Bandw2, you and Malachi are starting with different axioms so you will get different results, mathematically.
If you limit yourself to integers the very concept of "half" is undefined. 1/2 is not an integer.
yes but an integer divided by 2 is still half that original integer's there are halved of numbers, but there is not a .5, 1/2 are simply 2 numbers in arithmetic.
It's very clear that you do not round at every step of an equation,
or the game system would brake down and be inconsistent.Now you do not always round immediately when you have a .5 to deal with.
The question the becomes in the particular instance do I need to round at this particular point. NOBODY REALLY KNOWS!
Not 100%. if we don't have official input. It's ambiguous and up for personal interpretation.
It's only ambiguous if you ignore every other example in the book. Show me one single instance where you compare two numbers and one of them has a decimal point.
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9/2 = 4
Ah, I think I can see where you've gone wrong there!
9/2 = 4.5
pathfinder says simply that half of 7 is 3.
No it doesn't!
Occasionally the rules ask you to round a result or value. Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3
These are instructions of how to round, on those occasions when you do round. Not instructions that you must round. The line 'Unless otherwise stated, always round down' is saying that when you round always round down! Not 'always round'.
And when it says, 'For example, if you are asked to take half of 7, the result would be 3', this is an example of how rounding works (there's a clue in the title!), not how division works.
if you want to ignore this fact go ahead, but your not using mathematics to prove me wrong, that's for sure.
9/2 = 4.5. That's maths. That proves you wrong. That's how division works in both real life and PF. There is no rule in the game that says we use integer math. Rounding is not integer math. There is no rule that means we always round, just a rule that says when we round, we round down unless stated otherwise. There is no rule that says 7/2 = 3, just an example of rounding 7/2 down to 3 instead of up to 4.
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Hmm, I wonder how all you guys would rule on this:
Life Drinker (Su): At 19th level, each time the magus kills a living creature with the black blade, he can pick one of the following effects: the black blade restores 2 points to its arcane pool; the black blade restores 1 point to its arcane pool and the magus restores 1 point to his arcane pool; the magus gains a number of temporary hit points equal to the black blade’s ego (these temporary hit points last until spent or 1 minute, whichever is shorter). The creature killed must have a number of Hit Dice equal to half the magus’s character level for this to occur.Almost the exact same wording except the comparison 'equal to' replaces 'less than'.
Now, RAI probably is 'greater than or equal to', but according to the 'no rounding' ruling and RAW, this ability doesn't work at odd levels.
This one's easy. The law in Britain is that you have to be 18 years old in order to drink alcohol. This doesn't mean you have to be exactly 18, but at least 18.
The above ability means that the creature must have at least half the hit dice of the magus. So for a 19th level magus, the creature must have at least 10 HD; because 9 HD would not be 'at least' half of 19.
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yes but an integer divided by 2 is still half that original integer's there are halved of numbers, but there is not a .5, 1/2 are simply 2 numbers in arithmetic.Bandw2, you and Malachi are starting with different axioms so you will get different results, mathematically.
If you limit yourself to integers the very concept of "half" is undefined. 1/2 is not an integer.
I think your syntax got a little confused here, but the idea that multiplying by 1/2 is the same as dividing by 2 works in the rational numbers but not the integers, for the very reason that 1/2 is not defined and multiplication and division are not inverse operations in the integers, as has been previously noted(by you, I believe).
You can't have it both ways, where dividing by 2 and multiplying by 2 do not cancel, but dividing by 2 is the same as multiplying by 1/2. That leads to a contradiction. Here's a quick proof:
Given any integer a, assume that (a / 2) * 2 != a
If a / 2 = a * 1/2,
(a / 2) * 2 = a * 1/2 * 2,
(a / 2) * 2 = a * 1
(a / 2) * 2 = a, which is a contradiction.
So if multiplication and division are not inverse operations, dividing by 2 is not the same as taking half of something. Isn't math fun?
Simple. The rule is halve the 'damage' done, not halve each die of damage.
Damage has a particular number associated with it, which is the sum of the damage dice. I mean, this isn't even a difficult situation to adjudicate, it works exactly how it is supposed to work, and you round exactly where you're supposed to round.
What language would you even point to saying that you should round each individual die?
I see no such wording to support your supposition. According to the language of the spell fireball, the "damage" done by a fireball is 1d6 per caster level. Where in the rules does it state that you must add this damage together first before determining half value of a successful save? I could not find such a rule.
Yes, my argument is one of ad adsurdum, but I'm just pointing out that the rules on when to round are not as clear cut as it seems.
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Occasionally the rules ask you to round a result or value. Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3These are instructions of how to round, on those occasions when you do round. Not instructions that you must round. The line 'Unless otherwise stated, always round down' is saying that when you round always round down! Not 'always round'.
And when it says, 'For example, if you are asked to take half of 7, the result would be 3', this is an example of how rounding works (there's a clue in the title!), not how division works.
I've had my share of arguments with Malachi before, but this time I agree with him, and this quote is spot on. There is absolutely no reason to round in this scenario. The rules explain how to round when you have to, but IMO, you do not have to here.
I've had my share of arguments with Malachi before, but this time I agree with him, and this quote is spot on. There is absolutely no reason to round in this scenario. The rules explain how to round when you have to, but IMO, you do not have to here.
Okay then show me where the rules tell me "when I have to" because, and this has been said many times In the case of the monk, the DC of his stunning fist can be 14.5. You don't have to round, you can leave it like that. A save of a 14 is lower than 14.5 so the save fails. A roll of 15 his higher than 14.5 so it succeeds. See it works exactly like panache.
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Okay then show me where the rules tell me "when I have to" because, and this has been said many times In the case of the monk, the DC of his stunning fist can be 14.5. You don't have to round, you can leave it like that. A save of a 14 is lower than 14.5 so the save fails. A roll of 15 his higher than 14.5 so it succeeds. See it works exactly like panache.
The rules have been quoted dozens of times. "Occasionally the rules ask you to round a result or value."
This implies that it's not always necessary. "When I have to" is an abstract I used to define when it's necessary to do so.
In the case of stunning fist, you are calculating out a save DC. Save DC's use whole numbers, ergo, rounding is necessary.
In the case of determining whether something is greater or less than half a given level, no rounding is required to make this determination.
Completely different scenario's. They are far from exactly alike, as you claim.
I've clicked the FAQ, and will await a response. The argument is one I'd like to see an answer towards, because I do understand and even respect your argument. I just don't agree with it, as there is far too much grey area in this matter.
