Your examples are misleading. All of these require rounding, because the result of 'half of (whatever)' is used as a modifier or DC, which must be an integer.
Okay why does this have to be an integer? Why can't the DC of stunning fist be 12.5? Aren't you just comparing someone's Will save and determining a yes or no? Is it higher or not? Is it over the bar or under the bar? Wouldn't it be better, conceptually, if it stayed 12.5? I mean the rules don't tell me to round, you're just assuming that you have to.
But the actual rule in question doesn't require the result of 'half swashbuckler's level' to be an integer. It's not a modifier or a DC, it's not a number that is going to be used in the game. It's just an 'over/under' bar, the result of which will be 'yes' or 'no'.
Every DC is an over/under the result of which will be yes or no. EVERY DC. The DC is the target number, is my save over or under that target number? It is exactly the same, and you accept the rounding for DC's, but not for Swashbucklers. You are taking the same circumstances and applying the rules differently.
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It says it when it gives the example of when rounding is asked for 'Half of 7 is 3.'Where does it say that? It doesn't. It's an assumption you made, totally unsupported by the rules.My examples are required to be integers exactly as much as the example in the thread.
For all of those examples, if the result of the roll is less than the calculated value, you fail, otherwise you succeed. These are all over/under situations that you claim are better with fractional results. You can compare against fractional values just as easily as integer values, as you seem to insist. So no, these examples are 100% on point.
However, you are just plain incorrect. Every non-integer result is rounded unless specified otherwise. You've been challenged to find any contrary example to this and consistently failed to do so.
This should tell you something.
Exactly! That is an example of rounding, not division!
It's under the section entitled 'Rounding'. This means it only applies when rounding. It doesn't even make sense when you're not rounding.
It does not occur outside the section on rounding. It does not follow that all fractions are rounded down, it follows that, when rounding, round down.
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Your examples are misleading. All of these require rounding, because the result of 'half of (whatever)' is used as a modifier or DC, which must be an integer.Okay why does this have to be an integer? Why can't the DC of stunning fist be 12.5? Aren't you just comparing someone's Will save and determining a yes or no? Is it higher or not? Is it over the bar or under the bar? Wouldn't it be better, conceptually, if it stayed 12.5? I mean the rules don't tell me to round, you're just assuming that you have to.
But the actual rule in question doesn't require the result of 'half swashbuckler's level' to be an integer. It's not a modifier or a DC, it's not a number that is going to be used in the game. It's just an 'over/under' bar, the result of which will be 'yes' or 'no'.Every DC is an over/under the result of which will be yes or no. EVERY DC. The DC is the target number, is my save over or under that target number? It is exactly the same, and you accept the rounding for DC's, but not for Swashbucklers. You are taking the same circumstances and applying the rules differently.
The game system requires numbers used in the game to be integers, whether DCs, modifiers, hit points, damage, basically any number that you'd have to write down if you were publishing an adventure.
In an adventure module, a poison might have a save DC of 14, or a trap might have an attack modifier of +6. A creature will have a certain amount of hit points, so many HD, do so much damage, and every single one of these might be written down. All these must be integers.
But what needs to be written down here, that isn't an integer? The HD of the swashbuckler? Of the creature hit/critted? The number of panache points regained? All of these are integers anyway.
If a creature does 1d8+4 damage, and hits 14 times on average over 20 rounds, then what's the average damage it deals over 20 rounds? Average damage per hit = 8.5, multiplied by the 14 hits = 119 damage.
But wait! Average damage must be rounded down, so it only does 8 damage per hit therefore only does 112 damage?
No. You don't round down in the middle, only at the end and only if you need to. The end result for this ability is either 1 panache or none.
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Malachi, why does a 14 on a Fort Save succeed against a 3rd level Monk's Stunning Fist, assuming the monk has a 16 Wis?
Stunning Fist forces a foe damaged by your unarmed attack to make a Fortitude saving throw (DC 10 + 1/2 your character level + your Wis modifier), in addition to dealing damage normally.
14 is less than 14.5.
But what needs to be written down here, that isn't an integer?
