The Gaming Den

So, yes, you get slightly better swings with the following formulas.

Attributes are scaled 1-6, skills are scaled 1-6, your resolution is:

Hits = Skill + (Attribute - Skill + 3)D.

With the special caveat that you never roll less than 2D; if you'd only roll 1D, you sacrifice a hit and roll 3D instead.

In the situation where Skill >= Needed Hits,
You can forego rolling the extra D if you wish to do so, down to the minimum of 2D on any roll. This is called "playing it safe" and there are two cases you might wish to do this:
1) If Skill >= Needed Hits, it is strictly advantageous. Note - due to the way the E(N) and Var(N) play out, even if Skill = Needed Hits - 1, it is never to your advantage to forego dice; the only situation where this comes up is when you'd be guaranteed to succeed rolling no dice at all.
2) You may also wish to do this if you are more concerned about avoiding faults than you are about racking up hits, which will need to be fleshed out somewhat in the fault management.

Rolling the minimum 2D, your chance of a -1 fumble is roughly:
1/36 (chance of snake eyes) * 3/4 (chance either explosion die misses)
+ 10/36 (chance of anything else involving a 1) * 1/4 (chance neither explosion die nor other die hits). That's 13/144, which is only marginally different from 1/12.

Wait, are you discussing a die pool/auto-hit mechanic where the die pool has an expected value of zero? I'm not mistaken on that, right? Because that would be terrible.

Reliability is desirable for players. For the majority of rolls they will make, their chance of success is >50%. Failure is usually asymmetrically disadvantageous, so minimizing your chance of failure is better than maximizing the upper-bound of your success. Players have an incentive to reduce the size of their die pool as much as possible. When that fails at the task, you go as far in the opposite direction as possible; you want to maximize the probability spread over high success, so you take as much swinginess as you can.

DrPraetor wrote:1) If Skill >= Needed Hits, it is strictly advantageous. Note - due to the way the E(N) and Var(N) play out, even if Skill = Needed Hits - 1, it is never to your advantage to forego dice; the only situation where this comes up is when you'd be guaranteed to succeed rolling no dice at all.
2) You may also wish to do this if you are more concerned about avoiding faults than you are about racking up hits, which will need to be fleshed out somewhat in the fault management.

Basically, these two statements are the overwhelming majority of all cases. Even without fault penalties, look at a simple base weapon damage + accuracy combat mechanic; a 0 success attack is a huge step up from a minor failure. And if your players have a less than 50% chance of making the typical attack roll against a typical enemy, your game is probably bad. It's certainly unexciting.

Quick change in topic:

[*] It was said earlier that dicepools and shifting TNs creates problems when you're trying to simulate power level disparities, like a system that uses the same resolution mechanic for street fighting and naval combat. I'm actually starting to agree with this sentiment. What system would be best for this sort of thing with minimal resolution renormalization or system partitioning?

[*] Bell curve rolling. If you read my review of the Dragon Age RPG, they had a 3d6 bell curve rolling system where a special dice called the 'dragon dice' which did things in addition to just determining the check. What kind of traditional dice-manipulation shenanigans (die rerolling, die exploding, etc.) could you implement while keeping the math fairly easy to understand?

[*] Increase in die size for the system resolution. Going back to bell curve rolling yet again, instead of just flat-out increasing the linear addition modifier, what are the merits of increasing the bell curve size? For example, at three separate points in the game, instead of the base resolution mechanic being something like 3d6 + 5, 3d6 + 12, and 3d6 + 20, what if it was 3d6 + 5, 4d6 + 9, and 5d6 + 13?

Lago PARANOIA wrote:[*] Bell curve rolling. If you read my review of the Dragon Age RPG, they had a 3d6 bell curve rolling system where a special dice called the 'dragon dice' which did things in addition to just determining the check. What kind of traditional dice-manipulation shenanigans (die rerolling, die exploding, etc.) could you implement while keeping the math fairly easy to understand?

