A search for an optimal resolution mechanic

[RadiantPhoenix]

For somebody who makes so much noise about game mechanics, your grasp on the actual math is a bit weak really.

Calculation for TN 3, explodes on 1 and 6, as per your suggestion from the discussion with DrP above:

Rolls from 2-5 don't explode. That gives you a 4 out of 6 chance for a 3 out of 4 success, or a value of 2/3 x 3/4 = 1/2 for the part of a die that does not explode.

To this you need to add the remaining 1/3 of the die (1 and 6) that does explode into another die, which can in turn explode.

So what you actually get for an exploding TN 3 roll is

1/2 + 1/3 x (1/2 + 1/3 x (1/2 + 1/3 x ( .... ))))) and so on.

This is equal to

1/2 x (1 + 1/3 + 1/9 + 1/27 + ...)

The series in the brackets converges on 3/2, so your final expectation is

1/2 x 3/2 = 3/4.

The value of a non-exploding TN 3 roll is 2/3. 3/4 divided by 2/3 is 9/8, so when a d6 explodes as you suggested, the value of each die increases by 1/8 success compared to a non-sploding d6..

Do you see it now?

Let me try:
(Using Frank's H, B, D, and X)
A Hit adds one success, a Botch removes one

The expected number of successes per die rolled without exploding (X = 0) is (H - B)/D . Explosions only change the number of dice that wind up being rolled.

The number of dice you expect to roll per die you "roll" is the sum, from zero to infinity, of (X/D)^n . Wolfram Alpha tells me this is equivalent to -D / (X - D) which is equivalent to D / (D - X). Multiplying the expected number of successes per die by the number of dice rolled yields (H - B)/(D - X) successes per die "rolled".

[tenuki]

Let me try:
(Using Frank's H, B, D, and X)
A Hit adds one success, a Botch removes one

The expected number of successes per die rolled without exploding (X = 0) is (H - B)/D . Explosions only change the number of dice that wind up being rolled.

The number of dice you expect to roll per die you "roll" is the sum, from zero to infinity, of (X/D)^n . Wolfram Alpha tells me this is equivalent to -D / (X - D) which is equivalent to D / (D - X). Multiplying the expected number of successes per die by the number of dice rolled yields (H - B)/(D - X) successes per die "rolled".

You can't use (H-B)/D for the value of a single die. That's because all the dice you're finally left to count effectively have (D-X) sides -- you'd have to reroll the other ones because they explode. Also, botches get rerolled.

The value of a die that gets counted in the end is H/(D-X).

[Username17]

The part where you're confused is that the idea of exploding on 1s and 6s is not my suggestion, that's DrP's. It's a terrible suggestion for numerous reasons. If you want to rant about exploding on a 1 and a 6 instead of something vaguely sensible, you really need to put that explicitly into your posts, because just reading it, if you say that "dice explode" they are going to assume that they explode on just the high numbers. On account of that is how every exploding dice mechanic in history has worked because the alternative of exploding on low or midrange numbers is fucking retarded.

-Username17

[tenuki]

Your formula is horseshit even for mechanics without botches and where only the high numbers explode.

For TN 3, explodes on a 6, you get 3 hits out of 5 eligible events on the dice you end up counting. That's the number you want to multiply with the expected number of dice actually rolled (and add the expected number of extra successes because 6 and 1 don't balance each other any more).

[Previn]

Skipping the exploding dice issue for a moment.... wouldn't a TN of 3 push the Thresholds up really, really fast and narrow the scope of Thresholds you actually bother rolling against? I had assumed that the ability of Shadowrun to use basically the same Thresholds for most of it was a strength of the system.

[Username17]

Your formula is horseshit even for mechanics without botches and where only the high numbers explode.

For TN 3, explodes on a 6, you get 3 hits out of 5 eligible events on the dice you end up counting. That's the number you want to multiply with the expected number of dice actually rolled (and add the expected number of extra successes because 6 and 1 don't balance each other any more).

This word salad needs more croutons.