If I was playing a Gunslinger, I'd probably make a note on my character sheet saying something like, "Can regain 1 Panache by defeating a monster with at least X HD." If you think of X as a number, it needs rounding. If you're making the calculation differently, there's no X and it doesn't need rounding.
There's not going to be an agreement here...
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Malachi, why does a 14 on a Fort Save succeed against a 3rd level Monk's Stunning Fist, assuming the monk has a 16 Wis?
Stunning Fist forces a foe damaged by your unarmed attack to make a Fortitude saving throw (DC 10 + 1/2 your character level + your Wis modifier), in addition to dealing damage normally.14 is less than 14.5.
DCs are in whole numbers. If, and I stress if, the result is required to be a DC (or any other game number), then we must round, and we must use PF rounding rules.
The result of 'Does the target have fewer HD than half of your level' is not a number, it's 'yes' or 'no'. You either get a point of panache or not. Both your level and the target's HD are integers. There are no fractions to round.
The game system requires numbers used in the game to be integers, whether DCs, modifiers, hit points, damage, basically any number that you'd have to write down if you were publishing an adventure.
In an adventure module, a poison might have a save DC of 14, or a trap might have an attack modifier of +6. A creature will have a certain amount of hit points, so many HD, do so much damage, and every single one of these might be written down. All these must be integers.
But what needs to be written down here, that isn't an integer? The HD of the swashbuckler? Of the creature hit/critted? The number of panache points regained? All of these are integers anyway.
If a creature does 1d8+4 damage, and hits 14 times on average over 20 rounds, then what's the average damage it deals over 20 rounds? Average damage per hit =...
Just so I'm clear, rounding after the 1/2 level when dealing with panache is like rounding in the middle of the equation, but rounding the Monk's level for the stunning fist isn't like that because you write the DC down. Have I gotten your argument right? Do you see how crazy that sounds when you say it out loud?
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Just so I'm clear, rounding after the 1/2 level when dealing with panache is like rounding in the middle of the equation, but rounding the Monk's level for the stunning fist isn't like that because you write the DC down. Have I gotten your argument right? Do you see how crazy that sounds when you say it out loud?The game system requires numbers used in the game to be integers, whether DCs, modifiers, hit points, damage, basically any number that you'd have to write down if you were publishing an adventure.
In an adventure module, a poison might have a save DC of 14, or a trap might have an attack modifier of +6. A creature will have a certain amount of hit points, so many HD, do so much damage, and every single one of these might be written down. All these must be integers.
But what needs to be written down here, that isn't an integer? The HD of the swashbuckler? Of the creature hit/critted? The number of panache points regained? All of these are integers anyway.
If a creature does 1d8+4 damage, and hits 14 times on average over 20 rounds, then what's the average damage it deals over 20 rounds? Average damage per hit =...
That's about the size of it.
If I were writing the stat block for that monk, I could write that the save DC for his Stunning Fist was 14, but the game system doesn't allow it to be 14.5. Thus, rounding is needed.
What fraction would you need to write with this panache ability? You know your level; it's an integer. You know the target's HD; it's an integer. There is no fraction.
That's about the size of it.If I were writing the stat block for that monk, I could write that the save DC for his Stunning Fist was 14, but the game system doesn't allow it to be 14.5. Thus, rounding is needed.
What fraction would you need to write with this panache ability? You know your level; it's an integer. You know the target's HD; it's an integer. There is no fraction.
Look at that bolded part and tell me why the system doesn't allow it.
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DCs are in whole numbers. If, and I stress if, the result is required to be a DC (or any other game number), then we must round, and we must use PF rounding rules.The result of 'Does the target have fewer HD than half of your level' is not a number, it's 'yes' or 'no'. You either get a point of panache or not. Both your level and the target's HD are integers. There are no fractions to round.
Levels are whole numbers. Divinding them in half doesn't make them stop being whole numbers. 5/2=2.
So if you round down, before any math is done then I guess this mean you get nothing no matter how many times you take it?
Gunslinger: Add +1/4 to the number of grit points in the gunslinger's grit pool.
Err, if you don't do any math, there would never be a need to round at all. All of pathfinder is integers.