Just for bell curves, or are you still talking about dice pools? For dice pools, you could probably take some inspiration from this and say certain colors of dice never contribute botches/only contribute successes or never contribute successes/only contribute botches. It ups the complexity of the rolling, but doesn't really change the math any (on the player side, at least). I don't know much about bell curves, though. How does the 'dragon dice' thing work? Wait, you did a review, let's read that instead.

DSMatticus wrote:Wait, are you discussing a die pool/auto-hit mechanic where the die pool has an expected value of zero?

No, the dice pool has an expected value of D/2. But the expected value doesn't change when you turn explosion on and off.

I'm not mistaken on that, right? Because that would be terrible.

Actually, I don't see why it would be, but....

Reliability is desirable for players. For the majority of rolls they will make, their chance of success is >50%. Failure is usually asymmetrically disadvantageous, so minimizing your chance of failure is better than maximizing the upper-bound of your success. Players have an incentive to reduce the size of their die pool as much as possible. When that fails at the task, you go as far in the opposite direction as possible; you want to maximize the probability spread over high success, so you take as much swinginess as you can.

That is entirely correct.

DrPraetor wrote:1) If Skill >= Needed Hits, it is strictly advantageous. Note - due to the way the E(N) and Var(N) play out, even if Skill = Needed Hits - 1, it is never to your advantage to forego dice; the only situation where this comes up is when you'd be guaranteed to succeed rolling no dice at all.
2) You may also wish to do this if you are more concerned about avoiding faults than you are about racking up hits, which will need to be fleshed out somewhat in the fault management.

Basically, these two statements are the overwhelming majority of all cases. Even without fault penalties, look at a simple base weapon damage + accuracy combat mechanic; a 0 success attack is a huge step up from a minor failure. And if your players have a less than 50% chance of making the typical attack roll against a typical enemy, your game is probably bad. It's certainly unexciting.

No, you're misunderstanding.
Suppose that I need 4 hits to strike my foe, and I'm rolling 3 hits + 3 dice. I want to roll more dice, and I probably have a better than 50% chance of success.
Suppose that I need 3 hits to strike my foe, and I'm rolling 3 hits + 3 dice. I want to roll fewer dice, because if I'm rolling zero dice I automatically succeed.
UNLESS - and given the tradeoffs this will often be the case - I'd do more damage on 4 hits than on 3 hits. If this is the case, since the increase in the odds of getting <3 hits from rolling more dice is very small (because each die does add 0.5 to my expected number of hits) I probably want to roll more dice.

Is this really hard for people to wrap their heads around? It seems simple enough to me.

DrPraetor wrote:Hits = Skill + (Attribute - Skill + 3)D.

With the special caveat that you never roll less than 2D; if you'd only roll 1D, you sacrifice a hit and roll 3D instead.

DrPraetor wrote:No, the dice pool has an expected value of D/2

DrPraetor wrote:If Skill >= Needed Hits, it is strictly advantageous [to forego dice].

One of these statements absolutely does not make sense with the other two. These three things cannot all be true at the same time.

If every die has an expected value of .5, it is not strictly advantageous to give up dice for nothing. Every dropped die is dropping half a hit. A really trivial example would be skill = 2x(needed hits), die pool = needed hits. Your expected value is 1.5 skill, and your probability of failing with the die pool is zilch or low. If every success past the threshold accrues a benefit, then the increase in the expected value makes it strictly desirable to keep the dice.

You said your dice represent swinginess and risk-taking and not "being good." That is only true if the dice have an expected value of zero, OR you're trading dice for automatic hits at a ratio of the expected value. When taking the dice correlates to performing better at a task on average than not taking the dice, that means they represent "being good."

DSMatticus wrote:

DrPraetor wrote:Hits = Skill + (Attribute - Skill + 3)D.

If every die has an expected value of .5, it is not strictly advantageous to give up dice for nothing.