-Username17

[Lago PARANOIA]

Frank:

http://www.tgdmb.com/viewtopic.php?p=251791#251791

[tenuki]

Your formula is horseshit even for mechanics without botches and where only the high numbers explode.

For TN 3, explodes on a 6, you get 3 hits out of 5 eligible events on the dice you end up counting. That's the number you want to multiply with the expected number of dice actually rolled (and add the expected number of extra successes because 6 and 1 don't balance each other any more).

This word salad needs more croutons.

-Username17

Don't worry. You get a C for effort even if you comprehend only the first paragraph in my quote.

[RadiantPhoenix]

You can't use (H-B)/D for the value of a single die. That's because all the dice you're finally left to count effectively have (D-X) sides -- you'd have to reroll the other ones because they explode. Also, botches get rerolled.

Ah. I think we have a different definition of exploding.

My interpretation was thus:
d6, Hit on 3+, botch never, explode on 1 and 6

Number	Hit?	Botch?	Explode?
1	No	No	Yes
2	No	No	No
3	Yes	No	No
4	Yes	No	No
5	Yes	No	No
6	Yes	No	Yes

Under my interpretation, if you roll a hit that also explodes, you keep the hit but also roll another die, and likewise for botches.

[Username17]

Skipping the exploding dice issue for a moment.... wouldn't a TN of 3 push the Thresholds up really, really fast and narrow the scope of Thresholds you actually bother rolling against? I had assumed that the ability of Shadowrun to use basically the same Thresholds for most of it was a strength of the system.

The issue is that the game flat falls apart as soon as you put a dragon or an APC on the battlefield. At TN 5, there are PCs who can probably make a threshold of 2, and PCs who can probably make a threshold of 6. But there aren't any PCs who can reliably make a threshold of 12. But 12 isn't off the RNG for the PCs who have a modest confidence about a threshold of 4. You're left with lucky shots with thrown rocks blowing up tanks somehow and weird kludgy piles of automatic hits and "you must be this tall" signs to try to keep that from happening too often. It's not good.

In order to extend things higher (and for that matter lower), you actually need to be able to hit higher thresholds with less literal added dice. And you need to have the high-end black swan events reigned in. Lowering the target number accomplishes both. Now you can fight bigger things with bigger weapons without having to arbitrarily reset the RNG.

What if you make changing TNs:

Then it would be just like SR3's Vehicular Damage and Naval Damage hard resets of the game. The whole point of going fixed target number is so that things interact on the same scale and modifiers have predictable effects. If you vary target numbers, even if you do so in precisely defined tiers, it's still going to get messy as hell.

At TN 5+, a buff or curse needs to be about 3 dice before you consistently notice it. But at TN 3+, that's a 2 threshold bonus or penalty. So mixing low tier buffs and debuffs with higher tier characters becomes way overpowered in a really weird way.

Honestly, if I were going to deliberately make buffs and debuffs interact weirdly across tiers, I think I'd want it to go the other way. Where a BBEG or protagonist Warlord gave proportionately large bonuses to tiny men and skeleton minions so as to make them matter to the enemies that matter to them.

-Username17

[Username17]

Don't worry. You get a C for effort even if you comprehend only the first paragraph in my quote.

Better plan: I'm putting your ass on ignore for a month.

-Username17

[Lago PARANOIA]

At TN 5+, a buff or curse needs to be about 3 dice before you consistently notice it. But at TN 3+, that's a 2 threshold bonus or penalty. So mixing low tier buffs and debuffs with higher tier characters becomes way overpowered in a really weird way.

What's wrong with that? I am totally okay with Toki getting much more out of his attacking from higher ground bonus than Bruce Lee. Or Vash benefiting more with the defending from behind cover bonus than James Bond. Or Ryu Hayabusa abusing the sneaking in partial concealment bonus than Shredder. Similarly, I'm also okay with the idea of plucky young turks relying more on debuffs than buffs when attacking higher-level critters, especially across tiers.