I think I understand what you're trying to say, and even thought Malachi Silverclaw is saying that's what I'm doing, I'm really not. You round at the end of the equation before you compare it to the second number... Just like you do when talking about DC's. Going back to the 3rd level monk with a 16 WIS. the equation is:
DC = 1/2 Monk Level + WIS Modifier + 10.
DC = (1/2*3) + 3 + 10
DC = (1.5) + 13
DC = 14.5
That's the end of the first equation, so you round down, and the final answer is 14.
The second equation, which is the number we have to compare to the first number, if we use the same 3rd level monk with a 16 CON who rolls an 8 on the d20 is:
Save = Fort Save + CON Modifier + 1d20
Save = 3 + 3 + 8
Save = 6 + 8
Save = 14
and since 14 is an integer, we're done, and now we can compare the two. Is 14 equal to or greater than 14? Yes. Monk B is not stunned.
Now we can play the same game with the 3rd level Swashbuckler:
1/2 Level = 1/2*3
1/2 Level = 1.5
That is the end of the first equation, and since we have a decimal, we round down so the final answer is 1.
The second equation is even easier:
HD = Monster's Hit Die
HD = 2
Integer and we're done, now we can compare the two: Is 1 less than 2? Yes. Swashbuckler gets panache.
I can go though the hit points one too. We'll use a 3 Hit Dice (d8) monster.
Hit points = 4.5 * Hit Dice
Hit Points = 4.5 * 3
Hit Points = 13.5
This is the end of the equation, and since we ended up with a decimal, we round down. The final answer is 13.
Do you see how all three of those examples use exactly the same logic all the way through it. Do you see how it is internally consistent? I used the same interpretation of the rules in all three of those examples.
Now I'm not saying the devs may come out and say Malachi Silverclaw is right and it should be rounded up, what I am saying though, is that if they do that, it will be an exception to the rule.
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Do you see how all three of those examples use exactly the same logic all the way through it?
No!
The DC of the Stunning Fist is the final part of the equation, and needs rounding as that is the number in the stat block.
The modifier for the Fort save is also a final number, and that number is written in the stat block.
These things are final numbers, even though they may be used in saving throws later. This is how this game engine works.
The HD of any character is the result of all those class levels. This doesn't stop it being used in later calculations. When used to create a Simulacrum, then the new calculation (half HD of base creature) may result in a fraction, and the result must be an integer because creatures must have a whole number of hit dice, not because 'always round!'
But when the swashbuckler's HD is halved here, the final result of that whole calculation is either, 'yes, the creature hit has less than half my HD, therefore I don't regain panache', OR, 'no, the creature hit does not have fewer than half my HD, therefore I regain a point of panache'.
Things like HD, hit points, skill and save modifiers, save DCs for abilities possessed, all these things are part of the stat block that enables the character to interact with the game engine. They must be integers.
When these things are used later, then if the result of those calculations is a number, then you may have to round if the answer is required to be an integer. But if the answer of that later calculations is either 'yes' or 'no'.
Even if you are doing a calculation that requires rounding, that rounding doesn't take place half way through, only at the end. If half your HD is a fraction, it isn't rounded unless that is the final answer. But the final answer here is yes or no.
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I've not read through all these pages, but I might as well voice my opinion anyways. Two is less than half of five. You don't need to round every time a partial number appears in an equation. You only need to round if the final result would end in a non-integer value.
Checking what's a half of something is not a final result.
Things like HD, hit points, skill and save modifiers, save DCs for abilities possessed, all these things are part of the stat block that enables the character to interact with the game engine. They must be integers.
You have completely and arbitrarily made this whole cloth from your own imagination. None of what you say here is supported in any rational way by rules.
When these things are used later, then if the result of those calculations is a number, then you may have to round if the answer is required to be an integer. But if the answer of that later calculations is either 'yes' or 'no'.
And here's where you go wrong again. You think figuring out half of a level, figuring out a hit die, and comparing them are somehow all one big convoluted calculation... but you only think it's one calculation when we're talking about swashbucklers. You know exactly where to round in every other calculation. They are not one calculation.
