Says who? It certainly doesn't say that in the ability in question!
The ability just says, 'Confirming a critical hit on a ... creature that has fewer hit dice than half the swashbuckler's character level doesn't restore panache'.
There is absolutely no mandated way of ascertaining whether the target has fewer hit dice than half your level. You can do it any way that gives an accurate answer....
At this point, it's pretty obvious, without Dev intervention you'll never agree. You'll continue to make up rules and convince yourself that this one situation is wholly unique and special rules (the ones you make up mind you) have to apply.
I say it this way, because we both know that no where else in the entire game is "half your level" figured out that way. In every single instance when the rules say "half your level" you divide by two and round down. You have to see by now that you're completely making stuff up on the fly just to try to make your point. You're going so far out into left field, at this point you are either A) Doing it on purpose to see how long you can keep this going. or 2) You don't care what it should be, you're going to do it your way. Either way, no amount of logic will ever convince you.
RPG Superstar 2011 Top 32
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I agree with Malachi on this one. There is no need to round in this instance so rounding rules don't have to apply. I will concede that the issue is unclear, however. I find the FCB argument of "gain 1/x of a class feature" convincing that you don't round in all cases of a fraction.
I disagree with the blanket assertion that Pathfinder uses integer math. While the rounding system does match that of an integer number system, the jumps to "therefore PF uses integer math in all cases" and "therefore the other rules of integer mathematics apply" are not supported or provable. I find no indication in the rules that we are dealing with any number system besides the reals, with the normal operations allowed in such a system. There are just some exceptions like the rounding rules.
This is also a pretty minor issue. It can be a fun discussion but really how often do you fight creatures of the exact HD where this would come up? If you're a level 3 or 5 swashbuckler in PFS ask your GM when you sit down how it will work otherwise just work it out with your group. Honestly by level 7 you probably aren't fighting much with 3 HD anymore.
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Says who? It certainly doesn't say that in the ability in question!
The ability just says, 'Confirming a critical hit on a ... creature that has fewer hit dice than half the swashbuckler's character level doesn't restore panache'.
There is absolutely no mandated way of ascertaining whether the target has fewer hit dice than half your level. You can do it any way that gives an accurate answer....
At this point, it's pretty obvious, without Dev intervention you'll never agree. You'll continue to make up rules and convince yourself that this one situation is wholly unique and special rules (the ones you make up mind you) have to apply.
I say it this way, because we both know that no where else in the entire game is "half your level" figured out that way. In every single instance when the rules say "half your level" you divide by two and round down. You have to see by now that you're completely making stuff up on the fly just to try to make your point. You're going so far out into left field, at this point you are either A) Doing it on purpose to see how long you can keep this going. or 2) You don't care what it should be, you're going to do it your way. Either way, no amount of logic will ever convince you.
The swashbuckler is not instructed or required to divide his level by two.
We also know that PF does not use integer math. If it did, there would be no need for a section entitled, 'Rounding'.
What if you're the one who is wrong?
I'm not. I have every example in every single place in the rules to back me up. He has nothing except stuff he's made up on the fly.
Now, I'm not saying that the PDT (figured out what it meant) don't want Swashbuckler to be an exception, they might, but that's exactly what it would be, an exception.
As it's written right now, without an official answer to the FAQ, you have two choices: Accept that it is figured exactly like every other time that it ever happens in the rules, or assume this is the one exception to those rules.
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What if you're the one who is wrong?I'm not. I have every example in every single place in the rules to back me up. He has nothing except stuff he's made up on the fly.
Now, I'm not saying that the PDT (figured out what it meant) don't want Swashbuckler to be an exception, they might, but that's exactly what it would be, an exception.
As it's written right now, without an official answer to the FAQ, you have two choices: Accept that it is figured exactly like every other time that it ever happens in the rules, or assume this is the one exception to those rules.
Except that it is not an example of those rules. There is no instruction to find 'half the swashbuckler's level', therefore this is not an exception to the rounding rules. There is nothing to round.