This does of course mean that 'higher level' buffs don't give out much more in the way of dice than 'lower level' buffs, if at all.

[echoVanguard]

TN Shifting is great for mixing play levels

This might work OK if you defined your TN shifts rigorously (ex: by tier and by content type simultaneously). You should probably define some examples.

echo

[Lago PARANOIA]

You didn't do that to strawman me or mock me echoVanguard, but, please don't misquote me like that. I did not explicitly state that TN is great for mixing play levels, I'm right now exploring hypotheticals.

[Murtak]

To clear up the issue with Shadowruns original exploding dice system:

The idea behind the system is that your aptitude is represented by your dicepool while the difficulty is decided by the TN. How many hits you score determines degree of success. Nice, simple, obvious. That is, if you can increase the difficulty smoothly. When you get a +1 TN penalty for bad vision and it knocks your TN from 3 to 4 your chance of success per die drops 66% to 50% or by 25% of your original chance, depending on your point of view. But when you go from 4 to 5 it drops down to 33% (by 33%, coming from 50%) and when you go from 5 to 6 it drops by 50%. That is issue one: the drops get sharper and sharper. And then you get into exploding dice. Look what happens when your TN goes from 6 to 7. Nothing. At all. And when it goes from 7 to 8 it drops by 16%.

Look at this progression: 25 -> 33 -> 50 -> 0 -> 16

That is madness. The same +1 is worth anywhere from half of yoru dice to nothing at all. At the same time the original drastic increase in difficulty ensures that once you get to truly difficult tasks you need humongous piles of dice to have a chance to score even one hit. If logarithmic dice existed, where each progressive number was, say, 20% less like than the one before it, you could make such a system work. Without logarithmic dice you can't. It falls apart both for big numbers and at each explosion step.

[Username17]

Making log dice is not a problem. A 1 is worth 0, and every other number is worth +1 and explodes. Each increase in TN is 16.7% less likely to occur than the one before it.

The reason that sucks is not because it isn't mathematically elegant, but because it requires rolling dice ten times in series to do even simple tests. Pretty much only possible for a computer, at which point the fact that it can be rendered with physical dice is meaningless.

-Username17

[DrPraetor]

First, you were responding to my post about TN 4 being the most elegant solution for botchsploding dice. If you want dice to explode only one way, there is no elegant solution, as Tenuki correctly-pointed-out, because the expected number of hits changes (by however much), when you turn exploding dice on and off. A system of exploding dice is only "elegant" if it doesn't do that. This is a much more crucial distinction than having a TN of 4 or TN of 5. Furthermore, this is a repeat of an entirely valid criticism of that RNG, that you could actually get the same effect while using only one color of die. But, fine, we'll look at the more restricted space of the RNG in F'sCPFHB:AT - of course *I also designed that RNG*, so it hardly goes without saying that you're talking about that one instead.

We're not allowed to have botches, we have an artificial floor at 0 for the number we can generate from any pile of dice we roll, although we roll two piles at once and subtract them.

The variables you want to tune, rolling WD and BD, each of which has chance 1/n or 1/m of hitting respectively, are:
E(N) = WD/n - BD/m : Expected number of hits.
Var(N) = (1/n)(1-1/n)WD + (1/m)(1-1/m)BD : Variance in the number of hits.
E(faults) = BD/m : Expected number of hits lost to black dice, tracked on it's own for use later.

What value of n and m give us the best tuning control over these parameters in the smallest range of dice? Definitely we want m<3, because we may want to raise E(faults) *without* raising Var(N), and our best ability to do that is with m<3 (and if we didn't want to do this we'd only use one color of dice, see below). You can, as Frank sorta did, argue that n=3 or n=1.5 is better than n=2, because then you get a high E(N) without a high Var(N), although this requires big heaps of dice. This does make it *impossible* to do the reverse (low E(N) and high Var(N)) without rolling black dice.
But since we also want m=n if we can possibly do it, you can make an argument for TN=3 (m=1.5, n=1.5); you roll fewer dice in general, you can have a high E(faults) without having a high Var(N). OTOH, this causes funny things to happen when you turn exploding dice on and off. Exploding dice are *good* if you are rolling a lot of white dice and *bad* if you are rolling a lot of black dice - unless black dice don't explode in which case it's always good. But it moves E(N) around, and of course raises Var(N).