Yes it is, because (and only if!) the dice can botch. Frank insists that this is profoundly hard to understand - apparently there is something to his insistence there.

Suppose that you need 3 hits to succeed.
If you roll 3 hits and one die, there is a 1/12 chance that die will generate a botch and you will fail.
If you roll 3 hits and no dice, you succeed 100% of the time.

Now, the game should mostly be set up so that you're basically right - beating that threshold by 1 hit should generally be of enough extra benefit to be *worth* the 1/12 chance of botching.

But this is not a sure thing so you have the option of foregoing the extra dice.

example would be skill = 2x(needed hits), die pool = needed hits.

I think you are mistaking my notation above. The skill counts for auto hits and *reduces* the dice pool, but..

Your expected value is 1.5 skill, and your probability of failing with the die pool is zilch or low.

First, your expected value would be 2.5 x Skill, because each point of skill is worth a free hit, but given those pool sizes, okay. Your probability of failing from the dice pool would be extremely low in the case that Skill = 2X, dice pool = X, and threshold = X. In fact, it would be approximately 1/12-to-the-Xth-power, which is a really small number. But it's not zero, and it *would be zero* if dice pool were 0 instead of X. Does this make sense?

If every success past the threshold accrues a benefit, then the increase in the expected value makes it strictly desirable to keep the dice.

It is *probably* desirable to keep the dice but it is not *strictly* desirable to keep the dice. At least not on a "stress" test, where they can botch. On a non-stress test it is strictly desirable to keep the dice.

You said your dice represent swinginess and risk-taking and not "being good." That is only true if the dice have an expected value of zero, OR you're trading dice for automatic hits at a ratio of the expected value.

The second one - you are trading dice for automatic hits at a ratio of the expected value. At least, ideally.

When taking the dice correlates to performing better at a task on average than not taking the dice, that means they represent "being good."

Well, yes and no. The design intention is to have the number of automatic hits scale with the number of dice so that dice are used to represent swinginess rather than being good.
But, of course, if you are attempting to jump over a building, and the result is "swingy", that is, you may or may not be able to do it, that implies that you are really good, because normal people can't jump over a building.

But nonetheless the purpose of dice is to increase variance or unpredictability. If you are just "better" this is represented by keeping the dice pool/variance the same size, and adding free hits.

So for example, when tanks shoot each other with their cannons, they don't roll more soak dice than when people shoot each other with pistols. Instead, the tanks do higher base damage (soak threshold), have more defenses (free hits on the soak test) and then roll about the same number of dice.

DrPraetor wrote:Yes it is, because (and only if!) the dice can botch. Frank insists that this is profoundly hard to understand - apparently there is something to his insistence there.

Uhh, no. Failure has a lower utility, but it does not have to have infinitely lower utility. If beating the threshold by a higher number has greater utility than beating it by zero, then the fact that you've opened up a non-zero chance of failure can still lead to greater overall utility for that option.

Just to throw out simple examples, imagine that without your diepool you have a 0% chance of missing, and a 100% chance of killing in two hits; but with your diepool, you have a 10% chance of missing, and a 40% chance of killing in two hit, and a 50% chance of killing in one hit. If we measure utility with expected kills per round, you go from (1.0)(.5) = .5 to (.1)(0) + (.4)(.5) + (.5)(1) = .7. That's a .2 increase in utility, despite going from a 0% failure chance to a 10% failure chance.

Basically, you assumed that the utility of all degrees of success was the same, in which case yes, adding more percentage chance of failure will always be bad. But that's a mechanic with no degrees of success, so that's totally unlike anything in RPG's. And you basically go on to say this, so we seem to actually be on the same page here. The point is that it is not "strictly advantageous" to go for safety when you have degrees of success.