Uh, I would really like to see you prove that "2 is less than half of 5" with integer math.Sure. In order to find if the smaller number is less than half of the larger, simply double the smaller number; if double the smaller is less than the larger, then the smaller is less than half the larger.
Double 2 is 4.
2 is half of 4.
4 is less than 5.
Therefore, half of 4 (=2) is less than half of 5.
Therefore, 2 is less than half of 5.
No fractions, no mistakes, base ten.
Q, E, and indeed, D.
in integer math, multiplication and division are not considered opposites, thus (X/2)*2 are not necessarily equal to (X)
and thus
X*2<Y != X<Y/2
I don't know what you mean when you say 'Integer math'. What I'm talking about are calculations where each number in that calculation happens to be an integer.
In the real world, multiplication and division are indeed opposites.
In all honesty, do you think that the game uses your strange version of multiplication/division, or do you think that the game simply has us round fractions down? Bearing in mind that the game rules have this information in a section entitled 'Rounding', not 'Division'?
If it turns out that you know about an esoteric branch of mathematics that I don't, congratulations. You know more than me about 'Integer Math', whatever that is. But do you really think that the game engine uses this strange math, without telling us? Or do we just 'always round down'?
it not strange it is a form of mathematics that only uses integers. it is common in computer programming as integers are more space compact that floating points.
when the rules say always round down, you basically ARE doing integer math.
remember that math you did in 1st grade or so, where you have remainders? that is integer math. I don't actually remember what it is called, i simply remember being referred to as integer math in college when i was just getting into computer science. I think it may actually just be Modular Arithmatic, but it doesn't really matter what you call it.
yes, I think pathfinder does use this as it effectively is the same as always round down.
This 'Integer Math' is not used in Pathfinder. The only difference between PF math and normal math is the rule for rounding.
what he means is that in integer math 9/2 == 4 is factually accurate. it will always return true.
I agree with Malachi on this one. There is no need to round in this instance so rounding rules don't have to apply. I will concede that the issue is unclear, however. I find the FCB argument of "gain 1/x of a class feature" convincing that you don't round in all cases of a fraction.
I disagree with the blanket assertion that Pathfinder uses integer math. While the rounding system does match that of an integer number system, the jumps to "therefore PF uses integer math in all cases" and "therefore the other rules of integer mathematics apply" are not supported or provable. I find no indication in the rules that we are dealing with any number system besides the reals, with the normal operations allowed in such a system. There are just some exceptions like the rounding rules.
This is also a pretty minor issue. It can be a fun discussion but really how often do you fight creatures of the exact HD where this would come up? If you're a level 3 or 5 swashbuckler in PFS ask your GM when you sit down how it will work otherwise just work it out with your group. Honestly by level 7 you probably aren't fighting much with 3 HD anymore.
in FCB you never have the FCB have an effect until you have a full FCB. This had to be clarified, because many people didn't understand what 1/2 of a rogue talent was, not because it was an exception. anyway, fractions are easier to handle in integer math, you simply don't divide til the end though the use of (). so it becomes quite easily (6*1)/6. and this is effectively what happens. then 6*1/6 >= 1 is true and the effect takes place.
and I claim pathfinder use integer math, whenever it needs to always round down.
I also, claim that the half your level thing is EXACTLY like a DC, in that is can be recorded and then later referenced, exactly like a DC.
doing it any other way is needlessly pedantic and doesn't mesh well in play that you should recalculate it every time, as malachi is saying, as it is more likely he just has it memorized or written down some where, exactly like a DC would be. it's still some number must reach at least this value to take effect, and I don't understand the distinction from a rules stand point.
I love when people post stuff like this. Especially when the PDT come back and rule against them. :)What if you're the one who is wrong?I'm not. I have every example in every single place in the rules to back me up. He has nothing except stuff he's made up on the fly.
I love it when people quote part of post and remove the part that counters their snark comment.
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it not strange it is a form of mathematics that only uses integers. it is common in computer programming as integers are more space compact that floating points.