The rules have been quoted dozens of times. "Occasionally the rules ask you to round a result or value."
This implies that it's not always necessary. "When I have to" is an abstract I used to define when it's necessary to do so.
In the case of stunning fist, you are calculating out a save DC. Save DC's use whole numbers, ergo, rounding is necessary.
Where does it say Save DC's use whole numbers? It doesn't say that anywhere. You've just always done it that way, and so has everyone else. Nothing tells us to do it, we just know that when you compare two numbers in Pathfinder, you make them whole numbers.
In the case of determining whether something is greater or less than half a given level, no rounding is required to make this determination.
A Saving Throw is determining whether something is greater than or less than something else. Explain to me how this is any different than Panache.
Completely different scenario's. They are far from exactly alike, as you claim.
They aren't completely different. They aren't different at all. They just feel different in your mind. When you compare two numbers, you round before the comparison. It is exactly the same all through the rules. People, for some reason, want panache to be different.
I've clicked the FAQ, and will await a response. The argument is one I'd like to see an answer towards, because I do understand and even respect your argument. I just don't agree with it, as there is far too much grey area in this matter.
Only if you assume that they wanted Panache to be a completely unique mechanic. No one, so far, has been able to show any example where two numbers are compared and you don't round. Heck the only slight example of non-rounding is hit points and Favored Class Bonus, but both of those are actually rounded at the end. Hit points are obvious, so I'll show FCB:
FCB +1/6 Rouge TalentLevel 1: 1/6 rogue talent = .1666 round down = 0
Level 2: 2/6 rogue talent = .333 round down = 0
...
Level 6: 6/6 rogue talent = 1 round down = 1
Level 7: 1 1/6 rogue Talent = 1.1666 round down = 1
...
Level 12: 1 6/6 rogue talent = 2 round down = 2
Panache and DC are the same, they don't differ at all. We use the same mechanic for everything else and no one bats an eye, but for some reason, everything changes when it comes to Panache. I mean I get it, I had the same issues
First, Thank you for pointing out exceptions to the rounding rule.. These examples prove that you don't always round in every case.
In addition to HP, FC Bonus, My own example of half damage on a saving throw, I also found problems in the Massive Damage optional rule.
If you ever sustain a single attack that deals an amount of damage equal to half your total hit points (minimum 50 points of damage) or more...
So if my HP is 101, and someone hits me for 50, does massive damage rule apply? I posit it does not.
After scouring the rules, I believe the problem lies in the way Panache/Grit is written. Nearly all cases where a character examines half his level, you are left with no question as to what it means..
The Undead Lord can create burning skeleton companion that cannot exceed half her cleric level... This leaves no question.. 2.5 or 2 does not exceed half her level, and she can make the skeleton
Panache should have been written as clear as other examples of half-hit dice. But alas, it is not. That ambiguity requires an answer. Until then, a little common sense will tell you that two is not half of five hit die.
*Edit - Fixed the bad info per Born_of_fires suggestion.
25 points of damage never triggers the massive damage rule. It requires a hit of at least 50 points so your example needs to be if you had 101HP and took 50 damage
(Fix't my bad info)
First, Thank you for pointing out exceptions to the rounding rule.. These examples prove that you don't always round in every case.
Except the example I've given proves they are rounded every time.
In addition to HP, FC Bonus, My own example of half damage on a saving throw, I also found problems in the Massive Damage optional rule.
Let's take a look at your half damage post, it goes a long way to proving my point. We all agree that the way you posted it isn't the way it works. As you have pointed out, nothing tells us it doesn't work this way, but we've all read the rules and understand that it only makes sense and we apply the rules in a consistent manner and we all agree on the "right" way of doing it. There are no rules dictating HOW this is supposed to work, we just do it like we do everything else... and yet you don't want to apply the same logic to panache. You want to look at it, and since nothing dictates how it should be done, you want to do it differently than we've done everything else. No real reason why or examples that prove it should be done differently, you just think it should be.
If you ever sustain a single attack that deals an amount of damage equal to half your total hit points (minimum 50 points of damage) or more...So if my HP is 51, and someone hits me for 25, does massive damage rule apply? I posit it does not.
And you would be correct since it didn't do a minimum of 50 hit points of damage. However, if you had 151 hit points and someone hit you for 75 points of damage, if I were a GM and since it's an optional rule, I would round up in this instance since it benefits the player. On the other hand, if this became a PFS rule, say, and I had to play it as RAW as possible, then I would have to say yes Massive Damage would apply since that would make it consistent with every other example.
After scouring the rules, I believe the problem lies in the way Panache/Grit is written. Nearly all cases where a character examines half his level, you are left with no question as to what it means..
The Undead Lord can create burning skeleton companion that cannot exceed half her cleric level... This leaves no question.. 2.5 or 2 does not exceed half her level, and she can make the skeleton
Panache should have been written as clear as other examples of half-hit dice. But alas, it is not. That ambiguity requires an answer. Until then, a little common sense will tell you that two is not half of five hit die.
The general rule is unless stated otherwise, round down. I don't know why that's so difficult in this instance.
Again, the general rule is more than what you suggest it is.
Occasionally the rules ask you to round a result or value. Unless otherwise stated, always round down...
Are the rules asking you to round here? Not that I can see. You're assuming there is need here when logic suggests there is none.
Every time we round something, unless it specifically instructs us to round, we are making a judgment call on if we should or should not round. As you and I have both pointed out, there are numerous examples of times we shouldn't round, as well as times we should round. Each case we are making a judgment call based on common sense.
This is one of those examples where the rules do not ask you to round, and common sense says you should not round.
I eagerly await a Dev response. RAW is at best unclear, and I personally believe that the RAI in this case to not round.
Every time we round something, unless it specifically instructs us to round, we are making a judgment call on if we should or should not round. As you and I have both pointed out, there are numerous examples of times we shouldn't round, as well as times we should round. Each case we are making a judgment call based on common sense.
Actually there are no examples where you don't round. You tried to say since you don't take half of each die you don't round, but even you said that was a ridiculous statement. There are absolutely zero examples of no rounding at all.
9/2 = 4Ah, I think I can see where you've gone wrong there!
9/2 = 4.5
pathfinder says simply that half of 7 is 3.No it doesn't!
Occasionally the rules ask you to round a result or value. Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3These are instructions of how to round, on those occasions when you do round. Not instructions that you must round. The line 'Unless otherwise stated, always round down' is saying that when you round always round down! Not 'always round'.
