On Resonance and being a Nerd.


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The Resonance mechanic was introduced (leaked?) the other day and it has been a source of controversy since then.

For those who don't know, Resonance is PF2's new mechanic that regulates magic item use. Here are the basics: (devs please correct me if I am wrong so I can modify my code)

1) Characters have a Resonance Score of Level + CHA mod.
2) Worn Magic items use up one point of resonance, per item.
3) Use activated items (potions, scrolls, wands, etc.) use up Resonance per use.
4) If you run out of Resonance, you must make a Resonance Check in order to use another use activated item.
5) A Resonance Check is d20 VS DC 10.
6) Resonance Check DCs increase by 1 each time they are rolled.
7) Crit Failing a Resonance Check cuts you off from any more use activated magic item use for the day.

Being a nerd, I decided to write a program that would run 1 million simulations of characters making Resonance Checks to see how many uses of magic items you can reasonably be expected to get after you run out of Resonance.

My result was approximately 2.3 uses.

This means that, on average, a character can use a number of use activated items equal to their Resonance Score (Level + CHA mod.) + 2.3 times per day.

Keep in mind that party members can "pool" these points with intelligent item usage.

Whether or not this mechanic is acceptable is irrelevant to this post, but I felt that this information should be factored in to any discussion about the effectiveness/palatability of the mechanic.

Thanks for your time.

Don't judge me.


Pathfinder Adventure Path Subscriber
thflame wrote:

Being a nerd, I decided to write a program that would run 1 million simulations of characters making Resonance Checks to see how many uses of magic items you can reasonably be expected to get after you run out of Resonance.

My result was approximately 2.3 uses.

Could you modify it to get the distribution of possibilities? Mean is useful information, but it's a bit more helpful to know the specific odds of 0 extra activations, 1 extra activation, etc.


Ok, what can we do with 0.3 resonances?

Haha, just joking.
Good work, that's indeed useful.


Man, here I thought this was going to be a thread complaining about being disadvantaged for tanking charisma.

The numbers do seem a bit wierd to me though. Presuming that nat 01s don't actually crit fail (aka only fail by 10) a person isn't even under the threat of being cut off till the second use of dry resonance (nat 01 vs DC11).

Unless you mean you get an average of 2.3 successful (as opposed to attempts) uses before you choke up and get perma cut off which seems a bit more sensical.

And no judging for programming. Represent bro.


First up: props for doing some cool number-crunching!

Second, I feel like we need more info about the test methodology. Such as:

How were your million test cases derived?

What range of CHA scores did you test against? 3-18, as in a level 1 PC with no ancestry bonuses? 1-20, as in a PC with ancestral bonuses/penalties? 1-26, accounting for potential stat boosts at higher levels?

What's the distribution of CHA scores in the test set? That is, how many samples of any given score in set?

Did it take into account number of worn magic items?

Did it take into account level? If the mechanics given in the OP are correct, a level 10 PC with 12 CHA would have 11 Resonance points; if they're wearing five magic gizmos, they get six use-activated items (per day, I assume) before they even have to start making checks.

Liberty's Edge

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Tinalles wrote:

First up: props for doing some cool number-crunching!

Second, I feel like we need more info about the test methodology. Such as:

How were your million test cases derived?

What range of CHA scores did you test against? 3-18, as in a level 1 PC with no ancestry bonuses? 1-20, as in a PC with ancestral bonuses/penalties? 1-26, accounting for potential stat boosts at higher levels?

What's the distribution of CHA scores in the test set? That is, how many samples of any given score in set?

Did it take into account number of worn magic items?

Did it take into account level? If the mechanics given in the OP are correct, a level 10 PC with 12 CHA would have 11 Resonance points; if they're wearing five magic gizmos, they get six use-activated items (per day, I assume) before they even have to start making checks.

They were testing only the checks made after you run out of Resonance, which aren't at all modified by level or Charisma. It's just a flat 1d20 roll against a DC of 10, +1 per previous check.


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So that means is that everybody, on average, gets about 2 uses per day after they've already burned through all their free uses? Okay!

The operative question then becomes: how likely is a PC to burn through all their resonance in a single day at any given level?

