it would be a helpful thing

[J-H]

the last says, "for any weapon-specific feat, treat the text of that feat as though it referred to your chosen weapon
This one is a Warblade (ToB) class feature. Warblades get several high-level maneuvers that give you extra attacks (Time Stands Still, Avalanche of Blades) and they have access to the very important (for crit fishers) Blood in the Water stance (+1 hit & damage for every crit that lands, stacking indefinitely and lasting until you go a full minute without landing a crit).

[Biffoniacus_Furiou]

This one is a Warblade (ToB) class feature. Warblades get several high-level maneuvers that give you extra attacks (Time Stands Still, Avalanche of Blades) and they have access to the very important (for crit fishers) Blood in the Water stance (+1 hit & damage for every crit that lands, stacking indefinitely and lasting until you go a full minute without landing a crit).

No, the Warblade class feature lets you repick which weapons your select-a-weapon feats apply to, it doesn't work with feats that have a weapon printed in them like Lightning Maces.

The Aptitude Weapon magical weapon property is also in Tome of Battle, and it makes it so when you're using that weapon and use a feat that names a particular weapon, the enchanted weapon counts as the named weapon and can benefit from the feat. This applies to any feat that names one or more specific weapons, regardless of whether you were able to choose which weapon the feat applies to.

[eggynack]

Nigh-infinite. Not quite actually infinite. /pedant
Actually, if you get a crit on I think a 10 or more, then the process does in fact go infinite a certain percentage of the time. Sure, the fact you have to actually make the rolls means you personally can't access that infinity, but if we assume the rolls are being considered as occurring instantaneously, I'm pretty sure you get a certain percentage of infinite roll strings that don't feature a termination at any point. Not quite, "You get an infinite number of attacks," as was claimed, but the process we're working with isn't precisely non-infinite either. If you crit on a 12 or more, then you do necessarily terminate, and I'm not sure what exactly happens at 11 or more.

[lylsyly]

AFB, but... FTFY?

EDIT: also, look into those three feats. They're golden.

The Kaorti weapon makes the damage multiplier X4 instead of X2 and the Kensai class feature adds +1 x/per day.

And I would like to know the names of those feats (at least I could use them at the end).

Getting into Kensai is so feat intensive that I don't think I could squeeze a level of warblade in (I could but I want to get there ASAP).

[Bakkan]

Actually, if you get a crit on I think a 10 or more, then the process does in fact go infinite a certain percentage of the time. Sure, the fact you have to actually make the rolls means you personally can't access that infinity, but if we assume the rolls are being considered as occurring instantaneously, I'm pretty sure you get a certain percentage of infinite roll strings that don't feature a termination at any point. Not quite, "You get an infinite number of attacks," as was claimed, but the process we're working with isn't precisely non-infinite either. If you crit on a 12 or more, then you do necessarily terminate, and I'm not sure what exactly happens at 11 or more.

Going actually infinite requires you to be able to make multiple attacks off a single Lightning Maces proc. The best way I've seen to do this is with a ranged weapon with the Splitting property. That plus a critical range of 10-20 or better should give infinitely many attacks with positive probability.

Technically, even with just the Lightning Maces feat, getting infinitely many attacks is not impossible, it just has probability 0.

[eggynack]

Going actually infinite requires you to be able to make multiple attacks off a single Lightning Maces proc. The best way I've seen to do this is with a ranged weapon with the Splitting property. That plus a critical range of 10-20 or better should give infinitely many attacks with positive probability.

Technically, even with just the Lightning Maces feat, getting infinitely many attacks is not impossible, it just has probability 0.
I was assuming there was a source of a second attack. Generally snap kick, as I recall. Without such an extra attack, you're generally getting only reasonable finite quantities of hits, as opposed to a solid probablistic chance associated with each finite hit quantity that I'd consider nigh-infinite. And I'm pretty sure probability zero is the same thing as impossible here.