And when it says, 'For example, if you are asked to take half of 7, the result would be 3', this is an example of how rounding works (there's a clue in the title!), not how division works.
if you want to ignore this fact go ahead, but your not using mathematics to prove me wrong, that's for sure.9/2 = 4.5. That's maths. That proves you wrong. That's how division works in both real life and PF. There is no rule in the game that says we use integer math. Rounding is not integer math. There is no rule that means we always round, just a rule that says when we round, we round down unless stated otherwise. There is no rule that says 7/2 = 3, just an example of rounding 7/2 down to 3 instead of up to 4.
yes and since you are comparing 2 numbers you round, just like a DC.
DCs being written down meaning they need to be rounded, is in fact located no where in the rules and is an assumption you are making, with no evidence to back it up.
every other time you compare 2 numbers you round before the comparison, thus I am making an assumption that the game is behaving normally, or that no extra unwritten rules are in play.
Occasionally, as probably has been said before, is not an exclusionary term. It simply opens the possibility for values to be not rounded, but comparing there values is not one of them.
SO
round rules are in play and thus half of 9 is 4.
your argument repeatedly comes back to "that's not how it works" with no actual in engine evidence.
yes but an integer divided by 2 is still half that original integer's there are halved of numbers, but there is not a .5, 1/2 are simply 2 numbers in arithmetic.Bandw2, you and Malachi are starting with different axioms so you will get different results, mathematically.
If you limit yourself to integers the very concept of "half" is undefined. 1/2 is not an integer.
I think your syntax got a little confused here, but the idea that multiplying by 1/2 is the same as dividing by 2 works in the rational numbers but not the integers, for the very reason that 1/2 is not defined and multiplication and division are not inverse operations in the integers, as has been previously noted(by you, I believe).
You can't have it both ways, where dividing by 2 and multiplying by 2 do not cancel, but dividing by 2 is the same as multiplying by 1/2. That leads to a contradiction. Here's a quick proof:
** spoiler omitted **
So if multiplication and division are not inverse operations, dividing by 2 is not the same as taking half of something. Isn't math fun?
i explained earlier but you must not have read it.
when you are asked for half a value it is X/2. you do not Multiply anything by 1/2(you can;t multiply anything by a non-existent value), you divide by 2. or at the very least X*1/2, in the order as written. likewise when finding two thirds, it is (X*2)/3.
so it becomes
(a/2) = a*1/2
(a/2)*2 = (a*1/2)*2
which becomes
a*2/2 = a*1*2/2
2a/2 = 2a/2
a=a
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yes but an integer divided by 2 is still half that original integer's there are halved of numbers, but there is not a .5, 1/2 are simply 2 numbers in arithmetic.Bandw2, you and Malachi are starting with different axioms so you will get different results, mathematically.
If you limit yourself to integers the very concept of "half" is undefined. 1/2 is not an integer.
I think your syntax got a little confused here, but the idea that multiplying by 1/2 is the same as dividing by 2 works in the rational numbers but not the integers, for the very reason that 1/2 is not defined and multiplication and division are not inverse operations in the integers, as has been previously noted(by you, I believe).
You can't have it both ways, where dividing by 2 and multiplying by 2 do not cancel, but dividing by 2 is the same as multiplying by 1/2. That leads to a contradiction. Here's a quick proof:
** spoiler omitted **
So if multiplication and division are not inverse operations, dividing by 2 is not the same as taking half of something. Isn't math fun?
i explained earlier but you must not have read it.
when you are asked for half a value it is X/2. you do not Multiply anything by 1/2(you can;t multiply anything by a non-existent value), you divide by 2. or at the very least X*1/2, in the order as written. likewise when finding two thirds, it is (X*2)/3.
so it becomes
(a/2) = a*1/2
(a/2)*2 = (a*1/2)*2
which becomes
a*2/2 = a*1*2/2
2a/2 = 2a/2
a=a
You realize you just helped disprove your own side, right? The rounding side is claiming that 7/2 = 3, thus (7/2) * 2 = 6, which is not 7, which contradicts the proof you just posted. I'm not up to sifting back through several hundred posts to see exactly who made the claim that (a/2) * 2 != a was okay because integer math, but that claim was made. I'm just saying that you can't equate multiplying by 1/2 with dividing by 2 while also retaining the rounding rules of computer integer math, because that leads to a contradiction.
Half of a value is multiplying by 1/2. The fact that multiplying by 1/2 and dividing by 2 get you the same answer in normal arithmetic is a happy convenience, but it doesn't have to be true in all number systems. For example, it's not true in the integers - it can't be because 1/2 is undefined. The very concept of "half" doesn't work if you're restricted to integers. In a strict sense dividing an odd number by 2 doesn't have an answer in the integers either, much like taking the square root of a negative number doesn't have an answer in the real numbers.
I'm just posting this to debunk the statement that PF uses integer math because it pretty clearly doesn't, except maybe in a very loose computer science sense of "integer math."
As to the core question of the thread, I believe you round when you need to or are told to. Neither is the case here. But I also concede that the rule is ambiguous. I could be wrong.
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DCs being written down meaning they need to be rounded, is in fact located no where in the rules and is an assumption you are making, with no evidence to back it up.
There is evidence all over the place! In every single stat block published by Paizo, every single DC and modifier is an integer, even if the calculations leading to that result would leave a fraction.
every other time you compare 2 numbers you round before the comparison
And this is something for which there is no evidence. In order for clear evidence of this, you would have to show a stat block where there is a DC or a modifier which includes a fraction, and then show that this fraction is rounded down before 'comparing' it with another number.
There is a bit of language you've been twisting for ages in this thread: the idea that rolling a d20, adding a modifier, and trying to equal or exceed a DC is equivalent to 'comparing' two numbers, and that ascertaining if one person is taller than the other is 'comparing two numbers', thus creating a false equivalency that you can abuse to support your position.
If I want to see which person is taller, I can certainly write down their heights in feet and see which of those numbers is bigger: comparing numbers.
But the problem to be solved here (who is taller) is not fundamentally about comparing numbers! We can find out who is taller without ever comparing any number. The problem here is not about comparing numbers, just because you can compare numbers to solve it. You can also stand them next to each other to see who is taller, without ever knowing the exact height of either. Problem solved, no math, no rounding.
According to the 'logic' you are using, if you stand two people next to each other, the guy who is 5-feet tall is exactly the same height as the guy who is 5-feet 6-inches.