It's a strange form of mathematics where multiplication and division are not opposites. If 9/2=4, then 4x2=9.
when the rules say always round down, you basically ARE doing integer math.
remember that math you did in 1st grade or so, where you have remainders? that is integer math. I don't actually remember what it is called, i simply remember being referred to as integer math in college when i was just getting into computer science. I think it may actually just be Modular Arithmatic, but it doesn't really matter what you call it.
yes, I think pathfinder does use this as it effectively is the same as always round down.
If I understand you correctly, then what you mean by 'integer math' is that you simply ignore any fraction/remainder in any part of any calculation.
This is a different thing than simple 'rounding', where you keep all fractions all the way through the calculations, until you get to the final term used (like the DCs and modifiers in a stat block), where you then round as instructed.
Pathfinder, in these terms, uses rounding but does not use integer math. If average hit points per hit die were calculated using integer math, then the average of each d8 would be 4, not the real result of 4.5. In integer math, the average hit points of a creature with 5d8 HD would be (5 x 4 =) 20. Yet the PF maths is (5 x 4.5 =) 22.5, rounded down to 22.
On the topic of hit points:
There is a huge difference between design math which is specifically used to approximate a dice function and game play math. They should not be used as part of opposed arguments.
Easy way to tell them apart, if a rule tells you to average multiple dice rolls then you are doing game design. You can tell because if you were playing then the game would tell you to roll the dice. Don't let design shortcuts influence the way you read the rules for gameplay.
it not strange it is a form of mathematics that only uses integers. it is common in computer programming as integers are more space compact that floating points.It's a strange form of mathematics where multiplication and division are not opposites. If 9/2=4, then 4x2=9.
when the rules say always round down, you basically ARE doing integer math.
remember that math you did in 1st grade or so, where you have remainders? that is integer math. I don't actually remember what it is called, i simply remember being referred to as integer math in college when i was just getting into computer science. I think it may actually just be Modular Arithmatic, but it doesn't really matter what you call it.
yes, I think pathfinder does use this as it effectively is the same as always round down.
If I understand you correctly, then what you mean by 'integer math' is that you simply ignore any fraction/remainder in any part of any calculation.
This is a different thing than simple 'rounding', where you keep all fractions all the way through the calculations, until you get to the final term used (like the DCs and modifiers in a stat block), where you then round as instructed.
Pathfinder, in these terms, uses rounding but does not use integer math. If average hit points per hit die were calculated using integer math, then the average of each d8 would be 4, not the real result of 4.5. In integer math, the average hit points of a creature with 5d8 HD would be (5 x 4 =) 20. Yet the PF maths is (5 x 4.5 =) 22.5, rounded down to 22.
isn't average hit dice only used in PFS? and is it's own special rules on how your HP is calculated? if average hit dice are actually used in core pathfinder, please show me so I can be running on the most accurate information.
also the mean of HD are actually
(1+...+DieNum)/DieNum
in which case you simply do
NumberOfDice*(1=...+DieNum)/DieNum
also yes, in integer math you remove fractions and decimals and replace them with equivalent arithmetic. in it 9/2=4 but (9/2)*2=8
I love when people post stuff like this. Especially when the PDT come back and rule against them. :)What if you're the one who is wrong?I'm not. I have every example in every single place in the rules to back me up. He has nothing except stuff he's made up on the fly.
That's why they should add:
Now, I'm not saying that the PDT (figured out what it meant) don't want Swashbuckler to be an exception, they might, but that's exactly what it would be, an exception.
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If PF used integer math as part of its game engine, they would at least mention it!
They would be proud of this departure from the norm, remind us that we're using this strange form of math where multiplication and division are not opposite, and use it every chance they get.
If PF used integer math, then average HP/HD would proudly drop the fraction before multiplying by level.
If PF used integer math, then it would have a section entitled, 'Integer Math', or 'Fractions'. They would say that 'rounding' was a fundamental part of the game system, and it always happens at every stage of every calculation, to contrast it with the 'normal' rounding which only happens at the final answer.
So, what did they write?
Rounding: Occasionally the rules ask you to round a result or value.
'Occasionally'? Doesn't the game engine use this strange 'integer math' as a fundamental part of the game system?
Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3.
So, the example of '7 divided by 3' is an example of rounding! And the rules 'occasionally' ask you to round a result or value!