I think sounds like prime fodder for a playtest. So it's a good thing they've got one of those scheduled. ^_^


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This may be wrong (I'm in middle school) but it seems to me like you can calculate the theoretical probability of this by doing the chance of success multiplied by the chance of not critically failing before hand. The first would be .5*1, then .45*1, then .4*.95, then .4*.95*.9, etc. I put this in my calculator and got 2.151412608 but I may have put something in wrong.

Anyway, being a nerd is great!


Dasrak wrote:
thflame wrote:

Being a nerd, I decided to write a program that would run 1 million simulations of characters making Resonance Checks to see how many uses of magic items you can reasonably be expected to get after you run out of Resonance.

My result was approximately 2.3 uses.

Could you modify it to get the distribution of possibilities? Mean is useful information, but it's a bit more helpful to know the specific odds of 0 extra activations, 1 extra activation, etc.

Sorry, I've been busy today. It should be an easy tweak. I'll try to run that up tomorrow.


CactusUnicorn wrote:

This may be wrong (I'm in middle school) but it seems to me like you can calculate the theoretical probability of this by doing the chance of success multiplied by the chance of not critically failing before hand. The first would be .5*1, then .45*1, then .4*.95, then .4*.95*.9, etc. I put this in my calculator and got 2.151412608 but I may have put something in wrong.

Anyway, being a nerd is great!

I believe it isn't that neat of an equation, but your answer is pretty close to mine. There is the probability of success vs failure, plus the probability of critical failure, which prevents further rolls. I was working for hours trying to write a probability equation for it and kept getting weird results (I probably screwed up to be honest) so I just wrote a program to roll a d20 vs an increasing DC until I got a fail condition, then I had it do that 1,000,000 times.

Your answer is pretty close though, so you're probably right, or at least really close.


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CactusUnicorn wrote:

This may be wrong (I'm in middle school) but it seems to me like you can calculate the theoretical probability of this by doing the chance of success multiplied by the chance of not critically failing before hand. The first would be .5*1, then .45*1, then .4*.95, then .4*.95*.9, etc. I put this in my calculator and got 2.151412608 but I may have put something in wrong.

Anyway, being a nerd is great!

Nerds rule the world.

Anyway, this is actually a really good mechanic and also errs toward people taking more powerful, and more expensive, consumables rather than just relying on CLW Spam.


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I think it's one of those rules that a lot of people dislike at first, but comes to understand it later ^^


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I guess I had nothing better to do...

The probability of getting EXACTLY X uses is approximately:

0: 11.6%
1: 19.6%
2: 24.8%
3: 21.3%
4: 13.5%
5: 6.4%
6: 2.3%
7: 0.6%
8: 0.1%
9: 0.02%
10+: 0.0002%

The probability of getting AT LEAST N uses is:

1: 88.6%
2: 69.0%
3: 44.2%
4: 22.9%
5: 9.4%
6: 3.0%
7: 0.7%
8: 0.1%
9: 0.02%
10+: 0.0002%

Hope this helps people out.

Paizo Employee Designer

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Nice math nerding thflame and CactusUnicorn.

Here's another fun math challenge that you can try out that also lends itself to a similar Monte Carlo solution: PF1 dying!

Suppose your character has 200 Hit Points and is continually subjected to attacks that deal 16d6 damage. On average, after 4 such attacks, you've taken 224 damage, which in PF1 death and dying would put you at -24. But that's the average. What is the probability distribution of where your negative Hit Points will fall after the very first attack that drops you below 0 HP? Let's say you have 18 Constitution; what are the chances that you would survive using PF1's dying rules? For bonus points (and since these numbers are close to a local maximum of survivability such that lower or higher damage will change the results), try this with 18d6 damage and also with 13d6 damage


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I say!

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JRutterbush wrote:
They were testing only the checks made after you run out of Resonance, which aren't at all modified by level or Charisma. It's just a flat 1d20 roll against a DC of 10, +1 per previous check.

Do we know for a fact that this is how it will be done? What if the check is based on Use Magic Device and we should expect a modifier/penalty?

I highly doubt the final result will end up with a flat 1d20 result.

Edit: Checked on this myself and yes so far the only information we have says: "The check after you resonance is done appears to be a "flat check", which means its a d20 with no modifiers."

But I want to point out that it says "appears" which isn't a confirmation.