There are many way to solve the problem, 'is 2 less than half of 5', and just because you can divide 5 by 2, doesn't mean that the problem must be solved that way. In fact, if you insist on rounding, then that is a very poor method to solve that problem because you are deliberately introducing an inaccuracy that is easily avoidable by using a method which doesn't risk that inaccuracy.
When you roll to equal or exceed a DC, what alternate ways are there to solve that problem? What inaccuracies are avoided? In truth, this operation never involves a fraction in PF, because there is no DC or modifier which includes a fraction. There is nothing to round.
Choosing to describe 'rolling a check' as merely 'comparing two numbers' is an exercise in semantics to cynically twist the facts in order to support a spurious argument.
round rules are in play and thus half of 9 is 4.
'Rounding' is not 'division'. Half of 9 is 4.5. At this point, if rounding is needed, and if 'PF rounding' is being used, then you round 4.5 down to 4.
This does not mean that 4.5 = 4.
Nor does it mean that 9/2 = 4.
It does mean that, if rounding is required in this case, 4.5 gets rounded down to 4.
You realize you just helped disprove your own side, right? The rounding side is claiming that 7/2 = 3, thus (7/2) * 2 = 6, which is not 7, which contradicts the proof you just posted. I'm not up to sifting back through several hundred posts to see exactly who made the claim that (a/2) * 2 != a was okay because integer math, but that claim was made. I'm just saying that you can't equate multiplying by 1/2 with dividing by 2 while also...yes but an integer divided by 2 is still half that original integer's there are halved of numbers, but there is not a .5, 1/2 are simply 2 numbers in arithmetic.Bandw2, you and Malachi are starting with different axioms so you will get different results, mathematically.
If you limit yourself to integers the very concept of "half" is undefined. 1/2 is not an integer.
I think your syntax got a little confused here, but the idea that multiplying by 1/2 is the same as dividing by 2 works in the rational numbers but not the integers, for the very reason that 1/2 is not defined and multiplication and division are not inverse operations in the integers, as has been previously noted(by you, I believe).
You can't have it both ways, where dividing by 2 and multiplying by 2 do not cancel, but dividing by 2 is the same as multiplying by 1/2. That leads to a contradiction. Here's a quick proof:
** spoiler omitted **
So if multiplication and division are not inverse operations, dividing by 2 is not the same as taking half of something. Isn't math fun?
i explained earlier but you must not have read it.
when you are asked for half a value it is X/2. you do not Multiply anything by 1/2(you can;t multiply anything by a non-existent value), you divide by 2. or at the very least X*1/2, in the order as written. likewise when finding two thirds, it is (X*2)/3.
so it becomes
(a/2) = a*1/2
(a/2)*2 = (a*1/2)*2
which becomes
a*2/2 = a*1*2/2
2a/2 = 2a/2
a=a
that's because division hasn't happened yet, it made it more accurate by multiplying before the division, but you cannot divide and then multiply and always have it equal the same thing. they sometimes do, like 6/2 and then *2, will get 6 again, just because sometimes it can cause it to become equal does not mean EVERYTIME they can, thus they still are not equal and opposite reactions.
you keep using my numbers out of context, all i need to prove that they cannot equate on opposite sides is show one instance where they do not create the same solution.
i did that
3 <= 7/2 and 3*2 <= 7 do not create the same solution, they are not equal, and thus my proof still stands that they are not interchangable.
however, 7 == 7*2/2 is still true but 7 != (7/2)*2.
you haven't proved anything at all, but taken the math out of context.
DCs being written down meaning they need to be rounded, is in fact located no where in the rules and is an assumption you are making, with no evidence to back it up.There is evidence all over the place! In every single stat block published by Paizo, every single DC and modifier is an integer, even if the calculations leading to that result would leave a fraction.
you misinterpreted my point, my point was that there is no rule that specifically states that only they need to round. they never ask to round these numbers they simply do.
every other time you compare 2 numbers you round before the comparisonAnd this is something for which there is no evidence. In order for clear evidence of this, you would have to show a stat block where there is a DC or a modifier which includes a fraction, and then show that this fraction is rounded down before 'comparing' it with another number.
no I don't the DC is the value being compared, and thus it was rounded prior to comparison. how long before the comparison does not matter, only that my point still stands.
There is a bit of language you've been twisting for ages in this thread: the idea that rolling a d20, adding a modifier, and trying to equal or exceed a DC is equivalent to 'comparing' two numbers, and that ascertaining if one person is taller than the other is 'comparing two numbers', thus creating a false equivalency that you can abuse to support your position.
when you can prove that a d20+some values isn't itself a number when compared to a DC, then I will actually have something to fight against on this.
If I want to see which person is taller, I can certainly write down their heights in feet and see which of those numbers is bigger: comparing numbers.But the problem to be solved here (who is taller) is not fundamentally about comparing numbers! We can find out who is taller without ever comparing any number. The problem here is not about comparing numbers, just because you can compare numbers to solve it. You can also stand them next to each other to see who is taller, without ever knowing the exact height of either. Problem solved, no math, no rounding.
but you cannot actually prove that one is taller than another without first measuring them, turning their heights into numbers and showing that X value is higher than Y value.
According to the 'logic' you are using, if you stand two people next to each other, the guy who is 5-feet tall is exactly the same height as the guy who is 5-feet 6-inches.There are many way to solve the problem, 'is 2 less than half of 5', and just because you can divide 5 by 2, doesn't mean that the...
if, for some reason inches did not matter in the measurement then yes, they are effectively the same height. inches however are whole numbers and they are not fractions of feet, but feet are actually collections of inches. thus it is easily viable to compare them in inches.
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but you cannot actually prove that one is taller than another without first measuring them, turning their heights into numbers and showing that X value is higher than Y value.
Rubbish! Both are standing together, a blade slashes at a height of exactly 5-feet 1-inch. One dies, the other is untouched. You would have it that both are untouched, simply because the system you chose to measure this is deliberately inaccurate.
We know that the blade slashes at 5-feet 1-inch. We never need to measure either guy to know that the one who died was taller than the one who was too short to get hit.
Mathematics is not reality. Maths is just a way to measure reality, and it isn't the only way. It's usually a very good way, but 'garbage in, garbage out'. If you deliberately make your maths inaccurate, this changes absolutely nothing about the reality!
if, for some reason inches did not matter in the measurement then yes, they are effectively the same height
No, the system you are using to measure their height has no effect on their actual height.