This isn't evidence for the assertion that the game uses integer math! This is evidence against that assertion!
Incidentally, the fact that the game talks you through how to work out average hit points does not mean that this is an exception to the way PF usually works.
Why? It doesn't change the amusement generated by the "What if you're wrong?" "I'm not." "Actually...." chain.
We've had these discussions before, and the PDT has made calls that surprised a lot of people.
You're not getting what I'm saying. It won't surprise me at all if the PDT goes against my position. What I am saying is that if they do go against my position, it is because they want it to be an exception to the rules. Everything I've said is correct based on every example in the book. Even if PDT does go against my position, I still am not wrong. The rules clearly indicate you round before comparing numbers.
In none of my statements have I had to come up with my own rules like "doubling HD instead of dividing levels", or "it's only rounded when you have to write it down" to prove the veracity of my statements. My entire position is in the book it says_____. All of my statements are giving examples from the book.
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All of my statements are giving examples from the book.
Yes, and they are okay. But the ability we are discussing does not fall into that category.
In this ability, there is no establishing a DC, no working out a modifier, no creating a creature with a certain amount of hit points or HD, in fact we are not asked to calculate a number. We are being asked if one number is less than half another. We aren't told how to do this, so we can choose any way that gets the correct answer.
The result won't be a number of HD; it won't be a number at all! It will be either:-
• yes, the target has fewer HD than half your level, so you don't regain panache
OR
• no, the target does not have fewer HD than half your level, so you regain one point of panache
There is no 'rounding' of either result.
Occasionally the rules ask you to round a result or value.
This is not one of those occasions.
Yes, and they are okay. But the ability we are discussing does not fall into that category.
This is not one of those occasions.
Only because you don't want them to. They are exactly the same.
If PF used integer math as part of its game engine, they would at least mention it!
They would be proud of this departure from the norm, remind us that we're using this strange form of math where multiplication and division are not opposite, and use it every chance they get.
If PF used integer math, then average HP/HD would proudly drop the fraction before multiplying by level.
If PF used integer math, then it would have a section entitled, 'Integer Math', or 'Fractions'. They would say that 'rounding' was a fundamental part of the game system, and it always happens at every stage of every calculation, to contrast it with the 'normal' rounding which only happens at the final answer.
So, what did they write?
Rounding: Occasionally the rules ask you to round a result or value.'Occasionally'? Doesn't the game engine use this strange 'integer math' as a fundamental part of the game system?
Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3.So, the example of '7 divided by 3' is an example of rounding! And the rules 'occasionally' ask you to round a result or value!
This isn't evidence for the assertion that the game uses integer math! This is evidence against that assertion!
Incidentally, the fact that the game talks you through how to work out average hit points does not mean that this is an exception to the way PF usually works.
when ever someone says "always round down(at least when you are rounding)" they're using integer math, plain and simple. because that is exactly how it works.
they specifically use always round down, because it is WAY simpler than trying to explain integer math, which is what most game systems actually use anyway.
on the average health thing, i asked before but didn;t get a response. is this something only used in PFS or is it used elsewhere in the core rules? I only ask because because A. I am curious and B. PFS's method for dealing with health is not really using pathfinder's math in the strictest sense.
you emphasized the "occasionally", I emphasize the "unless otherwise stated".
Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3.
All of my statements are giving examples from the book.Yes, and they are okay. But the ability we are discussing does not fall into that category.
In this ability, there is no establishing a DC, no working out a modifier, no creating a creature with a certain amount of hit points or HD, in fact we are not asked to calculate a number. We are being asked if one number is less than half another. We aren't told how to do this, so we can choose any way that gets the correct answer.
The result won't be a number of HD; it won't be a number at all! It will be either:-
• yes, the target has fewer HD than half your level, so you don't regain panache
OR
• no, the target does not have fewer HD than half your level, so you regain one point of panache
There is no 'rounding' of either result.
