4d6 drop the lowest die

[dsatow]

What would you rate the limitation for a 4d6K where you drop the lowest die?  Would you only put the limitation on 1d6K (15 active) or on the whole 4d6K (60 active)?

 

Example: You roll 4d6K and get 1,3,4,6.  You would drop the lowest die, a 1, and get 13 for the 3,4, and 6.  You then determine stun normally.

[Hugh Neilson]

First, I'd want to assess why we're doing this. It skews the curve, making lower rolls less likely and higher rolls more likely.  My inclination if I did allow it would be to price it at 3 1/2d6, which averages 12.5, as this model will average about 12.25 (if I did the math right - no guarantees), not treat it as an advantage on 3d6 or a limitation on 4d6.

[dougmacd]

You're always getting 3d6, so I would only put a limitation on the 4th die of effect: 3d6 Killing Attack, plus 1d6 KA, Only adds damage if roll is higher than lowest face of other dice, Damage added is only equal to difference between this die and lowest face.

 

Someone could probably work out the probabilities, but -2 or more seems reasonable.

 

 

Doug

Ah the joys of typing on a kindle (-_-)

[Hugh Neilson]

If I were doling it as a limitation on the fourth die, it would be -1/2, due to the impact of moving this up 2 DC's in average damage from 3d6.

[dougmacd]

Yeah, looks like the average of 4d6 drop lowest is 12.24, so the last die is effectively rolling a standard effect of about 2 pips over the average of 10.5 on 3d6. The -1/2 limitation on last die sounds right; -2 is way too much.

 

Doug

Pips, not DC :-j

 

 

[LoneWolf]

Personally I would not allow it for one main reason. That is that it is going to over complicate things.   It significantly reduces the chance of rolling low and increases the chance of a high roll.  This ends up throwing the averages off by quite a bit. This makes things like penetrating more efficient.  How do you handle increasing the DC of the attack?  If I add 3 DC to the attack does it become a 5d6 drop the lowest or does it become 5d6 drop the two lowest?  Also how do you deal with damage negation?  If I have 3 levels of damage negation does the attack become a normal 3d5 or does it become a 3d6 drop the lowest dice?  Then there is the extra step of checking to see what the lowest.  It is too easy for a player to forget to drop the lowest die. 

[Derek Hiemforth]

My strongest opinion on this is that it definitely should not be a Limitation on all 4d6. Even at only -¼, that would drop the cost to 48. That's barely more than the cost of 3d6, and getting to roll 4d6 and keep the best 3 is way better than just a regular 3d6.

 

I think @dougmacd nailed it.  The right way to think about this is as 3d6 with a kicker... not as 4d6 with a Limitation.

[assault]

I'm still wondering why this is even an issue. Why would you ever want to do this?

[LoneWolf]

The reason to do this is obvious that it gives an advantage to the character.  It significantly reduces the chance of rolling low, and about doubles the chance of rolling high.  On a normal 3d6 roll the chance of you rolling a 3 is about .46%, on 4d6 drop the lowest it is .08%. The chances of rolling 18 on 3d6 are also .46%, but on 4d6 drop the lowest is .93%.  This throws off the whole curve and means the character will be rolling better damage a lot more consistently.  From the looks of it, it puts the damage very close to that of a 4d6 roll, but without the chance of a really good roll, and almost eliminates the possibility of a poor roll.  

 

If I did agree to this (And I would not) I would rate it as a -0 limitation.
 

[Hugh Neilson]

23 minutes ago, LoneWolf said:

If I did agree to this (And I would not) I would rate it as a -0 limitation.

That's no different than refusing it entirely.  Clearly 4d6 drop the lowest is less than 4d6.

 

I would change the base points, not apply a limitation, to align with the average damage (which is about +1/2 d6, so +10) or limit only the last die -1/2, which gets a comparable result.

 

I'd want to know what, exactly, this is supposed to simulate that would not be just as easily done with a 3 1/2d6 KA.

[unclevlad]

The difference is you increase the mean, increase the probability of high damage...but DON'T raise the max damage.  3 1/2 d6 maxes at 21, not 18.

 

I wouldn't buy it as a limited 4d6.  I'd buy it as an advantage on 3d6.  Probably +1/4, because it's not better than AP, and that's 11 points anyway...basically the same as the half die.

 

Another aspect:  this is an advantage impacting damage, so damage added elsewhere (STR, martial maneuvers, weapons master, deadly blow, skill levels) has to be adjusted for the advantage.  And that's good;  go up one more die, to 5d6 dropping the lowest, the improvement in the mean goes from 1.75 to 1.9.  

 

Great site here:

https://rumkin.com/tools/die-stats/#!/?dice=6d6D1

 

So additional damage is handled reasonably when you take this as an advantage.  

 

And even if this is on 1d6...the difference between 1d6+1 and 2d6, drop lowest, is low.  2d6 drop lower means 5 and 6 happen 58% of the time...but 1d6+1 gives 5-7 50% of the time.  2d6 drop low has a mean of 4.47;  1d6+1, 4.5.