But can you achieve the same while rolling only one color of die, with botches, and taking free hits, which explode on probability m and also fault&botchsplode on probability m:
E(N) = A + D/n
Var(N) = (1/n)(1-1/n)D + [~(1-1/n)*D/(m*n)*4]
E(faults) = [D/m + ...]

(Variance is the product of the variances, plus Var(A)*E(B) + Var(B)*E(A)... lessee]

The stuff in brackets only matters when botchsploding dice are on. EDIT: Yes, I said botchsploding, so the botches and the exploding are either both on or neither is on.
If we disregard fault counting, this is strictly better than the RNG above and it's best (in terms of ability to control E(N) and Var(N) with fewest possible dice) at m = 2 (TN 4).
Also, *unlike* the RNG above, the E(N) doesn't change when we turn fault,explode&botchsplode on or off, which is "elegant".
This is simpler than the RNG above mainly because it *only uses one color of dice*. It also needs marginally fewer dice to generate the same range of outcomes.
Now, it does have a problem in that Var(N) and E(faults) are strictly linked. Also ,it is counterintuitive in that rolling more dice is actually *bad*; skilled characters are rolling relatively few dice and getting free hits (A) instead.

But I don't have a problem with that from a game design standpoint, because basically it says: risk = risk. Rolling more dice = more risky. More risky = more chance to fail unexpectedly, more chance to succeed unexpectedly, and more chance to accumulate faults for the mission-emergency counter.

So in non-stressful situations, skilled characters have A > Threshold, and automatically succeed. Botches are *good* because they let you hand out those automatic successes, which you can then lose by rolling more dice. From a strictly utilitarian standpoint, this gives you the best possible control over E(N) and Var(N), without hitting hard-edges-at-0 and "you must be this tall to ride" signs.

[Username17]

First, you were responding to my post about TN 4 being the most elegant solution for botchsploding dice. If you want dice to explode only one way, there is no elegant solution, as Tenuki correctly-pointed-out, because the expected number of hits changes (by however much), when you turn exploding dice on and off. A system of exploding dice is only "elegant" if it doesn't do that.

Then you're defining "elegant" to be "stupid and undesirable".

Furthermore, the botchsploding die you described doesn't have the chances stay static when you turn the exploding on and off.

Number	Botching Die	Botchsploding Die	Botching 5-Again Die
1	Botch	Botch+Explode	Botch
2	Miss	Miss	Miss
3	Miss	Miss	Miss
4	Hit	Hit	Hit
5	Hit	Hit	Hit+Explode
6	Hit	Hit+Explode	Hit+Explode
Average:	1/3	1/2	1/2

The key information is that in the equation (H-B)/(D-X) then if your base chances are 1/2, then adding 1 to B and 2 to X leaves it at 1/2. But so fucking what? If you had a TN of 3+ (average 2/3) then you could add 2 botches and 3 explosion numbers and still balance the equation. Or whatever, because it's a really fucking simple equation and if you subtract numbers that are proportionally identical to the starting probabilities then it cancels out on average. Yeah, I managed to get through ratios and fractions in fourth grade too!

There is absolutely nothing privileged or elegant about choosing any particular number to explode on or to botch on. And perhaps more importantly still: there is an actual negative value in having an optional complicated mechanic if it doesn't change expected values.

-Username17

[DrPraetor]

Furthermore, the botchsploding die you described doesn't have the chances stay static when you turn the exploding on and off.