2 is less than 2.5. If you deliberately choose to use inaccurate maths, this doesn't change the reality that 2 is less than 2.5.
Q: A sheep has four legs. If you call it's tail a leg, how many legs does that sheep have?
A: It has four legs! You can call the tail whatever you want, it doesn't mean that it's a leg.
The way we choose to describe and understand reality has no effect on the reality we are observing.
Just because you choose to approximate 2.5 as 2, this doesn't mean that a post that is 2.5 feet high is actually only 2 feet high. And we don't need to use maths to answer a question just because maths can answer that question. There are other ways available.
Hmmn, how often do the rules actually ask you to round?
Actually, I agree now - the wording in the rounding section should be different. While I think it's pretty well accepted and established that you always round fractional values, this isn't what it actually says in the rules, thus is FAQ/errata worthy.
Anyway, you've made a good point, and I hope the wording gets fixed. Please tell me you're not planning to argue this in actual games tho, lol.
What I'll be planning to argue is for people to use common sense. This ability is clearly meant give Grit/Panache back only in cases where you take down a mob that is greater than or equal to half your level in HD.
The fact that people are trying to argue for and apply a vague game mechanic in an effort to squeeze out an unnecessary advantage that was never intended, is what I, and I hope any reasonable GM, would put a stop to.
Seriously, step back from the rounding argument for a second.. Does anyone here honestly think the intent was for grit to be recovered at less than half your HD?
@Dr Grecko
There are some that do.
I'm curious if you think your stance is also the RAI? The only value in arguing RAW is so you can get to the RAI, then accept that or house rule it differently if you don't like it.My stance is almost exclusively from RAI. Given the general feel of Pathfinder, it seems like the Devs (I don't know what PDT means) want the heroes to have the advantage. It's been stated that CR = Level - 1 because of this very reason. I get the general impression, that when possible, you err in favor of the players. When I first posted the question, I was thinking 5th level, which is the difference between level 2 and level 3 enemies. At 5th level it's not really much of a difference. Then I considered level 3. When you're 3rd level you'd only get panache back with a level 2 monster. That doesn't seem in favor of the player at all. This is what has me convinced that RAI is to round down. I don't know that's the case, but I believe it is.
The fact that the rules completely support that position helps.
I find Jodokai's reason for it (in bold above) to be flawed though. That reasoning just doesn't bear out when you look at player HP when gaining a new level and taking half the die. Or calculating save DC's for player abilities based on half-level. Rounding the fractions down in these cases certainly does not err in favor of the players.
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that's because division hasn't happened yet, it made it more accurate by multiplying before the division, but you cannot divide and then multiply and always have it equal the same thing. they sometimes do, like 6/2 and then *2, will get 6 again, just because sometimes it can cause it to become equal does not mean EVERYTIME they can, thus they still are not equal and opposite reactions.
you keep using my numbers out of context, all i need to prove that they cannot equate on opposite sides is show one instance where they do not create the same solution.
i did that
3 <= 7/2 and 3*2 <= 7 do not create the same solution, they are not equal, and thus my proof still stands that they are not interchangable.
however, 7 == 7*2/2 is still true but 7 != (7/2)*2.
you haven't proved anything at all, but taken the math out of context.
What context am I ignoring exactly? Your arguments seem a bit disjointed. As far as I can tell, you don't like my argument so you are blanket stating that I'm taking it out of context. How does context matter in a math proof? You have axioms and you prove a result from those axioms. That's what a math proof is. Context doesn't enter into it.
I took your "proof" as an axiom, which is to say I assumed it to be true. All I then did is show that by necessity if your proven nonequality exists we can't treat 1/2 the same as dividing by 2. That is a necessary logical consequence of your previous statements. I'm not warping your words or leaving out statements to give a false impression of your stance. I'm really not arguing in bad faith here. I'm just trying to keep the math side of this discussion accurate and honest.
@Dr Grecko
There are some that do.
I'm curious if you think your stance is also the RAI? The only value in arguing RAW is so you can get to the RAI, then accept that or house rule it differently if you don't like it.My stance is almost exclusively from RAI. Given the general feel of Pathfinder, it seems like the Devs (I don't know what PDT means) want the heroes to have the advantage. It's been stated that CR = Level - 1 because of this very reason. I get the general impression, that when possible, you err in favor of the players. When I first posted the question, I was thinking 5th level, which is the difference between level 2 and level 3 enemies. At 5th level it's not really much of a difference. Then I considered level 3. When you're 3rd level you'd only get panache back with a level 2 monster. That doesn't seem in favor of the player at all. This is what has me convinced that RAI is to round down. I don't know that's the case, but I believe it is.
The fact that the rules completely support that position helps.
I find Jodokai's reason for it (in bold above) to be flawed though. That reasoning just doesn't bear out when you look at player HP when gaining a new level and taking half the die. Or calculating save DC's for player abilities based on half-level. Rounding the fractions down in these cases certainly does not err in favor of the players.
I agree and would actually argue that you typically go the other way. While the game is generally designed for the players to win, pretty consistently whenever these types of questions come up, the Developers rule in the more conservative fashion, meaning they typically rule against the reading that is more permissive or beneficial to the player. So I generally read these ambiguities in the manner that is least beneficial to the player, unless directed otherwise. Rarely has that been wrong. Not exclusively, but rarely.
I run this with straight math because I don't think rounding is necessary here. But, as I've said a couple of times in this thread, it won't surprise me if the PDT would simply tell us to round down for the sake of ease and (relative) uniformity. Seems a bit silly and unnecessary to me, but I think that's probably the more likely outcome, all things considered. Until it's expressly stated, I'm not going to assume a blanket mandate on rounding in all scenarios, though.
Seriously, step back from the rounding argument for a second.. Does anyone here honestly think the intent was for grit to be recovered at less than half your HD?
As has been pointed out, yes I seriously believe that it was intended for you to get panache back if you are level 3 and defeat a level 1 monster.
I get what you're saying though. I've been in a lot of threads where I've thought "there's no way this guy doesn't know exactly what's intended and is just arguing because it's the way he wants it to be" I assure that is not going on here. Really how much of a difference does it make? Very little either way. No matter who's right, how often is it really going to come up? If I'm right, will that suddenly make swashbucklers way overpowered and ruin everyone's game? If you're right are swashbucklers suddenly so gimped as to be unplayable? Of course not. I genuinely believe that it was intended that you round down, just like in every other instance when taking half a level.