 

So I'd probably allow it as a general +1/4 advantage.  What does this simulate?  An attack that finds weak points better.  In a sense, you could think of it as a form of automatically spreading a bit, in order to find those little flaws in the defense.  Don't think of this as More Damage...but adjusting the style.  Much like AP or Penetrating.

[Hugh Neilson]

33 minutes ago, unclevlad said:

The difference is you increase the mean, increase the probability of high damage...but DON'T raise the max damage.  3 1/2 d6 maxes at 21, not 18.

 

It reduces the probability of a very low roll markedly, increases the chance of a very high roll slightly and shifts the average roll up from the mean of a 3d6 attack to the mean of a 3 1/2d6 attack. The use of an advantage model also ignore the reality that this is considerably more valuable for smaller numbers of dice, as it reduces the negative side of volatility.  On 12d6, how much benefit would making it 13d6, drop the lowest be?

 

2d6 drop the lowest means we go from 1 chance in 6 to roll a 1 to only one chance in 36.  A 1 or 2 comes up 1/3 of the time on 1d6, but on 1d6, drop the lowest, would come up only one time in 9.  It would move from a 3.5 mean to almost 4.5.  With that in mind, I would call this level equivalent to 1d6+1, so a 20 point base cost.

 

We're coming to similar results, as +1/4 would get a pretty similar result for both 1d6 (19 vs 20) and 3d6 (56 vs 55).

 

Advantage stacking, and just interaction with other advantages, becomes an issue pretty quick.  Dropping the chance, on that 1d6, of no penetrating damage from 1 in 6 to 1 in 36 seems pretty valuable.

 

To me, the bottom line is that other advantages change how the damage is applied, not the manner in which it is determined.  This belongs as a modifier to the base cost (the cost of the average and range of damage), in my view.

 

As to "it finds the weaknesses", no it doesn't.  It does more damage to someone who had no defenses to begin with, so it's finding no weaknesses there, and it's finding no weaknesses in defenses sufficient to bounce a 3d6 attack.

[unclevlad]

Advantage stacking could become an issue, that's true, but adding to the base damage

a)  doesn't scale well.  If this is 1d6, then it's 5 points.  If it's 3d6, then it's 10 points.  So...what's the cost?  

b)  doesn't impact additional damage from any source, and the more dice you add, the more this improves.

 

The biggest potential issue with advantage stacking, in my mind, is probably Autofire.  Damage Over Time might be another, but that's known to be problematic in the first place.  With Autofire, the fact that you are much more likely to get a good roll becomes far more significant.  We already have that autofire attacks against non-standard defenses require an additional +1, so one solution might be that this gets a similar treatment...+1/4, OR +1/2 when it's combined with Autofire.  That said:  yes, there's potential synergies here that are nasty.  That will be true either as a base booster like the +1 or +1/2d6, or as an advantage, I suspect.  THAT argument, tho, says either consider it as a yellow Caution power, or simply don't allow it.  I would allow it with explicit approval...so, not when I thought it would create problems...and that probably means, nothing else that impacts damage delivery/resolution.  AP, Penetrating (doubt this would be sensible anyway), Reduced Negation, Autofire, Double KB, AVAD...I don't want to go through all the issues.  Some might work;  some likely won't.

[Hugh Neilson]

1 hour ago, unclevlad said:

Advantage stacking could become an issue, that's true, but adding to the base damage

a)  doesn't scale well.  If this is 1d6, then it's 5 points.  If it's 3d6, then it's 10 points.  So...what's the cost?  

b)  doesn't impact additional damage from any source, and the more dice you add, the more this improves.

 

Adding +1 normally costs 5 points.  Adding 1/2d6 costs 10 points.  They increase mean base damage by +1 and +2 respectively. "Drop the lowest die" is a different way to increase base damage.

 

Penetrating gets more powerful if we have more base damage, and as such it increases the cost of the attack proportionate to that base damage.

 

I'd be interested in any indication that rolling 13d6 and dropping the lowest one (which will virtually always be a 1) would raise the average roll to a level consistent with 15d6 (52.5 average roll).  Even raising the average damage by 6, from 42 to 48, would  not get us there.  In fact, the mean becomes 44.4 - and I agree that's a very useful site.  Even 15d6 dropping the lowest 3 only gets us to 48.5, still not as good as 14d6, much less 15.  17, dropping 5 gets us to about 51.75

 

With that in mind, I don't think your method scales well either.

 

It does impact average damage rolled - similar to changing to d8s, and similar to adding more dice - so to me it is a base damage price, not an advantage or limitation.

 

The only other advantage I can think of that modifies the base damage is "increased STUN multiple", which scales consistently with the dice rolled.

[dsatow]

Thanks for the feed back.  Started a new job and was a bit busy for a while to check on this thread.

 

The idea for this is to create a situation where the user could increase the average damage but not the max damage.  For instance, a person who has a gun would be able to shoot and hurt a target better because of their skill and shot placement rather than adding power to the gun/bullet itself.  I didn't think about blast, but assume you would use a like amount on the blast.  Say a 9d6 Blast with the ability to replace 3d6.  