I believe I said to turn the *botchsploding* on and off, I'll fix it in a minute if I didn't. Anyway, that isn't the die i meant, I meant this (On a "non-stress" test, if A >= threshold, you just succeed without rolling.):

Number	Non-stress Die	Botchsploding Die
1	Miss	Botch+Explode
2	Miss	Miss
3	Miss	Miss
4	Hit	Hit
5	Hit	Hit
6	Hit	Hit+Explode
Average:	1/2	1/2

It's true that this doesn't change expected values - it changes *variance* however, which is what it's for (see fixed table in previous post).

It's undesirable to have a complicated mechanic that changes expected values in a hard-to-figure-out-why. This is simple to understand - if I expect to succeed, I don't want botschsploding dice. If I expect to fail, then I *do* want botchsploding dice. The fact that it doesn't change the average is desirable because then you don't have any ambiguous cases it's hard to figure out if botchsploding dice are to your advantage, or not.

Also I need to correct my previous post because I was interrupted mid-calculation.

Incidentally, these are the formulas I'd use:
A = Skill or Attribute, whichever is lower
D = |Attribute - Skill|

If you set things so that Skills are generally rated 1-4 and attributes are generally rated 1-6 (as in SR4), this works out that talented novices roll a lot of dice, and are swingy; while skilled people are reliable.

[Username17]

It's true that this doesn't change expected values - it changes *variance* however, which is what it's for (see fixed table in previous post).

It's undesirable to have a complicated mechanic that changes expected values in a hard-to-figure-out-why. This is simple to understand - if I expect to succeed, I don't want botschsploding dice. If I expect to fail, then I *do* want botchsploding dice. The fact that it doesn't change the average is desirable because then you don't have any ambiguous cases it's hard to figure out if botchsploding dice are to your advantage, or not.

OK, now that you've changed your statement to say that the botches and the explosions only go together, then I agree with you that they don't change the averages. That is however, not elegant. It's clunky and shitty. For the following reasons:

• Botches suck as a mechanic Getting a negative success for rolling more supposedly positive dice is shitty. If during a campaign you end up saying "If you hadn't been so talented and experienced, you never would have fucked up that badly" even once, your system is night soil. Getting a bonus should never end up penalizing you, because that is horse shit.
• Rolling with Explosion without a cost leads to shit. We've already been over this, if exploding dice is something that can be repeated for credit it leads to stupid take 20 shenanigans. If exploding dice is something that happens on mook rolls, then iterative probability says that protagonist heads will explode in some minor set piece. Exploding dice has to come with a cost or it's bad for the game.
• Spending something to get nothing is lame. If you spend some resource to get your dicesplosion on, you'd better fucking get something positive out of that, because you just spent a resource of some kind and took an action at the table.

While I grant that if you add botches and explosions in proportional amounts to a dice pool that you can leave the averages unchanged, that is in no way desirable. The only way explosions are even vaguely acceptable as a mechanic is if it's "spend an edge, make an exploding test". And spending an edge for am increase in expected hits per die is acceptable, but spending an edge to get no expected increase but more randomness and a longer resolution of your die roll is not.

Your definition of "elegant" is "undesirable in every possible way".

-Username17

[DrPraetor]

Frank, this is a problem with dice pool systems *in general*. The swingyness (variance) goes up as you get more skilled. Put another way, suppose you are dice pool A, and your opponent is dice pool B. On a TN 5 dice resolution system, you will have (A-B)/3 +/- sqrt(2/9*(A+B)) hits. If A>B, as A and B both rise, your chance of winning GOES DOWN. With no botches! Furthermore, as A and B both rise, your chance of some degree of success > 0 also goes up. That is, as everyone becomes more skilled (rolls more dice), the entire distribution of outcomes flattens out, so that when people are rolling large numbers of dice, rolling bonus dice doesn't even matter. 23 dice average one more hit than 20 dice, but that's 1 +/- sqrt(2/9*43) = 1 +/- 3 hits, meaning you'd have to roll about *36* challenges before you could be sure that the guy rolling 23 dice was better than the guy rolling 20 dice. This causes all kinds of problems with scaling the system to tanks, with having skilled players suffer black swan events all the time against relatively competent mooks, and so forth.