Occasionally the rules ask you to round a result or value.This is not one of those occasions.
the difference between meeting a DC and meeting half swashbuckler level is only in name.
both are some number must be this number or higher for this effect to happen. saying they're different is being pedantic.
if((10+casterLevel/2+intMod) <= NUMBER)
DO THE THING
if(GunslingerLevel/2 <= NUMBER)
DO THE THING
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Only because you don't want them to. They are exactly the same.Yes, and they are okay. But the ability we are discussing does not fall into that category.
This is not one of those occasions.
Or perhaps your applying a rule that shouldn't be applied in this instance.
Or perhaps your applying a rule that shouldn't be applied in this instance.
Based on what supporting evidence? That you don't round until you write it in a stat block or you double the Hit Die to find out half a level?
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when ever someone says "always round down(at least when you are rounding)" they're using integer math, plain and simple. because that is exactly how it works.
Well, that's just not true:-
• Problem: multiply 4.5 by 5
• Solution (normal math): 22.5
• Solution (integer math): 20
• Solution (round down): 22
Rounding is not the same as integer math. In integer math, fractions do not exist at any stage. With rounding, use normal math, including all fractions, but round the result as required (because there are different types of rounding: up, down, halves and greater up/lower than half down).
All of this is beside the point here, as division is not required for this ability.
when ever someone says "always round down(at least when you are rounding)" they're using integer math, plain and simple. because that is exactly how it works.Well, that's just not true:-
• Problem: multiply 4.5 by 5
• Solution (normal math): 22.5
• Solution (integer math): 20
• Solution (round down): 22
Rounding is not the same as integer math. In integer math, fractions do not exist at any stage. With rounding, use normal math, including all fractions, but round the result as required (because there are different types of rounding: up, down, halves and greater up/lower than half down).
All of this is beside the point here, as division is not required for this ability.
4.5 is made into 9/2, which in your equation becomes 9*5/2 (because 4.5 doesn't exist)
(we're using line math here since we can't as easily show that 9/2*5 is not 9/10) it's not a fraction but equivalent arithmetic. in essence it is still 2 numbers and not a single fraction of a number yet, which can still be simplified.
when ever someone says "always round down(at least when you are rounding)" they're using integer math, plain and simple. because that is exactly how it works.Well, that's just not true:-
• Problem: multiply 4.5 by 5
• Solution (normal math): 22.5
• Solution (integer math): 20
• Solution (round down): 22
Rounding is not the same as integer math. In integer math, fractions do not exist at any stage. With rounding, use normal math, including all fractions, but round the result as required (because there are different types of rounding: up, down, halves and greater up/lower than half down).
All of this is beside the point here, as division is not required for this ability.
I'm really, really curious how you calculate half of a level without division.
Just how do you do it?
lot's of subtraction? it's how computers do it.
i feel like my comment on computer division isn't entirely accurate. and is actually more wrong than right, a computer CAN do division by subtraction, but it isn't that efficient.
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when ever someone says "always round down(at least when you are rounding)" they're using integer math, plain and simple. because that is exactly how it works.Well, that's just not true:-
• Problem: multiply 4.5 by 5
• Solution (normal math): 22.5
• Solution (integer math): 20
• Solution (round down): 22
Rounding is not the same as integer math. In integer math, fractions do not exist at any stage. With rounding, use normal math, including all fractions, but round the result as required (because there are different types of rounding: up, down, halves and greater up/lower than half down).
All of this is beside the point here, as division is not required for this ability.
I'm really, really curious how you calculate half of a level without division.
Just how do you do it?
We are not asked, tasked or required to find a numerical value (integer or otherwise) for the swashbuckler's level divided by two.
We are asked to determine if the target just hit has fewer hit dice than half the swashbuckler's level.
There is no method mandated by the rules to ascertain this, and several ways are possible.
I recommend the following method. It has the benefits of perfect accuracy, ease of use (even a five-year-old would be expected to master it), and doesn't have fractions to round or decimals to ignore:-
Known values:-
• hit dice of target (HD)
• character level of swashbuckler (lvl)
Method: double (HD). If the result is less than (lvl), no panache is regained. If the result is equal to or greater than (lvl), one point of panache is regained.