Even if you are doing a calculation that requires rounding, that rounding doesn't take place half way through, only at the end. If half your HD is a fraction, it isn't rounded unless that is the final answer. But the final answer here is yes or no.
I'm going to keep this as simple as possible:
Is .5*5 a calculation?Yes.
That is the end of that calculation. Do you add anything else to it?
No
Do you subtract, divide, multiply, square, or use any other mathematical function?
No.
Then it is the end of the equation.
Now to ask it another way: If the developers say you must round the calculation down, where would you do the rounding? I mean where Ozy and I say it happens, you say is the middle. So if we are supposed to round, where else would we do it?
I've not read through all these pages, but I might as well voice my opinion anyways. Two is less than half of five. You don't need to round every time a partial number appears in an equation. You only need to round if the final result would end in a non-integer value.
Checking what's a half of something is not a final result.
Read the last two pages, answer the questions that no one else on "your side" seems to be able to answer, and see if you still agree.
Read the last two pages, answer the questions that no one else on "your side" seems to be able to answer, and see if you still agree.
That just made _Ozy_ and yourself look really stubborn, while still being wrong. You're still trying to round in a step that does not need rounding. In fact, I'll give a comparable example of how you're wrong:
The Invulnerable Rager gains DR/- equal to half their level. This DR is doubled against nonlethal damage. What is half of an odd level doubled? According to you, this rounding must occur immediately, therefore meaning a level 5 gets DR 2/-, 4 versus nonlethal. I am of the belief it sits at 2.5 until the DR needs to be applied to an attack, meaning doubling half a level = the level at all times.
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You have completely and arbitrarily made this whole cloth from your own imagination. None of what you say here is supported in any rational way by rules.
...and yet, there isn't a single stat block in the game where fractions are part of any modifier or DC.
And here's where you go wrong again. You think figuring out half of a level, figuring out a hit die, and comparing them are somehow all one big convoluted calculation... but you only think it's one calculation when we're talking about swashbucklers. You know exactly where to round in every other calculation. They are not one calculation.
Okay, terminology difference. I'm talking about the solution to a single problem, not each individual calculation used to solve that problem.
If the problem is, 'The simulacrum has half the HD of the original creature', then the solution to that problem is a number of HD, and HD needs to be an integer. So round as the very last step.
If the problem is, 'If the target has fewer than half your HD, then you don't regain panache.', then the solution is not a number but either yes or no. No rounding needed (or possible).
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How about instead of mischaracterizing our view, you ask? You don't round immediately, you round at the end of each calculation.
Level / 2 is the calculation for panache, level / 2 * 2 is the DR calculation.
Now, what does your mistake make you look like?
Alrighty. So you agree that the mathematical equation should first be completed before you round? Why, would you look at that. Inequalities are a part of mathematics. You either get to be right about the panache or the invulnerable rager, because your stance makes you wrong in one or the other as long as you apply the same rules to both questions.
Alrighty. So you agree that the mathematical equation should first be completed before you round? Why, would you look at that. Inequalities are a part of mathematics. You either get to be right about the panache or the invulnerable rager, because your stance makes you wrong in one or the other as long as you apply the same rules to both questions.
Yeah I think you're wrong about the Invulnerable Rager too (so does Hero Labs for what that's worth). Using Malachi's logic, you have to write DR down on a stat block so you have to round it down. So he should think you're wrong too.
And to use your logic, the Monk's Stunning fist DC is either 14.5 and the Swashbuckler's level is 2.5 or they're 14 and 2 since they are exactly the same type of equation, which both either need to be, or not be rounded in the same place, before the comparison.
I also find it funny that you call us "wrong" and "stubborn" when we're the ones citing actual rules and examples from the rules while you make stuff up based on your assumptions.
I think I understand what you're trying to say, and even thought Malachi Silverclaw is saying that's what I'm doing, I'm really not. You round at the end of the equation before you compare it to the second number... Just like you do when talking about DC's. Going back to the 3rd level monk with a 16 WIS. the equation is:
DC = 1/2 Monk Level + WIS Modifier + 10.
DC = (1/2*3) + 3 + 10
DC = (1.5) + 13
DC = 14.5
That's the end of the first equation, so you round down, and the final answer is 14.