The SRIV dice pool has a *fundamental flaw* because swinginess (variance) and expected degree of success are intrinsically linked, and you can't have one without the other. It's still a workable system within a certain range, but if we're asking: what is the optimal resolution mechanic? Well, the optimal resolution mechanic is one where how-swingy-you-are and how-good-you-are are not intrinsically linked, and that means that PEOPLE WHO ARE BETTER DO NOT ROLL MORE DICE. That's the *only way* to make is so that people who are better are not also more swingy - no ifs, buts or mayhows.

This isn't a problem with botches, it's a problem with dice pools. Now, botches and exploding dice merely aggravate this problem. In your example, if A > B, and dice only explode up, then you (the guy rolling A dice) are worse off if both sets of dice explode. Is that obvious to anyone? I think it's a very opaque mechanic that players have trouble dealing with, among the other problems. WoD has an absolutely awful system in every way, *including* an awful system for botches which aggravates this intrinsic problem with dice pool systems. But that doesn't mean that botches are bad, it means that WoD is bad.

On the other hand, if:
* Being better lowers the threshold *instead of giving you more dice*
* Chancy, but on average beneficial effects give you more dice
* Chancy, but on average determintal effects give you more dice AND raise the threshold

Everything works great, including botches. Since extra dice represnt chancyness rather than goodness, the fact that they can botch is a feature, not a bug. Being better does not "sometimes cause you to fail" because being better *doesn't give you more dice*. Being talented but untrained may give you more dice, and yeah that means sometimes you'll botch when you otherwise would've merely failed, but this is I think realistic, and in any case genre appropriate for the kinds of things that are *supposed* to happen to highly talented rookies.

Am I not being clear here? Because you're making a fundamental error in thinking that dice pool systems have to work like-they-do in SR or (shudder) WoD, and I'm saying that they *don't have to* work that way, and furthermore that having them work may way is intrinsically, fundamentally better as a resolution mechanic. You can control the expected degree of success and the variance *independently* by having really-good people roll small numbers of dice and get large numbers of free successes.

You're right that having a truly open RNG often causes problems - and for that reason, the RNG should sometimes be closed. I disagree that it should be closed for Mooks; instead, the characters should have some resource (Edge points, probably) that they can spend when a Mook explodes on them. But if the Mooks *can't severely injure* the PCs, especially mooks with fucking guns, it's going to break verisimilitude immediately; if the PCs have to use up finite luck points to avoid what would otherwise have been injuries to mooks with pistols, that's much better.

[Username17]

Frank, this is a problem with dice pool systems *in general*. The swingyness (variance) goes up as you get more skilled.

While it is true that your chances of rolling significantly above or below average increases as you become more skilled in dice pools of all sizes, your chances of actually rolling catastrophic failure only go up if you have botches. It's one thing to say "your chances of falling 3 less than your average increase as your average increases", but it's totally not fine to say "your chances of getting a negative 3 increase as your average increases".

Conflating relative failure and absolute failure is not helpful when discussing dice pools. Getting more dice should be good, not bad.

Edit:

On the other hand, if:
* Being better lowers the threshold *instead of giving you more dice*

This is not OK either. We've already seen games in which you get a large pile of free hits and a small number of dice. Sion, First Edition Shadowrun, Aberrant, and so on. It's crap. It makes people not even give a fuck about the die roll and just whore auto-hits. You might as well be playing Amber Diceless.

You can either embrace the fact that rolling more dice makes your averages and variance rise or you can dump dicepools as a mechanic. Trying to get a sweet spot by counting dicepools, botches, explosions, thresholds, and free hits is madness. You don't get a sweet spot by manipulating the RNG with so many levers, you get chaos.

-Username17

[DrPraetor]

Automatic Hits and so forth are only a disaster if you fail to tune the numbers properly, and if you never have botches which can then take them away. Botches work poorly without automatic hits, and automatic hits work poorly without botches. SR1 had all kinds of problems with their automatic hits, including that TN varied so the value of an automatic hit was tremendously different depending on what they were shooting at you.