Can you foresee any difficulties?
when ever someone says "always round down(at least when you are rounding)" they're using integer math, plain and simple. because that is exactly how it works.Well, that's just not true:-
• Problem: multiply 4.5 by 5
• Solution (normal math): 22.5
• Solution (integer math): 20
• Solution (round down): 22
Rounding is not the same as integer math. In integer math, fractions do not exist at any stage. With rounding, use normal math, including all fractions, but round the result as required (because there are different types of rounding: up, down, halves and greater up/lower than half down).
All of this is beside the point here, as division is not required for this ability.
I'm really, really curious how you calculate half of a level without division.
Just how do you do it?
We are not asked, tasked or required to find a numerical value (integer or otherwise) for the swashbuckler's level divided by two.
We are asked to determine if the target just hit has fewer hit dice than half the swashbuckler's level.
There is no method mandated by the rules to ascertain this, and several ways are possible.
I recommend the following method. It has the benefits of perfect accuracy, ease of use (even a five-year-old would be expected to master it), and doesn't have fractions to round or decimals to ignore:-
Known values:-
• hit dice of target (HD)
• character level of swashbuckler (lvl)
Method: double (HD). If the result is less than (lvl), no panache is regained. If the result is equal to or greater than (lvl), one point of panache is regained.
Can you foresee any difficulties?
you can only compare 2 numerical values, or at the least you have to prove 2 equations are equal by first showing that they are equal to a value.
if you do not do this you CANNOT prove that half your swashbuckler level is greater than some other value.
since
4*2 < 9
does not create the same solution as 4 < 9/2
they ARE NOT equivalent and cannot replace each other.
it specifically states to compare half your swashbuckler level, and not double the enemies HD, since they are not equivalent, they cannot be replaced.
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Division (mathematics), the inverse of multiplication.
This gives the lie to the statement:-
it specifically states to compare half your swashbuckler level, and not double the enemies HD, since they are not equivalent, they cannot be replaced.
In the nicest possible way, I believe Wikipedia over you. Also, my teachers, maths in the real world, the CRB which has no mention of 'integer math' whatsoever (and 'rounding' is not 'integer math'), basically...I believe reality over your fantasy.
Actually, you're (also) engaging in a logical fallacy, by assuming the result and using it as proof of the result. You are asserting that PF uses integer math, then (mis)interpret 'rounding' as if it were integer math, then saying 'Look! The CRB uses integer math!'
I've never been so embarrassed to be part of a thread in my life, so why do I keep posting? I keep thinking of that cartoon where the wife asks why the husband won't come to bed, and he passionately replies, 'Someone is wrong on the Internet!'
I've never seen anybody as 'wrong on the internet' as those who are seriously trying to assert that 2 is not less than half of 5.
Division (mathematics), the inverse of multiplication.This gives the lie to the statement:-
it specifically states to compare half your swashbuckler level, and not double the enemies HD, since they are not equivalent, they cannot be replaced.In the nicest possible way, I believe Wikipedia over you. Also, my teachers, maths in the real world, the CRB which has no mention of 'integer math' whatsoever (and 'rounding' is not 'integer math'), basically...I believe reality over your fantasy.
Actually, you're (also) engaging in a logical fallacy, by assuming the result and using it as proof of the result. You are asserting that PF uses integer math, then (mis)interpret 'rounding' as if it were integer math, then saying 'Look! The CRB uses integer math!'
I've never been so embarrassed to be part of a thread in my life, so why do I keep posting? I keep thinking of that cartoon where the wife asks why the husband won't come to bed, and he passionately replies, 'Someone is wrong on the Internet!'
I've never seen anybody as 'wrong on the internet' as those who are seriously trying to assert that 2 is not less than half of 5.
in the nicest way,
9/2 = 4
but 9 != 2*4
so multiplying both sides by 2 did not make an equivalent equation.
so, I literally have a mathematical proof that states otherwise. pathfinder says simply that half of 7 is 3. so I can assume half of 9 is 4. but double 4 is not 9. therefore, my point still stands. if you want to ignore this fact go ahead, but your not using mathematics to prove me wrong, that's for sure.
there is no logical fallacy, I'm simply doing what pathfinder says you do. since the 2 equations are not equivalent they cannot replace each other.
mathematics, a place where I can show a proof to be 100% true.