@bbangerter -
The key there is "when possible". The Devs made a call, you always round down. This probably had nothing to do with Hit Points at the time, it was just what they decided (or maybe it was the 1st, 2nd, 3rd, or 3.5 edition guys, who knows?). In order to give the player hit points they would have to start being inconsistent. Round down here, round up there, keep the fraction over there, etc. It was round down, so it wasn't possible to err in favor of the players on some things.
Again all that is my personal point of view, not trying to use it as an argument to prove anything.
Seriously, step back from the rounding argument for a second.. Does anyone here honestly think the intent was for grit to be recovered at less than half your HD?As has been pointed out, yes I seriously believe that it was intended for you to get panache back if you are level 3 and defeat a level 1 monster.
Really? Presuming the rounding rule applies here (to which there is no conclusive rules support), Do you honestly think it was design intent for Panache/Grit to be the ONE ability where taking half your level rounded down actually helps you rather than hinders you?
Really? Presuming the rounding rule applies here (to which there is no conclusive rules support), Do you honestly think it was design intent for Panache/Grit to be the ONE ability where taking half your level rounded down actually helps you rather than hinders you?
You are assuming the devs want you to be hindered. That their philosophy is to punish players whenever possible. That seems more of a stretch then assuming they err on the players side. Rounding hit points helps players too, because a 1 HD monster has 4 hp not 5 hp. The evil monk's stunning fist save is 14 not 15. So no this wouldn't be the only time it helps players. Rounding down in the general rule, sometimes it helps, sometimes it hinders. If we assume no bias for or against players, all we're left with is what is usually done. Rounding down is what is usually done (and by usually I mean there isn't a single instance where it isn't done that isn't specifically called out).
There's also support for "err on the players side" based on CR. CR = Level - 1 to give the advantage to the players. It's right there in the game design.
As far as "No conclusive rules support", there's no conclusive rules support that you round the Stunning Fist DC either, but you accept that.
Rounding hit points helps players too, because a 1 HD monster has 4 hp not 5 hp. The evil monk's stunning fist save is 14 not 15. So no this wouldn't be the only time it helps players.
You mis-interpreted what I said. I'll try again.
In all cases I'm aware of, rounding down hinders the entity which is the recipient of the rounding. In both of your listed cases, a 4 hp monster is hindered by rounding. The evil monks stunning fist is hindered by rounding. Whether it helps or hurts the players is irrelevant to the discussion. It's the recipient of the rounding that is hindered.
It's the same with an Level 5 Undead Lord only being able to create 2HD burning skeletons.
The rounding rule always hinders the recipient of the round..
Why would you think that suddenly Panache should work any different?
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Rounding hit points helps players too, because a 1 HD monster has 4 hp not 5 hp. The evil monk's stunning fist save is 14 not 15. So no this wouldn't be the only time it helps players.You mis-interpreted what I said. I'll try again.
In all cases I'm aware of, rounding down hinders the entity which is the recipient of the rounding. In both of your listed cases, a 4 hp monster is hindered by rounding. The evil monks stunning fist is hindered by rounding. Whether it helps or hurts the players is irrelevant to the discussion. It's the recipient of the rounding that is hindered.
It's the same with an Level 5 Undead Lord only being able to create 2HD burning skeletons.
The rounding rule always hinders the recipient of the round..
Why would you think that suddenly Panache should work any different?
I'm with you - but for different reasons. Not because of help/hinder. But because of what 1/2 means.
Half means half. Not slightly less than half or slightly more than half. Half means exactly half.
In Pathfinder context - it's almost always 'at least half', in effect if not actually worded that way. They worded the rounding rules the way they did because 98% of the time, 'at least half' means to round down.
but you cannot actually prove that one is taller than another without first measuring them, turning their heights into numbers and showing that X value is higher than Y value.Rubbish! Both are standing together, a blade slashes at a height of exactly 5-feet 1-inch. One dies, the other is untouched. You would have it that both are untouched, simply because the system you chose to measure this is deliberately inaccurate.
We know that the blade slashes at 5-feet 1-inch. We never need to measure either guy to know that the one who died was taller than the one who was too short to get hit.
Mathematics is not reality. Maths is just a way to measure reality, and it isn't the only way. It's usually a very good way, but 'garbage in, garbage out'. If you deliberately make your maths inaccurate, this changes absolutely nothing about the reality!
except, even when standing next to each other, you still have no proven one is actually taller than another. If i asked you to provide me with your evidence, you would be forced to simply show them next to each other, and then declare that one was taller than the other. I would still demand proof, because nothing had been recorded or analyzed.
In essence, something being obviously one or the other, does not count as proof. If one was 5 foot and the other was 5'1" I would definitely need tested measurements.
if, for some reason inches did not matter in the measurement then yes, they are effectively the same heightNo, the system you are using to measure their height has no effect on their actual height.
2 is less than 2.5. If you deliberately choose to use inaccurate maths, this doesn't change the reality that 2 is less than 2.5.
Q: A sheep has four legs. If you call it's tail a leg, how many legs does that sheep have?
A: It has four legs! You can call the tail whatever you want, it doesn't mean that it's a leg.
The way we choose to describe and understand reality has no effect on the reality we are observing.
Just because you choose to approximate 2.5 as 2, this doesn't mean that a post that is 2.5 feet high is actually only 2 feet high. And we don't need to use maths to answer a question just because maths can answer that question. There are other ways available.
it does effect their height, if your measuring to see who is of a taller height category, and the categories are in feet, you really do not need to know inches, however, using more precise standards will impact results. thus the system effected their effective height.
this is all assuming you have some reason you want to round, if you want definitive, who is taller to the nth accuracy. then you would not round.
however, pathfinder wants all of it's calculations to be simple and to not get math intensive, so you cut off fractions and decimals so that your sheet is neat, and your math is quick.
if you call a sheeps tail a leg, then when you are told to list everything on a sheep that is a leg, you would have 5 things on your list. seeing as whether something is or is not something is purely based on what your define the word as, so if you add in that tails are legs, that is another type of leg that you count.
a less straw man argument is if you have a collection of balls. 3 orange, 4 red, 6 green, and 2 blue. you are supposed to count how many red balls you have and determine if they are the most plentiful, but orange is counted as red. so you have 7, and they're the most plentiful since they beat out every other population.
if you want to prove that your system is even possible you must prove that at least one exception to my "when ever you compare 2 numbers, round before the comparison" exists.