But if you have both, and if you tune them properly, you get nice normally distributed outcomes that you can scale back and forth *without breaking the RNG*.

First, on your assertion that if you have botches, then your chance of catastrophic failure rises as you roll more dice, is not true. Let's suppose that a catastrophic failure = 0 net hits, and you're rolling the die I described. From my previous formulas:
E(N) = D * stuff
Var(N) = D * stuff

Your chances of getting zero hits are monotonically related to (go up and down with) sqrt(Var(N))/E(N). You don't need to do any fancy analysis to see that sqrt(N*stuff)/N*stuff is GOING TO GO DOWN AS N RISES. So your chance of catastrophic failure drops as N goes up.

Now the *swing* still rises, so if you *want* to use this mechanic to inrease the chance of catastrophic failure, you can do so - buy giving someone dice and taking away hits. Or, you can reduce the chance of catastrophic failure by giving hits and taking away dice.

Now, OWD botches didn't have this property, because the target number was 10 and thus E(N) = 0. But that is a special case of an extremely bad RNG which I would not inflict on anyone.

For your other objections, are you actually reading my responses?

[*] Diceplosion is only turned on in stressful situations: it's not something you use resources to activate. This means that you aren't spending resources for diceplosion.

[*] Diceplosion is only turned on in stressful situations: this means you can't roll forever because, if you have unlimited attempts to do something without adverse consequences, it isn't stressful by definition.

To take your lockpicking example, either the lockpicking attempt isn't stressful, and you don't get exploding dice - OR, it is stressful, which means faults are being accumulatively tracked and if you fail three times the popos are going to show up. The long-term fault tracking was your idea, how is this hard to understand?

[Username17]

Automatic Hits and so forth are only a disaster if you fail to tune the numbers properly, and if you never have botches which can then take them away. Botches work poorly without automatic hits, and automatic hits work poorly without botches.

But Auto-hits work poorly with botches and botches work poorly with auto-hits. For fuck's sake, you're talking about first edition Vampire. Those mechanics just plain honest-to-goodness work poorly. There isn't a "properly tuned" version where they work in smoothly, because in actual play these modifiers are handed out one at a time and end up adding up to "retarded" all the time.

I mean, let's start with the fact that 2 auto hits succeeds at threshold 1 or 2 all the time and is thus better than dice against those thresholds. But it succeeds against a 3 never. Meanwhile, with just 2 dice, you succeed at a threshold of 3 nearly 8% of the time, which makes it "better" even though it's supposed to be half as much and less reliable. That is horse shit.

Players should not have to calculate complicated infinite series to figure out their chances on simple tests. That would be an example of a very bad mechanic, because normal players can't evaluate it. When your infinite series goes up and down, you don't even hit cutoffs where you can simply stop calculating "because you've already reached the threshold" or whatever.

Basically, you're sounding exactly like the people who fap to variable target numbers, because theoretically you could generate any probability by varying the dicepool size and the TN. While that may be true, in actual play, it doesn't work. Just as the stuff you're babbling about right now would never actually work.

Botches are a bad mechanic. They make "getting better" into a potentially dangerous thing. That is design so bad that it will get you justifiably made fun of even by people who can't follow the intricate math. The flaws are so obvious that you will be made fun of by middle schoolers.

If you absolutely insist on tracking negative hits, the penalty dice mechanic works pretty well. Botches on normal dice does not.

-Username17

[DrPraetor]

This is entirely different from variable TNs. With variable TNs, yes you can achieve any range of outcomes, but when you move piles of dice from one range to another everything goes unscaled. The whole point of this RNG is that everything stays in scale no matter how you translate it up and down.

As far as whether you can make it work in practice, it just requires some thought - which the authors of 1st edition vampire chose not to do. You make different size dice pools, see what outcomes they expect to get (so yes, 3 dice will get you a +3 ~8% of the time), and go from there.