DrPraetor wrote:First, your expected value would be 2.5 x Skill, because each point of skill is worth a free hit

My math actually was wrong, but not quite in the way you thought it was, I think. Let S be skill, and N be number of dice. N = S/2 in my example. E(S) = S (1 hit for every skill, right?). E(N) = N/2 (.5 hit for every die). E(S) + E(N) = E(S) + E(S/2) = S + S/2/2 = 1.25S.

Not really important, though. The point is, that even in the worst case scenario (without botchsplosion), the die pool can only cancel 1/2th the skill, so bare minimum success is guaranteed (without botchsplosion). Meanwhile, with botchsplosion, failure is still an incredibly remote chance, and if you have degrees of success failure would have to have a really steeply low utility to make the extra degrees of success not worth it.

DrPraetor wrote: It is *probably* desirable to keep the dice but it is not *strictly* desirable to keep the dice.

Touche. I yelled at you for saying strictly when it was not and then did the exact same damn thing. To be more clear, it will be strictly desirable without botchsplosions when failure is still impossible, and with botchsplosions it is strictly desirable so long as the utility of failure isn't supermassively low by comparison. Botching is just "a possibility with a utility even lower than failure," and its presence isn't necessary to make it undesirable. Failing an Evil Knievel canyon stunt jump is a really, really bad failure, even without botching.

DrP wrote:If you roll 3 hits and one die, there is a 1/12 chance that die will generate a botch and you will fail.

This is why it is unacceptable. Not simply because rolling more dice makes you fail sometimes, although of course that is a deal breaker by itself. But because you can't get the probabilities right and you wrote the damn thing.

Yes, the result of 1, 2 is a net -1, but the result of 6, 1, 1, 2 is also a net -1, as is the result of 1, 6, 1, 2. I would be quite surprised if it all converged to a 1/12 chance of a net -1 or worse. Calculating it out to the 4th possible die, I get values that are about 3% higher than 1/12 and I doubt it converges sharply down after that. and that is bullshit. Nothing should be that complicated in a table top RPG, ever.

DrP wrote: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?

Because that's not in genre at all. In genre is for the talented rookie to show promise and to be able to pull his shit together to do something awesome when the shit gets real. A 7.6% chance on each die roll is not that at all. More than 9 times out of 10, when the rookie really needs to show his potential, he's just going to fail. And meanwhile he's going to be doing a super-professional job at completely random times that are in no way plot appropriate.

The way to show the plucky guy with big potential is to give them a smaller dice pool and allow them to buy more dice periodically. That allows them to come in big when it is dramatically necessary that they do so.

Fair dice have no sense of drama.

-Username17

This is why it is unacceptable. Not simply because rolling more dice makes you fail sometimes, although of course that is a deal breaker by itself. But because you can't get the probabilities right and you wrote the damn thing.

It makes you fail sometimes in the unique circumstance that you would otherwise succeed *automatically*.

If you need even +1 hit from the pile of dice you are rolling, you always want to roll more dice.

Furthermore, if you care more about being +2 and succeeding well than you do about being -1 and failing, you want to roll more dice; rolling more dice when otherwise guaranteed a success therefore represents additional risk for potentially greater reward.

Yes, the result of 1, 2 is a net -1, but the result of 6, 1, 1, 2 is also a net -1, as is the result of 1, 6, 1, 2. I would be quite surprised if it all converged to a 1/12 chance of a net -1 or worse. Calculating it out to the 4th possible die, I get values that are about 3% higher than 1/12 and I doubt it converges sharply down after that. and that is bullshit. Nothing should be that complicated in a table top RPG, ever.

Of course it converges down sharply after that it's dropping by a factor of 1/6 every time you require another exploding die. It's true that 1-M has the same net effect as the series 6-1-1-M, but from any given condition 1-M happens ~1/12th of the time, while 6-1-1-M happens ~1/512 of the time which is already vanishingly small even before multiplying in other contingencies.