[Bakkan]

I was assuming there was a source of a second attack. Generally snap kick, as I recall. Without such an extra attack, you're generally getting only reasonable finite quantities of hits, as opposed to a solid probablistic chance associated with each finite hit quantity that I'd consider nigh-infinite. And I'm pretty sure probability zero is the same thing as impossible here.

I am leery of Snap Kick myself, since it seems that in order for it to be useful you table has to interpret it in such a way that 1) it gives an extra attack for each attack in a single action, and 2) the penalties for using Snap Kick more than once in a round do not stack. Ruling 2) is reasonable, though the precedent of Manyshot would provide evidence against such a ruling. Ruling 1) seems to contradict the implication in the feat text that a full attack only generates one Snap Kick.

While impossible events have probability 0, not all events with probability 0 are impossible. In the current example, rolling a 20 on a die over and over again ad infinitum has probability 0, but it's not impossible. In fact, if you choose any infinite sequence of die rolls (e.g. 1,2,3,1,2,3,1,2,3,...), the probability of rolling that precise sequence is 0. However, if you were to somehow roll an infinite sequence of dice, it would have to create one of those such sequences.

This is equivalent to the following problem: Imagine that you will select a random real number uniformly between 0 and 1 (that is, the probability of choosing a number in the interval (a,b) is b-a). The probability of choosing any given real number is 0. However, when you do actually select your random number, you will have observed a clearly not impossible event which a priori had probability 0.

[Hawkstar]

Improved Critical requires a BAB of +8, so your feat progression needs to be updated appropriately.

[Quertus]

Nigh-infinite. Not quite actually infinite. /pedant

No, actually infinite, with calculatable probability of going infinite. Happily, a fellow playgrounder provided the formula from his math class. To-do: link to previous threads on the topic.


No, the Warblade class feature lets you repick which weapons your select-a-weapon feats apply to, it doesn't work with feats that have a weapon printed in them like Lightning Maces.

The Aptitude Weapon magical weapon property is also in Tome of Battle, and it makes it so when you're using that weapon and use a feat that names a particular weapon, the enchanted weapon counts as the named weapon and can benefit from the feat. This applies to any feat that names one or more specific weapons, regardless of whether you were able to choose which weapon the feat applies to.

Lightning Maces, that's one of them. Aptitude Weapon... oops, not a feat, apparently.


Actually, if you get a crit on I think a 10 or more, then the process does in fact go infinite a certain percentage of the time. Sure, the fact you have to actually make the rolls means you personally can't access that infinity, but if we assume the rolls are being considered as occurring instantaneously, I'm pretty sure you get a certain percentage of infinite roll strings that don't feature a termination at any point. Not quite, "You get an infinite number of attacks," as was claimed, but the process we're working with isn't precisely non-infinite either. If you crit on a 12 or more, then you do necessarily terminate, and I'm not sure what exactly happens at 11 or more.

You can calculate the probability of going infinite, and roll percentiles.


Going actually infinite requires you to be able to make multiple attacks off a single Lightning Maces proc. The best way I've seen to do this is with a ranged weapon with the Splitting property. That plus a critical range of 10-20 or better should give infinitely many attacks with positive probability.

Technically, even with just the Lightning Maces feat, getting infinitely many attacks is not impossible, it just has probability 0.

Never thought of trying it with splitting...

[lylsyly]

Improved Critical requires a BAB of +8, so your feat progression needs to be updated appropriately.

Doh! Actually, I did change it on my sheet, but forgot to update the text file I pasted from :smallredface:

[lylsyly]

Sorry for double posting but ...

I talked to my DM. he will let me pull off Neutral Evil if I agree to play a straight up mercenary (only in it for the money yada ...).

I wasn't looking at Disciple of Dispater before due to the alignment thing. Now that I have, I've got a question.

I can take the improved critical feat before I get the double crit class feature ...

If Improved crit takes me from 18-20 (with one of the 4 (?) weapons with that range) to 15 to 20 (a total of six #), does the doubling of the class feature double the 6 or just add three?

And what happens at Dis of Dis 8 when I get triple?

And can you support it by RAW?

I appreciate all your responses.