DC = 1/2 Monk Level + WIS Modifier + 10.
DC = (1/2*3) + 3 + 10
DC = (1.5) + 13 [I have to ask why you didn't round here if it is also a calculation]
DC = 14.5
I'm not sure I understand your question, but I didn't round there because the equation wasn't over yet. In some instances that .5 might have come into play. If for example the equation called for 1/2 the WIS modifier it would have been 1.5 + 11.5 and = 13.
As has been said repeatedly you don't round until the end of the equation. The problem people keep having is, in this swashbuckler's case, and the swashbuckler's case alone, they think the equation isn't over until after the comparison. They agree with it in every other instance, just the swashbuckler is for some odd reason, different in their minds.
I'm curious. If I'm playing a Swashbuckler and the GM asks me "Hey what Hit Die monster do you get Panache back from?" do I have to answer "Well, gee I don't know, you see I can't actually do the equation until you tell me the Hit Die. There's no way to calculate before hand"? Because that's really what you guys are saying when you say we're rounding before the equation is over.
Or even better, if I write on my character sheet:
Hit Die to get Panache Back____
can I THEN put 2 in that block? I mean since the Monk can put 14 in his block.
You either get to be right about the panache or the invulnerable rager, because your stance makes you wrong in one or the other as long as you apply the same rules to both questions.
This is why "the world hates you" is a handy way to deal with rounding. "Whatever works out as least favourable to the PC's" means that such inconsistencies end up hand-waved in a consistent manner. I'm not sure it's a written rule anywhere though; I think it might be a carry over from either from the old days, like Gygax's time, or one of the much older editions of the game anyway.
Yeah I think you're wrong about the Invulnerable Rager too (so does Hero Labs for what that's worth). Using Malachi's logic, you have to write DR down on a stat block so you have to round it down. So he should think you're wrong too.And to use your logic, the Monk's Stunning fist DC is either 14.5 and the Swashbuckler's level is 2.5 or they're 14 and 2 since they are exactly the same type of equation, which both either need to be, or not be rounded in the same place, before the comparison.
I also find it funny that you call us "wrong" and "stubborn" when we're the ones citing actual rules and examples from the rules while you make stuff up based on your assumptions.
At least you're consistent. The equation for the swashbuckler is dynamic, in that it requires an enemy of X hit dice to initiate the calculation. Stunning Fist and other DC-based effects require no enemy input; they're always going to end at the same relative values (+/- a bit for circumstantial bonuses or penalties). So the comparison you've given is a dynamically calculated effect against a constant.
In case you're wondering, I believe the equation for swashbuckler is as follows: [(0.5*X) < Y], since inequalities can be placed in mathematical equations.
And yes, y'all are stubborn. That's the word for people that fill at least three pages without changing an opinion. In fact, I think I'm going to keep out of this conversation from now on, to keep myself from becoming stubborn as well.
At least you're consistent. The equation for the swashbuckler is dynamic, in that it requires an enemy of X hit dice to initiate the calculation. Stunning Fist and other DC-based effects require no enemy input; they're always going to end at the same relative values (+/- a bit for circumstantial bonuses or penalties). So the comparison you've given is a dynamically calculated effect against a constant.
It is no more dynamic than a Fortitude save in that it requires a DC to initiate the calculation. Fortitude saves are actually MORE dynamic because you have the variable of the d20. Half my level is a constant.
And going back to my previous post, you're saying I can't tell the GM how many hit dice I need to get panache back because I can't work the equation until I have a monster? And that really makes sense to you?
In case you're wondering, I believe the equation for swashbuckler is as follows: [(0.5*X) < Y], since inequalities can be placed in mathematical equations.
Following that logic, to find out if you're stunned by the Monk's fist the equation is [((0.5*X)+10+WIS) < Y] which means it's 14.5 Let's stay consistent you like that.
And yes, y'all are stubborn. That's the word for people that fill at least three pages without changing an opinion. In fact, I think I'm going to keep out of this conversation from now on, to keep myself from becoming stubborn as well.
And again we're stubborn, but the people on the other side, who are completely ignoring logical examples of rules as written, and are going off of their own imaginations and interpretations of the rules, are just trying to get through to us "stubborn folk"?