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I can't believe this thread is still going ...
Wow, what an unexpectedly large number of posts for such a seemingly simple question. To answer the question, you always round down whenever you come up with a fractional value, and at every step of the calculation.
For example, say you have a creature that is vulnerable to fire and incorporeal (takes half damage from all attacks). If it gets hit by a 31 damage fireball and makes its save:
It will take:
31/2 = 15.5 => round to 15 (save)
15/2 = 7.5 => round to 7 (incorporeal)
7*1.5= 10.5 => round to 10 (vulnerable)
=> 10 damageNOT:
31/2 = 15.5 (save)
15.5/2 = 7.75(incorporeal)
7.75*1.5= 11.625(vulnerable)
11.625 => round to 11 damage
And if you think that simple, logical and obvious answer is going to end the debate, you ain't been readin' the thread. Hang on, you're in for a rough ride.
In the nicest possible way, I believe Wikipedia over you. Also, my teachers, maths in the real world, the CRB which has no mention of 'integer math' whatsoever (and 'rounding' is not 'integer math'), basically...I believe reality over your fantasy.
Actually, you're (also) engaging in a logical fallacy, by assuming the result and using it as proof of the result. You are asserting that PF uses integer math, then (mis)interpret 'rounding' as if it were integer math, then saying 'Look! The CRB uses integer math!'
I've never been so embarrassed to be part of a thread in my life, so why do I keep posting? I keep thinking of that cartoon where the wife asks why the husband won't come to bed, and he passionately replies, 'Someone is wrong on the Internet!'
I've never seen anybody as 'wrong on the internet' as those who are seriously trying to assert that 2 is not less than half of 5.
And what you're doing is another logical fallacy called the straw man. You're acting like he said 2*2 doesn't equal 4, and attacking that point, leaving out the harder stuff that you don't really have a response for. He's describing how Pathfinder does math using examples from the book, and you're trying to make it sound like he's an idiot for not knowing that 2*2 = 4.
You say you like to believe reality, but I disagree. The reality is that every example given in the book works against your position. You've had to come up with your own set of rules that you completely made up just to keep your argument going. That alone should be convincing enough to make you say "Meh, all of that may be true, but I think the intention is to use 2.5" Boom argument's over, and you may even be right in that belief. But making up rules and trying to pass them off as an actual argument? No one's going to buy that.
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Wow, what an unexpectedly large number of posts for such a seemingly simple question. To answer the question, you always round down whenever you come up with a fractional value, and at every step of the calculation.
For example, say you have a creature that is vulnerable to fire and incorporeal (takes half damage from all attacks). If it gets hit by a 31 damage fireball and makes its save:
It will take:
31/2 = 15.5 => round to 15 (save)
15/2 = 7.5 => round to 7 (incorporeal)
7*1.5= 10.5 => round to 10 (vulnerable)
=> 10 damageNOT:
31/2 = 15.5 (save)
15.5/2 = 7.75(incorporeal)
7.75*1.5= 11.625(vulnerable)
11.625 => round to 11 damage
Setting aside the fact that rounding at every step violates rounding rules for every instance of rounding in real life ever, how did you determine your order of operations there? Because if you round at each step it matters:
31*1.5= 46.5 => round to 46 (vulnerable)46/2 = 23 (no rounding needed, incorporeal)
23/2 = 11.5 => round to 11 (save)
See? Change the order of operations and you get a different final result. That's why you wait until the end to round.
Wow, what an unexpectedly large number of posts for such a seemingly simple question.
Man, if I could take half of these posts (rounded down) and throw them in the trash, i would. ;)
Playing out the rounding aspect to the extreme. Why total the dice before halving the damage on a successful save? For example, if the total is 31 and the fireball damage was:
5+5+5+5+5+5+1 = 31
Could we not say, half damage is this?
2+2+2+2+2+2+0 = 12
Instead of 15?
I for one find no reason to round when determining Grit/Panache, but would gladly like to hear a dev weigh in on this.