[eggynack]

While impossible events have probability 0, not all events with probability 0 are impossible. In the current example, rolling a 20 on a die over and over again ad infinitum has probability 0, but it's not impossible. In fact, if you choose any infinite sequence of die rolls (e.g. 1,2,3,1,2,3,1,2,3,...), the probability of rolling that precise sequence is 0. However, if you were to somehow roll an infinite sequence of dice, it would have to create one of those such sequences.

This is equivalent to the following problem: Imagine that you will select a random real number uniformly between 0 and 1 (that is, the probability of choosing a number in the interval (a,b) is b-a). The probability of choosing any given real number is 0. However, when you do actually select your random number, you will have observed a clearly not impossible event which a priori had probability 0.

I'm aware that those problems are equivalent. I'm just not even sure you can pick that real number in the first place, which would imply the event of picking a number and seeing it's .0101... isn't a real thing that we can then consider a counterfactual event. We can make general claims about the probability space without encountering problems, and work with partitions of the real numbers, but you run into trouble when you start trying to work with these numbers that individually have infinite information.

No, actually infinite, with calculatable probability of going infinite. Happily, a fellow playgrounder provided the formula from his math class. To-do: link to previous threads on the topic.
Yep. That was mine, over here (http://www.giantitp.com/forums/showthread.php?502881-Lightning-Mace-and-Actual-Infinity). Hence my response in this thread. There's a link to a longer thread from before mine in that thread also.

[Quertus]

Yep. That was mine, over here (http://www.giantitp.com/forums/showthread.php?502881-Lightning-Mace-and-Actual-Infinity). Hence my response in this thread. There's a link to a longer thread from before mine in that thread also.

Yeah, that's the one - thanks for that!

[eggynack]

Actually, is the, "Can I choose some arbitrary real number," equivalent to the axiom of choice? It seems like it is, but I'm not axiom of choice knowledgeable enough to say for sure. So, the question of whether this particular zero probability aligns with impossibility would be weirdly opinion based. It's always fun to have a math argument where someone's position could reasonably start with, "In my opinion..."

[AvatarVecna]

This sequence never reaches actual infinite, merely "high-infinitely improbable", which is close enough but not quite the same. You can definitely reach a point where an attack is more likely to increase the number of attacks left than decrease the number of attacks left, but no matter how many attacks you're making, and no matter what your critical threat range is, the chance of decreasing the number of attacks remaining is always greater than 0%.

If you made 50 critical threats last round, then this round you're making 100 attacks; if your critical threat range is 2-20, and you hit on a 2, then each attack has a 90.25% chance of generating two attacks, a 4.75% chance of generating one attack, and a 5% chance of generating no attacks. Sure, you're making 100 attacks, so the chances of generating no attacks over the course of the round are a so small, they're barely worth mentioning...but the chances of reducing the number of attacks you get to make next turn compared to this turn are much higher. Of course, they're not as high as the chances of getting to make more attack next turn, but they chance is still there.

TL;DR: The chances of generating a literally infinite number of attacks is 0%, but the chances of generating a non-infinite but still nigh-uncountable number of attacks is a non-0% that rises with both the number of attacks made in the previous round and the size of your critical threat range.

[eggynack]

This sequence never reaches actual infinite, merely "high-infinitely improbable", which is close enough but not quite the same. You can definitely reach a point where an attack is more likely to increase the number of attacks left than decrease the number of attacks left, but no matter how many attacks you're making, and no matter what your critical threat range is, the chance of decreasing the number of attacks remaining is always greater than 0%.

If you made 50 critical threats last round, then this round you're making 100 attacks; if your critical threat range is 2-20, and you hit on a 2, then each attack has a 90.25% chance of generating two attacks, a 4.75% chance of generating one attack, and a 5% chance of generating no attacks. Sure, you're making 100 attacks, so the chances of generating no attacks over the course of the round are a so small, they're barely worth mentioning...but the chances of reducing the number of attacks you get to make next turn compared to this turn are much higher. Of course, they're not as high as the chances of getting to make more attack next turn, but they chance is still there.