Sczarni RPG Superstar Season 9 Top 16, RPG Superstar 2015 Top 32

Sorry for the double posting but I want to ask:

What could we expect to see if the check was modified? What would each +1 bonus give us?


Resonance is your UMD pool. There won't be a UMD skill, especially since every single character automatically increases every single skill at every single level.

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Bloodrealm wrote:
Resonance is your UMD pool. There won't be a UMD skill, especially since every single character automatically increases every single skill at every single level.

Do you have a source on that? My sources do not have anyone confirming UMD from being cut from the skill list.

Also, I'm unclear on what you mean about increasing every skill. Comments still point to there being skill ranks that must be invested into a skill, but that the system is going to have less of a difference between different characters. There are still going to be varying bonuses as far as I can tell.


No, the way skills and attacks work is that you always add your character level and ability mod to them. Then there are 5 levels of proficiency that give -1, +0, +1, +2, and +3. You select proficiency increases every few levels.


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Pathfinder Adventure Path Subscriber
Mark Seifter wrote:


Here's another fun math challenge that you can try out that also lends itself to a similar Monte Carlo solution: PF1 dying!

Okay, I guess it's my turn to do some of the nerd work around here:

Results

I ran 1 million samples (evil pinky finger) of each. See the tabs at the bottom to toggle between the results. The 16d6 had a 27.8% chance of dropping between -1 and -17, the 13d6 had a 27.4% chance (must be an artifact of the damage averages making it more likely that it will knock you close to 0 on its second-to-last blow) and the 18d6 damage has gives you only 17.6% chance of survival. Oh dear.

Not surprising, blowing right past the negative hit point threshold was a pretty common problem in higher-level Pathfinder.


Bloodrealm wrote:
No, the way skills and attacks work is that you always add your character level and ability mod to them. Then there are 5 levels of proficiency that give -1, +0, +1, +2, and +3. You select proficiency increases every few levels.

Are you sure? Can I have a source on that?

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Bloodrealm wrote:
No, the way skills and attacks work is that you always add your character level and ability mod to them. Then there are 5 levels of proficiency that give -1, +0, +1, +2, and +3. You select proficiency increases every few levels.

Now that you lay it out I remember reading it in more words somewhere. EDIT: I do not have a source, and echo a request for one to confirm your statement.

Still, my question stands. What can we expect for different levels of proficiency if it happens to use a skill like Use Magic Device?

If it doesn't use a skill, but abilities/feats/traits add a bonus to the roll, what can we expect with +1 to +4 modifiers?

Paizo Employee Designer

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Dasrak wrote:
Mark Seifter wrote:


Here's another fun math challenge that you can try out that also lends itself to a similar Monte Carlo solution: PF1 dying!

Okay, I guess it's my turn to do some of the nerd work around here:

Results

I ran 1 million samples (evil pinky finger) of each. See the tabs at the bottom to toggle between the results. The 16d6 had a 27.8% chance of dropping between -1 and -17, the 13d6 had a 27.4% chance (must be an artifact of the damage averages making it more likely that it will knock you close to 0 on its second-to-last blow) and the 18d6 damage has gives you only 17.6% chance of survival. Oh dear.

Not surprising, blowing right past the negative hit point threshold was a pretty common problem in higher-level Pathfinder.

Well done! Your Monte Carlo simulations get similar results to my numbers (unsurprisingly). And yes, the 13d6 being unintuitively more deadly than the 16d6 is exactly because it has bad parity (it's more likely to knock you to about 18 HP and then kill you) and 16d6 has pretty good parity and might spare you on a below-average roll. And that low chance to get knocked out without an instakill didn't even include the possibility to get a crit that spikes you to double the damage!

As you say, this is a good demonstration of why the PF1 death and dying system didn't really work if you played at high levels and didn't want huge lethality (and/or didn't carry tons of breaths of life everywhere).


Mark Seifter wrote:

Nice math nerding thflame and CactusUnicorn.

Here's another fun math challenge that you can try out that also lends itself to a similar Monte Carlo solution: PF1 dying!