 

It does add a very small amount of complexity, but I think its fairly negligible compared to other parts of the game.  It might break certain habits for players if forced on everyone, but like most things in Hero, it only affects the player and/or GM who implements it on one of their characters.  And thus the only one it really effects from a game implementation point of view is the user.

 

My initial idea was to use it as an additional die (3d6 + 1d6 where the 1d6 had limitations on it).  People adding strength or aiding the killing attack would aid the core base or the additional.  Because the +1d6 was an additional die, the advantages had to line up with the original attack.  It would not be allowed to be pro-rated by design since it was replacing a die roll unless the die roll being replace was a full die.  But I was also thinking that it really is a 4d6 killing attack with a kind of damage cap.  So I got torn as to what kind of implementation would be serviceable in game play.

 

For those that would use it, would you roll 4d6 and drop the lowest one or roll 3d6 and decide whether to replace one of the dice with the additional die?  Yes, this is functionally the same, but in actual play, people thought processes would be different.

[Hugh Neilson]

I'd roll 4d6 and drop the lowest base don the initial description - there is never a drawback in doing so, and that makes it a single die roll with no decision in the middle, speeding game play.

 

My analysis was based on the increase to average damage, which suggested a 10-point cost for the added die and drop the lowest as compared to 15 points for just adding another die.  The likelihood of a roll of 19-24 on 4d6 exceeding 18 is a bit under 10%, so "4d6, max damage 18" would not be very limited compared to, say, 4d6, Activate 15- (a bit less than a 5% chance of not getting a roll at all). "4d6, drop the lowest" will also have lower damage if rolling under 19, so it is more limited.

 

Consider that +1d6 (14- activation) would cost 10 points and +1d6 (8- activation) would cost 5 points, there's a pretty tight range for what this should save.  The average roll for 3d6, +1d6 14-, would be 13.65, so higher than 4d6 drop the lowest (about 12.25), so that could argue for a lower cost.  If it activate 8-, the average would now be 11.375, so -2 on the extra die is too big.  The added average is about 1/2d6, so if you called the limitation -1 (act 11-) or -1 1/4 (10-?) on the extra die, that would be comparable.  I might go as high as -1 based on that.

 

 

 

 

[unclevlad]

I agree with Hugh, just roll all four, drop the lowest.  For one thing, there's really almost no decision.  You'd always re-roll a 1 (91 of 216 3d6 rolls have at least 1) as there's no potential loss.  You'll re-roll a 2 because potential gain is MUCH better than the risk (125 cases have no 1;  of these, 64 have no 2, so you have 61 more cases with a 2, but no 1).  So we're up to 152 out of 216 where the re-roll is a no brainer.  Flip side:  when all 3 dice are 4 and higher, re-rolling is more likely to cost.  That's 27 cases.

 

So by and large...the only borderline case is when the lowest roll's a 3.  All dice 3+ has 64 cases;  all dice 4+ has 27.  So there's 37 cases where you might do this.  It's slightly advantageous to re-roll, but remember that all 3 dice are 3+ in this scenario, so there's lots of 13+ showing.  LOSING some damage may be worse than gaining some.  Which also brings up potential metagame considerations that I'd rather avoid, particularly when it's simply not going to be an issue often enough.

 

As for using this on Blast, allowing possibly multiple dice...a LONG!!! time ago, the group I was playing with did some Legend of the Five Rings.  L5R has the full "roll D, keep K" mechanic...but it was built into the system, including in pricing.  IIRC, skill levels added unkept dice;  baseline characteristics added kept dice.  The characteristics were FAR more expensive.  Now, ok, in L5R you also had exploding dice...d10's, so exploding didn't happen often...but that makes for a very complex analysis.  I remember doing a fair bit of Monte Carlo crunching...exploding dice means you don't have a fixed, finite set of rolls...for all sorts of combinations.  What's better, 4 keep 3 (4K3) or 5K2?  It was interesting, but I'm pretty sure I've lost all those notes;  that was a couple moves ago.

 

Here, we don't have exploding dice, but the value of these extra dice is still tricky to evaluate.  It'll vary, depending on how many kept dice, how many dropped dice you have...if the attack is 6 dice, then adding 2 droppers will have a better cost-benefit balance than adding 4.  A 10 die attack, tho, can likely do better with 4 droppers.  (I suspect the sweet spot is gonna be when about 1/3 of the dice you roll, get dropped.  10 kept, 4 dropped is 14, so dropping 4 is about right.)  And the more droppers you add, the more this does risk dragging things down a bit...particularly as attack power rises.  12d6 with drop-5?  That's 17 dice, finding the lowest 5 will take a bit.

 

Another issue here, generally:  the basic mechanic does modify damage, so it needs to be considered in DC evaluations and/or attack active point caps.  So I'd definitely start slow...adding a single dropped die option to killing attacks is pretty straightforward.  Adding multiple dropped dice...to KAs or normal attacks...is rather harder.