TL;DR: The chances of generating a literally infinite number of attacks is 0%, but the chances of generating a non-infinite but still nigh-uncountable number of attacks is a non-0% that rises with both the number of attacks made in the previous round and the size of your critical threat range.
The math just doesn't agree with you on this point. The chance of decreasing the number of attacks remaining is indeed always above zero, but that does not imply that the chance of an infinite string is zero. This is because the probability of a terminating string of attack losses reduces as the quantity of attacks you have increases, and the sum of all those terminating string probabilities converges somewhere besides 100%. The book I linked in the thread I linked above is rather clear on this stuff. The chance of generating a literally infinite number of attacks, far from being zero, gets incredibly (perhaps asymptotically) close to 100% as you increase the starting number of attacks (and you can consider any position in the lightning maces string as the starting number, so the probability of infinity increases as you continue to succeed). The chance is never 100%, but, at a certain extra attack chance, it's never 0%.

[AvatarVecna]

The math just doesn't agree with you on this point. The chance of decreasing the number of attacks remaining is indeed always above zero, but that does not imply that the chance of an infinite string is zero. This is because the probability of a terminating string of attack losses reduces as the quantity of attacks you have increases, and the sum of all those terminating string probabilities converges somewhere besides 100%. The book I linked in the thread I linked above is rather clear on this stuff. The chance of generating a literally infinite number of attacks, far from being zero, gets incredibly (perhaps asymptotically) close to 100% as you increase the starting number of attacks (and you can consider any position in the lightning maces string as the starting number, so the probability of infinity increases as you continue to succeed). The chance is never 100%, but, at a certain extra attack chance, it's never 0%.

So you can show me a series of attacks at any point in the sequence that has no chance of terminating? If you can't, it's not infinite, it's just nigh-infinite, or if you prefer nigh-infinitely improbable. You will always always always have a non-100% chance of starting the next round with more attacks, and will always always always have a non-0% chance of starting the next round with less attacks. Nigh-infinite? Absolutely. Actually infinite? No. But nigh-infinite is good enough.

[eggynack]

So you can show me a series of attacks at any point in the sequence that has no chance of terminating? If you can't, it's not infinite, it's just nigh-infinite, or if you prefer nigh-infinitely improbable. You will always always always have a non-100% chance of starting the next round with more attacks, and will always always always have a non-0% chance of starting the next round with less attacks. Nigh-infinite? Absolutely. Actually infinite? No. But nigh-infinite is good enough.
That's not how it works. I can't show you a series of attacks that has no chance of terminating. However, you can't show me a point in the sequence that has a 100% chance of ever terminating. I have the odds of actual true infinity in that thread I linked.

[AvatarVecna]

That's not how it works. I can't show you a series of attacks that has no chance of terminating. However, you can't show me a point in the sequence that has a 100% chance of ever terminating. I have the odds of actual true infinity in that thread I linked.

A bit of research outside of D&D forums (into dedicated math forums and the like), as well as a quick discussion with an IRL friend who's a long time math geek, and as near as I can tell it turns out to be truly infinite past a certain point, despite how odd that seems. :/ Huh, okay.

[Bakkan]

Actually, is the, "Can I choose some arbitrary real number," equivalent to the axiom of choice? It seems like it is, but I'm not axiom of choice knowledgeable enough to say for sure. So, the question of whether this particular zero probability aligns with impossibility would be weirdly opinion based. It's always fun to have a math argument where someone's position could reasonably start with, "In my opinion..."

No, the Axiom of Choice is somewhat more complicated and subtle at the same time. I have a suspicion that what we're running into is the difference between practical mathematics, which is bound by such things as finite levels of precision in the universe ultimately (maybe) based on such limits as the Planck length, and pure mathematics, which does not constrain itself that way. In the first sense, you are completely correct of course that no person could even write down the decimal representation of an irrational real number, as the number of digits required (infinitely many) exceeds the number of possible states of particles in the universe. At the same time, if we are placing such practical restrictions on things, then it is impossible for the critfisher to make infinitely many attack rolls because game night has to be over by 1 A.M.