Suppose your character has 200 Hit Points and is continually subjected to attacks that deal 16d6 damage. On average, after 4 such attacks, you've taken 224 damage, which in PF1 death and dying would put you at -24. But that's the average. What is the probability distribution of where your negative Hit Points will fall after the very first attack that drops you below 0 HP? Let's say you have 18 Constitution; what are the chances that you would survive using PF1's dying rules? For bonus points (and since these numbers are close to a local maximum of survivability such that lower or higher damage will change the results), try this with 18d6 damage and also with 13d6 damage

Hey, we should ask if we can get paid for this....

I'll accept access to the current playtest materials as payment! I promise I'll keep it on the down-low. Pinky swear! Honest!

No? Not going for that?

Well, I tried....

Silver Crusade

Pathfinder Adventure Path Subscriber

I’m not math nerdy enough to do this but what happens if you get double negative con thanks to Mythic (assuming still a 200 hp total)


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Mark Seifter wrote:
Dasrak wrote:
Mark Seifter wrote:


Here's another fun math challenge that you can try out that also lends itself to a similar Monte Carlo solution: PF1 dying!

Okay, I guess it's my turn to do some of the nerd work around here:

Results

I ran 1 million samples (evil pinky finger) of each. See the tabs at the bottom to toggle between the results. The 16d6 had a 27.8% chance of dropping between -1 and -17, the 13d6 had a 27.4% chance (must be an artifact of the damage averages making it more likely that it will knock you close to 0 on its second-to-last blow) and the 18d6 damage has gives you only 17.6% chance of survival. Oh dear.

Not surprising, blowing right past the negative hit point threshold was a pretty common problem in higher-level Pathfinder.

Well done! Your Monte Carlo simulations get similar results to my numbers (unsurprisingly). And yes, the 13d6 being unintuitively more deadly than the 16d6 is exactly because it has bad parity (it's more likely to knock you to about 18 HP and then kill you) and 16d6 has pretty good parity and might spare you on a below-average roll. And that low chance to get knocked out without an instakill didn't even include the possibility to get a crit that spikes you to double the damage!

As you say, this is a good demonstration of why the PF1 death and dying system didn't really work if you played at high levels and didn't want huge lethality (and/or didn't carry tons of breaths of life everywhere).

I feel like that could have been solved by simply adding a clause that says you can't get oneshot from positive HP to dead, and it instead drops you to (negative Con) +1 so that you still get a save.

Ripping out the mostly good death rules because "at really high levels, if you get massive damage focus-firing a single character before anyone can react, the unmodified, context-less math says they'll probably die" exists and exchanging it with a worse-in-general system that technically fixes that problem but raises several new ones... just sounds like poor game design.

Paizo Employee Designer

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DM_aka_Dudemeister wrote:
I’m not math nerdy enough to do this but what happens if you get double negative con thanks to Mythic (assuming still a 200 hp total)

As you keep multiplying your Con, your cushion eventually becomes so close to the size of the chunks of damage you're taking (remember we cut out criticals here) that you basically can't die without being attacked after you're down at lower levels. You will still eventually hit a level where you're in really bad shape again even without crits, simply because damage scales a lot faster than 2*Con score, but it won't be until later than the 13d6 era, at least.


Bloodrealm wrote:
No, the way skills and attacks work is that you always add your character level and ability mod to them. Then there are 5 levels of proficiency that give -1, +0, +1, +2, and +3. You select proficiency increases every few levels.

The podcast mentioned skill ranks.

So I think there are two systems: proficiencies (which are as you describe), and skills (which are purchased with ranks as PF1).

Liberty's Edge

Bloodrealm wrote:
No, the way skills and attacks work is that you always add your character level and ability mod to them. Then there are 5 levels of proficiency that give -1, +0, +1, +2, and +3. You select proficiency increases every few levels.

That comes from my speculation (that got an "on the right track" response from a dev). But it was -2 for Untrained, not -1, because the first level characters in the podcast were rolling stat -1 for their Untrained checks.

1 - 2 = -1

And even then, "on the right track" doesn't necessarily mean I was spot on, there could be details we just don't know yet.


DM_aka_Dudemeister wrote:
I’m not math nerdy enough to do this but what happens if you get double negative con thanks to Mythic (assuming still a 200 hp total)

Assuming a CON score of 17 and a 20th level character with 200 HP, taking 16d6 of damage repeatedly, I got these results.

Negative CON kills 75% of the time.
Negative double CON kills 27% of the time.
Negative CON plus Level (I was curious) kills 22% if the time.