I have proven several exceptions to your "multiply the other side by 2" posit and your posit on the system not effecting your effective statistics, and provided a more inclusive theorem of how pathfinder behaves. You must prove that pathfinder doesn't behave this way by listing an in engine example, if you cannot find one, then it is unlikely the engine works under your theory.
that's because division hasn't happened yet, it made it more accurate by multiplying before the division, but you cannot divide and then multiply and always have it equal the same thing. they sometimes do, like 6/2 and then *2, will get 6 again, just because sometimes it can cause it to become equal does not mean EVERYTIME they can, thus they still are not equal and opposite reactions.
you keep using my numbers out of context, all i need to prove that they cannot equate on opposite sides is show one instance where they do not create the same solution.
i did that
3 <= 7/2 and 3*2 <= 7 do not create the same solution, they are not equal, and thus my proof still stands that they are not interchangable.
however, 7 == 7*2/2 is still true but 7 != (7/2)*2.
you haven't proved anything at all, but taken the math out of context.
What context am I ignoring exactly? Your arguments seem a bit disjointed. As far as I can tell, you don't like my argument so you are blanket stating that I'm taking it out of context. How does context matter in a math proof? You have axioms and you prove a result from those axioms. That's what a math proof is. Context doesn't enter into it.
I took your "proof" as an axiom, which is to say I assumed it to be true. All I then did is show that by necessity if your proven nonequality exists we can't treat 1/2 the same as dividing by 2. That is a necessary logical consequence of your previous statements. I'm not warping your words or leaving out statements to give a false impression of your stance. I'm really not arguing in bad faith here. I'm just trying to keep the math side of this discussion accurate and honest.
by context I mean you are giving my numbers a different context.
you thought I was doing 4*(1/2), which I wasn't I was doing 4*1/2. in normal order of operations that becomes 2. you suggested that the 1/2 didn't exist, which it doesn't, it was 1 divided by 2. not 0.5.
that is all.
you are stating that X/2 is not equal to X*(1/2), which I agree with.
I am saying X/2 is equal to X*1/2
order of operations are P E M D A S, so multiplication always get's moved higher in the turn order.
this is pure left to right order of operations. so by context again to clarify, I believe you misunderstand what I mean by 1/2 and my order of operations. 1/2 is not "half", 1/2 is half of 1. like wise X/2 is half of X, you can have half of a value but half itself does not exist. half exists as an action or a adjective only not a noun.
so four times half of one, is a logical statement, but four times a half is not, but once again half of 4 is still logical. If this doesn't clarify it for you, I will have trouble finding better ways to say it.
Rounding hit points helps players too, because a 1 HD monster has 4 hp not 5 hp. The evil monk's stunning fist save is 14 not 15. So no this wouldn't be the only time it helps players.You mis-interpreted what I said. I'll try again.
In all cases I'm aware of, rounding down hinders the entity which is the recipient of the rounding. In both of your listed cases, a 4 hp monster is hindered by rounding. The evil monks stunning fist is hindered by rounding. Whether it helps or hurts the players is irrelevant to the discussion. It's the recipient of the rounding that is hindered.
It's the same with an Level 5 Undead Lord only being able to create 2HD burning skeletons.
The rounding rule always hinders the recipient of the round..
Why would you think that suddenly Panache should work any different?
I'm with you - but for different reasons. Not because of help/hinder. But because of what 1/2 means.
Half means half. Not slightly less than half or slightly more than half. Half means exactly half.
In Pathfinder context - it's almost always 'at least half', in effect if not actually worded that way. They worded the rounding rules the way they did because 98% of the time, 'at least half' means to round down.
except that in every case of "half your level" you round down. so we have precedent.
Rounding hit points helps players too, because a 1 HD monster has 4 hp not 5 hp. The evil monk's stunning fist save is 14 not 15. So no this wouldn't be the only time it helps players.You mis-interpreted what I said. I'll try again.
In all cases I'm aware of, rounding down hinders the entity which is the recipient of the rounding. In both of your listed cases, a 4 hp monster is hindered by rounding. The evil monks stunning fist is hindered by rounding. Whether it helps or hurts the players is irrelevant to the discussion. It's the recipient of the rounding that is hindered.
It's the same with an Level 5 Undead Lord only being able to create 2HD burning skeletons.
The rounding rule always hinders the recipient of the round..
Why would you think that suddenly Panache should work any different?
So you're going with the "you don't round because the devs want to screw you over" theory? And you're asking me if I'm serious?
to be clear, lower half level means that an additional level of enemy can be used to gain panache at odd levels... it is a very situation and minor buff.
@ Dr Grecko and Jodokai argument since i'm not sure if they're actually arguing the same thing at each other.
It matters most at low levels -- you are far more likely to be fighting a foe with one hit die at 3rd level than you are to be fighting one with 10 hit dice at 20th level.
to be clear, lower half level means that an additional level of enemy can be used to gain panache at odd levels... it is a very situation and minor buff.
@ Dr Grecko and Jodokai argument since i'm not sure if they're actually arguing the same thing at each other.
That was what I was saying, it's really not going to change anything either way.
@ Dr Grecko - So what if the monsters are hindered? They are NPC's so hindering them helps the people actually playing the game. The monsters were screwed when CR became level - 1... which was actually done to give PC's the advantage... Which goes against your "the devs want to screw us" theory.
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by context I mean you are giving my numbers a different context.
you thought I was doing 4*(1/2), which I wasn't I was doing 4*1/2. in normal order of operations that becomes 2. you suggested that the 1/2 didn't exist, which it doesn't, it was 1 divided by 2. not 0.5.
that is all.
you are stating that X/2 is not equal to X*(1/2), which I agree with.
I am saying X/2 is equal to X*1/2
order of operations are P E M D A S, so multiplication always get's moved higher in the turn order.
this is pure left to right order of operations. so by context again to clarify, I believe you misunderstand what I mean by 1/2 and my order of operations. 1/2 is not "half", 1/2 is half of 1. like wise X/2 is half of X, you can have half of a value but half itself does not exist. half exists as an action or a adjective only not a noun.
so four times half of one, is a logical statement, but four times a half is not, but once again half of 4 is still logical. If this doesn't clarify it for you, I will have trouble finding better ways to say it.
I think you are using a lot of words to express the idea that you think multiplication and division aren't commutative in this number system. The problem is, once you throw away commutivity, you lose the idea that division is in any way related to multiplication.
Saying X/2 = X*1/2 is a vacuous statement. It contains no useful information, except that you still consider 1 to be the multiplicative identity.