If we are talking about literally infinite attacks, and I am very happy that we are, then we have already left the realm where practical concerns like "how to I, as a human, randomly select a real number" are obstacles.

[eggynack]

No, the Axiom of Choice is somewhat more complicated and subtle at the same time. I have a suspicion that what we're running into is the difference between practical mathematics, which is bound by such things as finite levels of precision in the universe ultimately (maybe) based on such limits as the Planck length, and pure mathematics, which does not constrain itself that way. In the first sense, you are completely correct of course that no person could even write down the decimal representation of an irrational real number, as the number of digits required (infinitely many) exceeds the number of possible states of particles in the universe. At the same time, if we are placing such practical restrictions on things, then it is impossible for the critfisher to make infinitely many attack rolls because game night has to be over by 1 A.M.
I dunno, they seem pretty identical. We have this infinite quantity of digit slots, each containing nine different numerical possibilities. If the axiom of choice isn't assumed, then we cannot necessarily make a selection for each digit slot in even a theoretical sense. You're asserting that we can, not manually but in a mathematical space, point to some arbitrary real number, one out of the infinity produced by this interval, and note that such a number could have this property. I'm not sure you can point in the first place. Unless I'm mistaken that the axiom of choice applies to countable infinities as well as those uncountable. We can say real numbers exist, and we can say that they have certain properties, but selecting one might be beyond us, in a sense.

[Bakkan]

I think I am following you. The reason why the Axiom of Choice would not apply to the situation I was describing is that it involves selecting only one element, a real number, from a single set, the interval [0,1). Decimal representations are only ways of describing the real numbers, and they're not even unique. Once a real number has been selected via the theoretical random process, calculating the necessary decimal digits to represent it is a simple calculation not requiring the Axiom of Choice.

An axiom I am using, however, is the Axiom of Infinity; that is, the axiom that states that an infinite set exists.

[eggynack]

I think I am following you. The reason why the Axiom of Choice would not apply to the situation I was describing is that it involves selecting only one element, a real number, from a single set, the interval [0,1). Decimal representations are only ways of describing the real numbers, and they're not even unique. Once a real number has been selected via the theoretical random process, calculating the necessary decimal digits to represent it is a simple calculation not requiring the Axiom of Choice.

An axiom I am using, however, is the Axiom of Infinity; that is, the axiom that states that an infinite set exists.
Maybe. Still, if we return to our original case of infinite dice rolls, then we can, in fact, point to an infinite number of distinct sets. It would seem that the axiom of choice would apply to these sets, and if the dice rolls are equivalent to this interval, and it seems like they are, then the selfsame axiom should apply similarly to the selection of a real numbers.

[Bakkan]

Maybe. Still, if we return to our original case of infinite dice rolls, then we can, in fact, point to an infinite number of distinct sets. It would seem that the axiom of choice would apply to these sets, and if the dice rolls are equivalent to this interval, and it seems like they are, then the selfsame axiom should apply similarly to the selection of a real numbers.

It depends on which way you are going. If your process is "for each of infinitely many rolls, select a value, and then write a decimal corresponding to that roll", you need the Axiom of Choice. If your process is "select a real number, write it as a decimal in an appropriate base, and use the digits for the values of infinitely many rolls", then you do not need the Axiom of Choice. However, and this was something that escaped me until halfway through my previous post, the second process, as I have written it, may not be well-defined. This is because if my real number has a decimal representation of, say, 0.123000000..., then it also has a decimal representation of 0.1229999999.... One can modify the process I described to avoid this issue, though.

[lylsyly]

No, the Axiom of Choice is somewhat more complicated and subtle at the same time. I have a suspicion that what we're running into is the difference between practical mathematics, which is bound by such things as finite levels of precision in the universe ultimately (maybe) based on such limits as the Planck length, and pure mathematics, which does not constrain itself that way. In the first sense, you are completely correct of course that no person could even write down the decimal representation of an irrational real number, as the number of digits required (infinitely many) exceeds the number of possible states of particles in the universe. At the same time, if we are placing such practical restrictions on things, then it is impossible for the critfisher to make infinitely many attack rolls because game night has to be over by 1 A.M.