Just to keep the record straight, I'm the one who started this thread. When I started it, I could see the issue from both sides. When Flying Hanger first posted, I had pretty much decided that you used 2.5. It wasn't until I read logical posts that presented the rules as written and other examples that I decided it should be 2. So in the space of this thread, I went from not knowing, to being pretty sure it was one way, to being absolutely convinced it's the other way. So my opinion has changed. I think Tri has been convinced to lean a little more our way, so who knows. If we can get the rest of you to quit trying to say things that are exactly the same are different, may ya'll come around too.
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Yeah I think you're wrong about the Invulnerable Rager too (so does Hero Labs for what that's worth). Using Malachi's logic, you have to write DR down on a stat block so you have to round it down. So he should think you're wrong too.
Yep. The DR is written in the stat block, so must be a whole number. If they had a separate DR versus non-lethal equal to their level, then that would be DR/5 versus non-lethal. But that's not what it says. It says that DR is doubled versus non-lethal, so that DR/2 gets doubled to DR/4. Strange, but true.
And to use your logic, the Monk's Stunning fist DC is either 14.5 and the Swashbuckler's level is 2.5 or they're 14 and 2 since they are exactly the same type of equation, which both either need to be, or not be rounded in the same place, before the comparison.
DRs are values written in the stat block. They must be integers. The fact that they are used in comparisons in later calculations doesn't mean that the calculation of the DR is half way through.
DRs are values written in the stat block. They must be integers. The fact that they are used in comparisons in later calculations doesn't mean that the calculation of the DR is half way through.
Half the level is a value. The fact that they are used in comparisons in later calculations doesn't mean that the calculation of half the level is half way through.
When I opened the thread, I was convinced it would be 2.5... but, by the conclusion I think it is pretty clearly 2. Making it 2.5 requires special pleading which doesn't really make sense in this case: I can't think of a single other example that would work in this fashion, which sends warning bells.
Also, what's with this stat block must be integers that keeps coming up? Where is this mentioned in the rules text? I can have non-integer numbers in my stat block that interact directly with the rules (age, weight, carried weight). It just so happens the vast majority of numbers on the stat block are integers. There's no applicable rule here.
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Critical Hit with a Light or One-Handed Piercing Melee Weapon: Each time the swashbuckler confirms a critical hit with a light or one-handed piercing melee weapon, she regains 1 panache point. Confirming a critical hit on a helpless or unaware creature or a creature that has fewer Hit Dice than half the swashbuckler's character level doesn't restore panache.
There is no formula mandated to find out if one of those numbers is less than half of the other. You are not required to use division to find the answer, you can use any way that works.
The term, 'swashbuckler's HD/2' is not required at any point. We can find the answer to the question 'Is the target's HD less than half the swashbuckler's HD', guaranteed 100% accurate and 100% guaranteed never to feature a fraction at any point of the calculation.
We can mathematically prove that '2' is less than half of '5', without ever using division.
If you assert that '2' is not less than half of '5', then you are provably wrong.
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I'm going to go eat half of my taco.
Funnily enough, I've actually heard that a firm claims that it's product has zero calories in it's entire one litre carton.
When this was tested, it was found to contain loads. The firm said that the stuff had less than one calorie per milli-litre, which they round down to zero, using normal rounding of less than half rounds down.
Then, they multiply that zero by 1000 (because there are 1000ml in a litre), and get a total of zero. Y'know, instead of the 400-odd calories that are actually in it.
You round after the conclusion of each arithmetic calculation
No, you really don't! The above story illustrates why. Only if you're deliberately trying to get an inaccurate result would you do that. If you round at all, you don't do it until the final answer.
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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.
If you assert that '2' is not less than half of '5', then you are provably wrong.
And yet the Pathfinder rules say 3 is half of 7, go figure.
I'm going to go eat half of my taco.Funnily enough, I've actually heard that a firm claims that it's product has zero calories in it's entire one litre carton.
When this was tested, it was found to contain loads. The firm said that the stuff had less than one calorie per milli-litre, which they round down to zero, using normal rounding of less than half rounds down.