"6,1,1,2" is impossible unless you started with 1 die. It's a geometric series it converges; but the point is that the higher order terms are dropping by a factor of 6; even if it's actually not 13.5% but actually 13.53%, I really don't care; I'll put together a table of the expected outcomes at some point.

Deleted

Look, Frank - run the same examples with 6, 8, 10 and whatever die pools against TN 5, and explain how they better reflect genre than the dice pools I have. You're right that the dice pools from my post are too small, even giving the maximum possible swing at TN 4. So I made them 2 dice bigger and rookies now have a sizeable chance of outperforming.
Are you saying - "I want fighters to be lucky; but I want it to be actual luck. If having some power is making me lucky by giving me extra dice, that's not enough"? A statement you ridiculed.
Or are you saying - "I want some luck mechanic by which the talented rookie can succeed when the shit hits the fan?" Well, you can have bonus dice or bonus hits or whatever from edge points.

With this system, in the absence of edge points, you have yes fair dice. If you then want to make things unfair, you can do it, but it's not desirable to obscure that.

Look, Frank - run the same examples with 6, 8, 10 and whatever die pools against TN 5, and explain how they better reflect genre than the dice pools I have.

That's a weird request, but sure. For TN 5 games, generally 2 hits is a good success and 5 hits is a critical success.

Dice	2 Hits	5 hits
6	65%	2%
8	80%	9%
10	90%	21%

So your basic pro is making your threshold 2 tests about two thirds of the time, and gets crits almost never. Meanwhile, your basic ninja crits a bit better than one in five shots and gets his threshold 2 tests on nine out of ten times.

Failure still happens a noticeable, but not game paralyzing amount of the time, but critical success happens dramatically more as characters get more dice. That is exactly what the system is supposed to do. And it's fairly easy to calculate.

-Username17

I'm trying to follow along, but I must have missed something: When Dr. P says that rolling 1d6 has a 1/12 chance of botching, is that because the 1 is re-rolled and then either a 'confirmed botch' on a 1-3 and an 'avoided botch' on 4-6? Otherwise I can't figure out how you'd get 1/12 chance for botch on a 1d6. I don't know if I missed the explanation of it somewhere or it was assumed from some other premise I was unaware of.

Stubbazubba wrote:I'm trying to follow along, but I must have missed something: When Dr. P says that rolling 1d6 has a 1/12 chance of botching, is that because the 1 is re-rolled and then either a 'confirmed botch' on a 1-3 and an 'avoided botch' on 4-6? Otherwise I can't figure out how you'd get 1/12 chance for botch on a 1d6. I don't know if I missed the explanation of it somewhere or it was assumed from some other premise I was unaware of.

He's having dice succeed on a 4-6, botch on a 1, and explode on a 6 and 1.

He gets 1/12 because you roll a 1 and then you get an extra die, which provides a hit and cancels the botch on a 4-6. This is still wrong, however, because 6s still make extra dice and those dice can come up 1s.

So rolling a 1 followed by a 6 followed by a 1 followed by a 3 is still a botch. Rolling a 6 followed by a 1, followed by another 1, followed by a 2 is also a botch.

It all converges to be about 3% more than 1/12. Saying it is "1/12" is only correct to a couple percentage points of error. One of the many reasons this proposal is extremely sub optimal.

-Username17

Ah, I see.

I agree with you, then, that infinitely exploding dice are a bad mechanic idea, if not for mathematical reasons, then for simply the fact of how long it would take to resolve rolls.

What if you just had 1s botch and 6s give two hits? The mean would remain the same, but the variance would be much greater than just a binary hit/miss with TN 4. You could spend edge or what-not to mitigate botches and/or re-roll them. The odds for black swan events would be higher, I believe, simply because for every die rolled, you have 1/6 chance of getting 2 hits, instead of 1/12.

Alternatively, since botches are justifiably unpopular, you could make 1-4 misses, 5 is a hit, and 6 is 2 hits. That actually gives you the same expected value as TN 4, but gives you the positive extra range from the botch/2 hits model above while the bottom remains at zero.