"A" half is "one" half. The article "a" implies one of something, it's just a shorthand. And no, in the integers "half" is an undefined concept. You can't just pull things in from other number fields like the reals and use them willy-nilly. In integers 7 divided by 2 doesn't have an answer. It's not rounded, it's undefined. Similarly once you write 1/2 in the integers you are basically dividing by 0 - either division gets you no answer.
I think we're about done. At this point we're pretty much going in circles as you keep repeating the same arguments - which to be fair, are somewhat reasonable for someone who knows a little bit of math well but hasn't explored some of its more abstract concepts. You seem like a computer-science type person, and I have no idea where you are in your life, but you would probably do well in upper/graduate level math classes where abstract stuff really gets delved into, if you have a grounding in basic math like calculus. You certainly have a mind for math concepts I just think you lack some information about how math is fundamentally "built." I think I've represented my point that Pathfinder uses more than just the integers for its math. We need at least the rational numbers or else fractional values have no meaning.
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Who doesn't love discussion of commutative rings in the morning?
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except that in every case of "half your level" you round down. so we have precedent.Rounding hit points helps players too, because a 1 HD monster has 4 hp not 5 hp. The evil monk's stunning fist save is 14 not 15. So no this wouldn't be the only time it helps players.You mis-interpreted what I said. I'll try again.
In all cases I'm aware of, rounding down hinders the entity which is the recipient of the rounding. In both of your listed cases, a 4 hp monster is hindered by rounding. The evil monks stunning fist is hindered by rounding. Whether it helps or hurts the players is irrelevant to the discussion. It's the recipient of the rounding that is hindered.
It's the same with an Level 5 Undead Lord only being able to create 2HD burning skeletons.
The rounding rule always hinders the recipient of the round..
Why would you think that suddenly Panache should work any different?
I'm with you - but for different reasons. Not because of help/hinder. But because of what 1/2 means.
Half means half. Not slightly less than half or slightly more than half. Half means exactly half.
In Pathfinder context - it's almost always 'at least half', in effect if not actually worded that way. They worded the rounding rules the way they did because 98% of the time, 'at least half' means to round down.
You totally ignored the point of my post.
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So you're going with the "you don't round because the devs want to screw you over" theory? And you're asking me if I'm serious?
That's not what I'm saying at all. It has absolutely NOTHING to do with "screwing" anybody over, and everything to do with consistent game design... I'll try to explain again.
Panache/Grit, is the ONLY game mechanic involving half/level for ANY Class, Monster, NPC, ect, where rounding helps them instead of hinders.
More examples:
A Clerics Channel Save DC is hindered by the 1/2 rule
The Save DC's against Oracle Revelations is hindered by the 1/2 rule
@ Dr Grecko - So what if the monsters are hindered? They are NPC's so hindering them helps the people actually playing the game. The monsters were screwed when CR became level - 1... which was actually done to give PC's the advantage... Which goes against your "the devs want to screw us" theory.
Again, missing the point here.. This has nothing to do with "devs wanting to screw us" and everything to do with "devs being consistent in game design".
The CR = Level - 1 is irrelevant to the consistent 1/2 argument so I wont bother addressing it.
Again I'll say that Panache/Grit is the ONLY exception (that I could find) to the 1/2 rule.. whether it's Players or GM's controlling the character/monsters is irrelevant. Do you SERIOUSLY think this was intentional?
Again I'll say that Panache/Grit is the ONLY exception (that I could find) to the 1/2 rule.. whether it's Players or GM's controlling the character/monsters is irrelevant. Do you SERIOUSLY think this was intentional?
Ah nicely done. Since you can't come up with any examples where you round up, you have to change the tactic and make me come up with completely irrelevant examples that have no actual bearing on game design, despite your claims.
Do you honestly believe this is how the conversation went:
Dev 1: Let's say they get Panache back if the monster is at least half their level.
Dev 2: What if they're at an odd level?
Dev 1: We round down just like always.
Dev 2: But wait, won't that actually benefit them? I mean in ever other place rounding down isn't good?
Dev 1: Oh snap, you're right! We should totally change the way we do things to make sure they don't benefit.
Dev 2: Totally. Should we include something about de facto rounding up in the this ability since it's the ONLY place we do it?
Dev 1: Nah, they'll figure it out on their own, they should know rounding would never benefit them, I mean it's a core rule everybody understands.
The Devs (some devs, probably way back at Gary Gygax) decided the general rule would be to round down. Whether that benefits or hinders is completely and totally irrelevant, and I'm forced to wonder if you realize that, and are just trying anything to prove your side of the argument.
EDIT: as far as CR, yes, it probably would be best to ignore arguments that disprove your interpretation of how the game was designed
/FACEPALM
Lets go over this line by line.
Ah nicely done. Since you can't come up with any examples where you round up, you have to change the tactic and make me come up with completely irrelevant examples that have no actual bearing on game design, despite your claims.
I've never claimed anywhere that you round up, classical straw-man there. What I have done is provide evidence that satisfies my burden of proof that Panache/grit is the only rounding mechanic where rounding down is beneficial. Unless you can provide evidence otherwise, that argument stands.
Do you honestly believe this is how the conversation went: **Fictional Conversation Omitted**
No. I do not believe the conversation went that way. That would imply intent, I clearly stated that if anything, Panache/Grits Uniqueness to the general rule was UN-intentional.
My own made up conversation would go something like this.
Dev 1: Let's say they get Panache back if the monster is at least half their level.
Dev 2: Sounds good, lets do it.
... Sometime during testing
Dev 1: Ok, so my level five Gunslinger kills the monster, What was his HD?
Dev 2: Two
Dev 1: Dang! not quite half. Maybe that big guy over there will get me some grit back!
The Devs (some devs, probably way back at Gary Gygax) decided the general rule would be to round down.
Yes, that is the general rule.
Whether that benefits or hinders is completely and totally irrelevant, and I'm forced to wonder if you realize that, and are just trying anything to prove your side of the argument.
I'm suggesting it is absolutely NOT irrelevant. Consistency matters. And I fully believe that you were never intended to gain grit back on a 2HD creature at L5. It's an unintentional oversight.
In spite of ALL that, if you read the RAW in the strictest sense, you still don't need to round here.
EDIT: as far as CR, yes, it probably would be best to ignore arguments that disprove your interpretation of how the game was designed
I'm ignoring it because it truly is irrelevant to any of the arguments being made here.