I can tweak the HP/CON/Level numbers if you like or, better yet, I can send you the code and let you tweak it yourself.

EDIT: Corrected values. I was accidentally rolling 16d6 - 16.


CactusUnicorn wrote:

This may be wrong (I'm in middle school) but it seems to me like you can calculate the theoretical probability of this by doing the chance of success multiplied by the chance of not critically failing before hand. The first would be .5*1, then .45*1, then .4*.95, then .4*.95*.9, etc. I put this in my calculator and got 2.151412608 but I may have put something in wrong.

Anyway, being a nerd is great!

Your number may be slightly different because when calculating odds of success against DC 10 with a d20 roll, the odds are 0.55.


I actually like this. I've been using 3/day wands for years and my players like them too (although we don't use them when doing APs). I hate running out of charges for my favorite wands and dislike when players burn 15 charges in a wand of cure light wounds, rather than play with good tactics.


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WhiteMagus2000 wrote:
I actually like this. I've been using 3/day wands for years and my players like them too (although we don't use them when doing APs). I hate running out of charges for my favorite wands and dislike when players burn 15 charges in a wand of cure light wounds, rather than play with good tactics.

Wands with charges per day sounds a LOT better than Resonance. A lot simpler, too, not to mention that the cheaper ones would still be useful even after you get a more powerful one.

I don't think the CLW wand spamming usually has to do with not playing with good tactics, but rather with extending the adventuring day so that you can keep playing.


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As a bonus that wand change would effect only itself rather than breaking other things.


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It's not breaking anything. It is improving the game ^^


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Igwilly wrote:
It's not breaking anything. It is improving the game ^^

I fail to see how it would be an improvement at all.


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Arssanguinus wrote:


I fail to see how it would be an improvement at all.

I've explained several times what this mechanic will improve.

This is not the apocalypse of magic items. From what we have heard, this will not make all items besides healing potions and weapons obsolete because somehow we'll need EVERYTHING to it. This will add a new layer of tactics and strategy to the game.
Not only this will solve the wand-spamming problem, this will make all items more interesting to use.
Designers will be forced to come up with cool items and potions worth enough to spend a resonance point.
Wands, rods, staves, rings and such, will be constant and durable items, instead of disposable ones.
No longer "you must have X items at Y level". Giving out too much items will not be a huge issue, because it will cost resonance. Neither will be giving less items, because you can spend all points in a magical sword or whatever.
This will give a nice utility to Charisma that is closer to old-school charisma than "Making friends and lying to people".
It will be actually easier to note your resonance instead of each item's X/day uses, A charges, Y hours/day, and so on. That cool sword's power, that cool potion, that cool ring, etc. will be easier to interact and weight the options.
This is not such a HUGE issue that will RUIN the game for magic items.


Mark Seifter wrote:

Nice math nerding thflame and CactusUnicorn.

Here's another fun math challenge that you can try out that also lends itself to a similar Monte Carlo solution: PF1 dying!

Suppose your character has 200 Hit Points and is continually subjected to attacks that deal 16d6 damage. On average, after 4 such attacks, you've taken 224 damage, which in PF1 death and dying would put you at -24. But that's the average. What is the probability distribution of where your negative Hit Points will fall after the very first attack that drops you below 0 HP? Let's say you have 18 Constitution; what are the chances that you would survive using PF1's dying rules? For bonus points (and since these numbers are close to a local maximum of survivability such that lower or higher damage will change the results), try this with 18d6 damage and also with 13d6 damage

So 16d6 averages to 8*7=56 damage per attack from 16 to 96, heavily skewed somewhere in that middle. Given your starting HP, you can ignore the top of the damage curve and just focus on the hit that drops you down, as there should be enough variance to mean that the low HP numbers are (approximately) equally probable.

Given this, I'd probably try to work my way back from the maximum negative HP you can reach (-94) to determine the probability of hitting that number from a non-negative range vs going from something in the unconscious range (-1 to -17) to that number, and then weight it by the probability of those events relative to the whole.

I think you can (roughly) compute that number exactly rather than simulating it, though as I said, it's dependent on low HP totals being relatively equally probable.