Then, they multiply that zero by 1000 (because there are 1000ml in a litre), and get a total of zero. Y'know, instead of the 400-odd calories that are actually in it.
You round after the conclusion of each arithmetic calculationNo, you really don't! The above story illustrates why. Only if you're deliberately trying to get an inaccurate result would you do that. If you round at all, you don't do it until the final answer.
the fact they multiplied the number they gained shows explicitly the calculation was not finished, they rounded well before they were done.
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
Critical Hit with a Light or One-Handed Piercing Melee Weapon: Each time the swashbuckler confirms a critical hit with a light or one-handed piercing melee weapon, she regains 1 panache point. Confirming a critical hit on a helpless or unaware creature or a creature that has fewer Hit Dice than half the swashbuckler's character level doesn't restore panache.There is no formula mandated to find out if one of those numbers is less than half of the other. You are not required to use division to find the answer, you can use any way that works.
The term, 'swashbuckler's HD/2' is not required at any point. We can find the answer to the question 'Is the target's HD less than half the swashbuckler's HD', guaranteed 100% accurate and 100% guaranteed never to feature a fraction at any point of the calculation.
We can mathematically prove that '2' is less than half of '5', without ever using division.
If you assert that '2' is not less than half of '5', then you are provably wrong.
math can be translated to and from english or other languages
the bolded makes the equation
HD < ((SCL*1)/2)
and from my above post this can NOT be altered to
HD*2 < SCL
as the 2 equations are not equal.
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If you assert that '2' is not less than half of '5', then you are provably wrong.And yet the Pathfinder rules say 3 is half of 7, go figure.
That is a misrepresentation of what was written, and you know it.
The example you quoted was not an example of how division works, but how rounding works. The title of that paragraph is, 'Rounding'.
If we divide 7 by 3, the result is 3.5. 'Normal' rounding would have us round that up to 4. 'Pathfinder' rounding has us round that down to 3.
As it happens, at no point are we required to divide a number by 2 to solve the question of 'Is the smaller number less than half of the larger'. We can get the answer every time, with no dividing needed.
Example: D'Artagnan is a 9th level swashbuckler, and he's just critted a target. The DM knows that the target has 4 HD, so he doubles 4 and gets 8. 8 is less than 9, so the DM knows, without any doubt whatsoever, that the target has fewer than half D'Artagnan's HD.
Next round, D'artagnan crits a 5 HD target. The DM doubles that to 10. 10 is not less than half of 9, so the DM knows beyond doubt that the target does not have fewer than half D'Artagnan's HD, and awards him a point of panache.
Where is 'Pathfinder rounding' required at all?
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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'?
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Refusing to do the math properly doesn't make your argument right.If you assert that '2' is not less than half of '5', then you are provably wrong.And yet the Pathfinder rules say 3 is half of 7, go figure.That is a misrepresentation of what was written, and you know it.
The example you quoted was not an example of how division works, but how rounding works. The title of that paragraph is, 'Rounding'.
If we divide 7 by 3, the result is 3.5. 'Normal' rounding would have us round that up to 4. 'Pathfinder' rounding has us round that down to 3.
As it happens, at no point are we required to divide a number by 2 to solve the question of 'Is the smaller number less than half of the larger'. We can get the answer every time, with no dividing needed.
Example: D'Artagnan is a 9th level swashbuckler, and he's just critted a target. The DM knows that the target has 4 HD, so he doubles 4 and gets 8. 8 is less than 9, so the DM knows, without any doubt whatsoever, that the target has fewer than half D'Artagnan's HD.
Next round, D'artagnan crits a 5 HD target. The DM doubles that to 10. 10 is not less than half of 9, so the DM knows beyond doubt that the target does not have fewer than half D'Artagnan's HD, and awards him a point of panache.
Where is 'Pathfinder rounding' required at all?
My math is error free.
You don't determine the threshold by multiplying the targets level, you determine it by halving your level.
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.
In Pathfinder, 4 is both half of 8 and half of 9. Welcome to integer math.
This 'Integer Math' is not used in Pathfinder. The only difference between PF math and normal math is the rule for rounding.