If we are talking about literally infinite attacks, and I am very happy that we are, then we have already left the realm where practical concerns like "how to I, as a human, randomly select a real number" are obstacles.


It depends on which way you are going. If your process is "for each of infinitely many rolls, select a value, and then write a decimal corresponding to that roll", you need the Axiom of Choice. If your process is "select a real number, write it as a decimal in an appropriate base, and use the digits for the values of infinitely many rolls", then you do not need the Axiom of Choice. However, and this was something that escaped me until halfway through my previous post, the second process, as I have written it, may not be well-defined. This is because if my real number has a decimal representation of, say, 0.123000000..., then it also has a decimal representation of 0.1229999999.... One can modify the process I described to avoid this issue, though.


Maybe. Still, if we return to our original case of infinite dice rolls, then we can, in fact, point to an infinite number of distinct sets. It would seem that the axiom of choice would apply to these sets, and if the dice rolls are equivalent to this interval, and it seems like they are, then the selfsame axiom should apply similarly to the selection of a real numbers.


I think I am following you. The reason why the Axiom of Choice would not apply to the situation I was describing is that it involves selecting only one element, a real number, from a single set, the interval [0,1). Decimal representations are only ways of describing the real numbers, and they're not even unique. Once a real number has been selected via the theoretical random process, calculating the necessary decimal digits to represent it is a simple calculation not requiring the Axiom of Choice.

An axiom I am using, however, is the Axiom of Infinity; that is, the axiom that states that an infinite set exists.


I dunno, they seem pretty identical. We have this infinite quantity of digit slots, each containing nine different numerical possibilities. If the axiom of choice isn't assumed, then we cannot necessarily make a selection for each digit slot in even a theoretical sense. You're asserting that we can, not manually but in a mathematical space, point to some arbitrary real number, one out of the infinity produced by this interval, and note that such a number could have this property. I'm not sure you can point in the first place. Unless I'm mistaken that the axiom of choice applies to countable infinities as well as those uncountable. We can say real numbers exist, and we can say that they have certain properties, but selecting one might be beyond us, in a sense.


The math just doesn't agree with you on this point. The chance of decreasing the number of attacks remaining is indeed always above zero, but that does not imply that the chance of an infinite string is zero. This is because the probability of a terminating string of attack losses reduces as the quantity of attacks you have increases, and the sum of all those terminating string probabilities converges somewhere besides 100%. The book I linked in the thread I linked above is rather clear on this stuff. The chance of generating a literally infinite number of attacks, far from being zero, gets incredibly (perhaps asymptotically) close to 100% as you increase the starting number of attacks (and you can consider any position in the lightning maces string as the starting number, so the probability of infinity increases as you continue to succeed). The chance is never 100%, but, at a certain extra attack chance, it's never 0%.


This sequence never reaches actual infinite, merely "high-infinitely improbable", which is close enough but not quite the same. You can definitely reach a point where an attack is more likely to increase the number of attacks left than decrease the number of attacks left, but no matter how many attacks you're making, and no matter what your critical threat range is, the chance of decreasing the number of attacks remaining is always greater than 0%.

If you made 50 critical threats last round, then this round you're making 100 attacks; if your critical threat range is 2-20, and you hit on a 2, then each attack has a 90.25% chance of generating two attacks, a 4.75% chance of generating one attack, and a 5% chance of generating no attacks. Sure, you're making 100 attacks, so the chances of generating no attacks over the course of the round are a so small, they're barely worth mentioning...but the chances of reducing the number of attacks you get to make next turn compared to this turn are much higher. Of course, they're not as high as the chances of getting to make more attack next turn, but they chance is still there.

TL;DR: The chances of generating a literally infinite number of attacks is 0%, but the chances of generating a non-infinite but still nigh-uncountable number of attacks is a non-0% that rises with both the number of attacks made in the previous round and the size of your critical threat range.