EDIT: Though now that I'm considering it, you probably want to work this from the other direction, consider all HP totals from 95 down and do the computation from there... Monte Carlo is probably much simpler :-P.


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Igwilly wrote:


Designers will be forced to come up with cool items and potions worth enough to spend a resonance point.

And they will no longer be able to create small, inexpensive items that aren't worth spending a Resonance point, like a Traveler's Any-Tool. Also, nobody will ever use things that are just cool to have because that eats into Resonance they might need for something mechanically important like "not dying".

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Bloodrealm wrote:
Igwilly wrote:


Designers will be forced to come up with cool items and potions worth enough to spend a resonance point.
And they will no longer be able to create small, inexpensive items that aren't worth spending a Resonance point, like a Traveler's Any-Tool. Also, nobody will ever use things that are just cool to have because that eats into Resonance they might need for something mechanically important like "not dying".

Who says that's true? If it didn't take a charge or slot before, why would it take resonance?


I think cool minor things that don’t take resonance/a slot will be more popular rather than less. If Treaveller’s Any-Tool were to take a point of resonance to change form in the new version, I’d be a little sad about that. I think it’d be understandable, though, given how much more difficult bonuses are to come by. I’d almost want a free-to-use version without the bonus, just serving as mundane tools. Any minor necklaces, capes, belts, or headbands will have substantially improved odds of getting used.


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What I meant was that if everything needs Resonance either consumed or invested, then small things like the Any-Tool won't get used. I didn't mean that if those things DON'T use Resonance then they won't get used; that'd be silly.

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Bloodrealm wrote:
What I meant was that if everything needs Resonance either consumed or invested, then small things like the Any-Tool won't get used. I didn't mean that if those things DON'T use Resonance then they won't get used; that'd be silly.

So instead of assuming everything is awful, let's advocate for minor magic items that don't require resonance. Write it down as something to look for and playtest in August. Be a constructive analyst/ playtester.


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I’m just hoping resonance is one of those systems where they put out the extreme version so it can be walked back.


They've explicitly said not every item will use resonance. For example, using a magical weapon won't consume resonance. I generally think this is a good approach overall, though I'd suggest the following:

1) You may wear a number of permanent magical items up to exactly your resonance.
2) You may consume magic items up to your resonance without chance of them failing, then beyond that implement what they had been doing.

Basically, I'd split apart the permanent magic items from consumables. Yes, I'm limited to X magic items based on my level and charisma, but the number I use doesn't reduce the number of potions/consumables I can use in a day (also based on my level and charisma).

And yes, I'd definitely have some items not consume resonance at all, but I think that's already in their game plan.


KingOfAnything wrote:
So instead of assuming everything is awful, let's advocate for minor magic items that don't require resonance.

I'd rather assume it's all awful and be pleasantly surprised if it's better than think it's going to be awesome and find out it sucks. :P


Bloodrealm wrote:


And they will no longer be able to create small, inexpensive items that aren't worth spending a Resonance point, like a Traveler's Any-Tool. Also, nobody will ever use things that are just cool to have because that eats into Resonance they might need for something mechanically important like "not dying".

Yeah, I know how that works. "I may need it later". Never uses it.

That's just bad tactics. People will grow out of it. It happened to my 4e group ;)

Also, to correct some stuff here: it's not only consumables which spends a use. Cool powers of items like magic swords and wands spend a point. That's why you have a bunch of them ^^

Also, it is your Level + Charisma, not Charisma modifier ;)


Arssanguinus wrote:
I’m just hoping resonance is one of those systems where they put out the extreme version so it can be walked back.

There's no extreme version here. This is not extreme in any way. If people want to overthink every aspect and think about all things that physically may go wrong, I'm not able to stop it. But that's just non-sense. It's a great mechanic that a bunch of people are screaming for reasons that don't exist.

I'm tired of this. Let the playtest begin so we may talk about it later.

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graystone wrote:
KingOfAnything wrote:
So instead of assuming everything is awful, let's advocate for minor magic items that don't require resonance.
I'd rather assume it's all awful and be pleasantly surprised if it's better than think it's going to be awesome and find out it sucks. :P

See, the present value of happiness now seems much greater than the future value of happiness later. Disappointment later is also mitigated by playtest feedback, which I can only expect will be more satisfying than griping on the forums.

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