You just need to choose the right *ranges* of thresholds and modifiers so that things work cleanly. Since there are situations were you want to forego dice, you also have to give people the option of foregoing dice (probably with a mimimum of 1 in stressful situations). Remember - dice are risk-taking or swinginess, not goodness.

Dex 4, Skill 2 - 2 AutoHits + 3 Dice vs. 6 Dice
Dex 3, Skill 3 - 3 Autohits + 1 Die vs. 6 Dice
Dex 4, Skill 4 - 4 Autohits + 1 Die vs. 8 Dice
Dex 6, Skill 4 - 4 Autohits + 3 Die vs. 10 Dice

By all means, fill out the same list with 6,8 or 10 dice against TN 5 and explain to me how the result is in any way better. It's true that someone rolling 6 dice has a *significant chance* of failing to walk and chew bubblegum at the same time, if you consider that a feature.

Dex 4, Skill 2 -
(2, non-stressful) - Just passes
(3, non-stressful) - Passes 92% of the time
(4, non-stressful) - Passes 50% of the time
(5, non-stressful) - Passses 8% of the time

Dex 3, Skill 3 -
(2 or 3, non-stressful) - Just passes
(4, non-stressful) - Passes 50% of the time

So right here we have a perfectly reasonable genre conceit, that the talented rookie can perform at a super-professional level 8% of the time, while the mediocre journeyman cannot; but the mediocre journeyman will not fail in journeyman level tests *ever*, while the talented rookie will screw those up with equal probability.
You think this is a problem why?

We can immediately turn this into threshold meanings -
Threshold 1 - Basic Stuff; Automatic for anyone who knows what they're doing.
Threshold 2 - Normal Stuff; Automatic for people with training.
Threshold 3 - Advanced Stuff; People with basic training often cannot do this, but it's still routine for experts.
Threshold 4 - Difficult Stuff; People with significant training are 50:50 on doing this.
Threshold 5 - Expert Stuff; Only experts can ordinarily do this.
That's a pretty good range we're getting and we're rolling THREE DICE OF A SINGLE COLOR.

Dex 4, Skill 4 -
(2-4, non-stressful) - Just passes
(5) - Passes 50% of the time.

Dex 6, Skill 4 -
(5) - Passes 92% of the time.
(6) - Passes 50% of the time.
(7) - Passes 8% of the time.

So here you have two experts, one of whom is a natural genius and the other isn't. They can both do the competent stuff all of the time; the savant has a noticeably better chance of performing at an expert level; and the savant has a reasonable to meagre chance of exceeding what most people would think of as human limits.
Totally smooth and within genre conventions.

And crucially, if we transform all of these people into Macross JetRobots and the center of gravity for everyone goes up by 20 competency levels? The range of outcomes doesn't move.

For that matter, the 1-6 range of attributes and 1-4 range of skills may not be best. 3-8 for attributes and 1-6 for skills would give you about x1.5 the dynamic range, you'd tend to end up rolling 2-5 dice instead of 1-3 dice, and you'd get a little more black swan overlap. But the point I'm making is that this is entirely tunable.

I'll do the same thing for blotchsploding dice later, but the centers of gravity don't move, just all of the tails get bigger.

Crucially, and before you even start, yes you have the option of foregoing dice and sometimes you will wish to use this option; you always have to roll 1 die.

This means that for threshold = skill, you always have a 1/12 chance of failing. For threshold = skill - 1, you always have a 1/72 chance a similarly embarassing fumble, and so on by orders of 6. Being talented does not help with this; which either bothers you or it doesn't (I think it fits nicely into spy movie genre conceits.) Obviously this range of fumble frequencies isn't going to be ideal for all circumstances, but it's a reasonable fit for what you see in competitive figure skating or boxing.

This is *flat superior* to TN 5 with no botches, because with TN 5 and no botches your variance spreads out as your dice pool rises, so a skilled character has a higher chance of failling 2 pips below their expected outcome than an unskilled character, which is why the RNG breaks when people try to turn into Macross JetRobots.