Actually, is the, "Can I choose some arbitrary real number," equivalent to the axiom of choice? It seems like it is, but I'm not axiom of choice knowledgeable enough to say for sure. So, the question of whether this particular zero probability aligns with impossibility would be weirdly opinion based. It's always fun to have a math argument where someone's position could reasonably start with, "In my opinion..."


Yeah, that's the one - thanks for that!


I'm aware that those problems are equivalent. I'm just not even sure you can pick that real number in the first place, which would imply the event of picking a number and seeing it's .0101... isn't a real thing that we can then consider a counterfactual event. We can make general claims about the probability space without encountering problems, and work with partitions of the real numbers, but you run into trouble when you start trying to work with these numbers that individually have infinite information.

Yep. That was mine, over here (http://www.giantitp.com/forums/showthread.php?502881-Lightning-Mace-and-Actual-Infinity). Hence my response in this thread. There's a link to a longer thread from before mine in that thread also.

Help, I've been hijacked! :smalltongue:

[eggynack]

It depends on which way you are going. If your process is "for each of infinitely many rolls, select a value, and then write a decimal corresponding to that roll", you need the Axiom of Choice. If your process is "select a real number, write it as a decimal in an appropriate base, and use the digits for the values of infinitely many rolls", then you do not need the Axiom of Choice. However, and this was something that escaped me until halfway through my previous post, the second process, as I have written it, may not be well-defined. This is because if my real number has a decimal representation of, say, 0.123000000..., then it also has a decimal representation of 0.1229999999.... One can modify the process I described to avoid this issue, though.
Unless you're weirdly turning real numbers back into rolls though, it seems like the axiom of choice would indeed be required for the actual dice version of this situation. Probably. I suppose my point is that the selection process implied by the dice rolling means that the real number situation also likely involves the axiom if the two situations are to have parity. A real number selected by a theoretical infinity of dice rolls would be unresolvable without the axiom, in other words, even if we can identify real numbers that exist. I think that makes sense.

Help, I've been hijacked! :smalltongue:
If you didn't expect a thread about critical hits to become about nigh versus true infinity, zero probability versus the actually impossible, and the axiom of choice, then we're clearly hanging out in two separate forums.

[lylsyly]

If you didn't expect a thread about critical hits to become about nigh versus true infinity, zero probability versus the actually impossible, and the axiom of choice, then we're clearly hanging out in two separate forums.

So, have we figured out how to make the camel talk yet? :smallbiggrin:

[AvatarVecna]

So, have we figured out how to make the camel talk yet? :smallbiggrin:

I'm pretty sure there's a Core spell granting animals sentience.

EDIT: Without looking it up, I'll even hazard a guess that it's a fairly well-known Druid spell. :smallwink:

[lylsyly]

I'm pretty sure there's a Core spell granting animals sentience.

EDIT: Without looking it up, I'll even hazard a guess that it's a fairly well-known Druid spell. :smallwink:

Yes, but with that spell, you cannot be a companion or familiar :smallfrown:. Hmm ... wonder how well a camel would do as a Crit Fighter ;)



I talked to my DM. he will let me pull off Neutral Evil if I agree to play a straight up mercenary (only in it for the money yada ...).

I wasn't looking at Disciple of Dispater before due to the alignment thing. Now that I have, I've got a question.

I can take the improved critical feat before I get the double crit class feature ...

If Improved crit takes me from 18-20 (with one of the 4 (?) weapons with that range) to 15 to 20 (a total of six #), does the doubling of the class feature double the 6 or just add three?

And what happens at Dis of Dis 8 when I get triple?

And can you support it by RAW?

I appreciate all your responses.

[eggynack]

Yes, but with that spell, you cannot be a companion or familiar :smallfrown:.
If you're doing this companion style, I'd think exalted companion plus a pearl of speech would do it. Don't think celestial animals pick up common automatically, and I'd be really hesitant about claiming that a pearl of speech on a two intelligence animal would work (but maybe?), but the combination seems legitimate.