Stubbazubba - the problem with no-botches is that then you can't have no-guaranteed-hits, without guaranteed successes.

Consider this fundamental flaw with non-botching/non-exploding dice:
If you want to average 2 successes, you have to roll 6 dice, which gives you 2 +/- sqrt(2/3) hits.
If you want to average 4 successes, you have to roll 12 dice, which gives you 4 +/- sqrt(4/3) hits. There is *no way* to generate 4 +/- sqrt(2/3) hits!
How would you try? Well, you could generate 2 hits + 6 dice, which would give you 4 +/- sqrt(2/3) hits, but it would also mean you have zero chance of failing anything that takes 2 hits to succeed. Consider - 3 hits below expectation (1) is impossible, but 3 hits *above* expectation (7) is going to happen 2% of the time.

This gets worse and worse as dice pools get larger - that is, everything breaks down when the tanks come out.

A more mathy explanation - with the spreadsheet with the exact probabilities of different outcomes geared to match the 65/80/90 vs. 2/9/21 that Frank says he wants - is forthcoming but work has been a bitch.

DrP wrote:Consider this fundamental flaw with non-botching/non-exploding dice:
If you want to average 2 successes, you have to roll 6 dice, which gives you 2 +/- sqrt(2/3) hits.
If you want to average 4 successes, you have to roll 12 dice, which gives you 4 +/- sqrt(4/3) hits. There is *no way* to generate 4 +/- sqrt(2/3) hits!

That's not a fundamental flaw, that's the whole point of using a dicepool instead of rolling a straight number generator and adding modifiers to it. The chances change as your dicepool gets bigger. Specifically, your chances of beating tests that are currently marginally challenging goes up noticeably without actually having failure chances hit zero or near zero as you go up in skill. Meanwhile, the tasks that are impossible or near impossible become dramatically more achievable. Gaining skill makes moderate challenges easier but doesn't make them go away, while it brings near impossible challenges into striking distance.

In short: it does exactly what RPG players say they want.

People don't want to be told they win without rolling the dice, and they want to be faced with challenges today that were the stuff of nightmares yesterday and they want to win. They want to fight dragons and armies and they don't want Orc Thug #3 pushed completely off the RNG. And dice pools deliver on all that. Simple fixed target number, no explosions, no botches, and it works.

If you wanted to maintain the same spread of numbers around the average when players leveled up, you'd roll a d20 or 3d6 or something and add a bonus. Because a fixed RNG with a variable bonus provides that by default. You use dicepools because you want the range to increase as skill increases. Because you want to be fucking Superman, who punches through brick walls and giant robots but still ducks when mooks throw their guns at him just in case. You want to be Rand Al'Thor, who chews his way through an army of darkspawn, but still has to defend himself when a single beastman breaks into his chambers. You want to have the game represent the physics of the vast majority of heroic literature, where despite the fact that characters are doing absolutely ridiculous things on a routine basis, they still can't be completely complacent in the face of angry hobos or pots being thrown at their head.

From Hercules and Xena to Lord of the Rings to Die Hard, heroic characters in fiction live in a strange dichotomy where they regularly push the limits of the impossible and take on ludicrous odds while still acting like knives and thrown rocks are something they need to avoid. And dicepools deliver that, because even when the super heroic tasks become well within the reach, the chances of failing at the merely heroic tasks never actually go away.

DrP wrote:This gets worse and worse as dice pools get larger - that is, everything breaks down when the tanks come out.

This part I will agree with. When your game system is based around John McClane having a real (albeit small) chance of getting injured by a drunkard with a broken bottle while still being able to drive a car off the roof of a parking garage into an enemy attack helicopter and leap to safety, then it's not going to support tanks very well. Very tough characters in a dicepool system can't just stand there while Palestinian children hit them with sticks. And for purposes of representing the heroes of these stories, that's good emulation. But it necessarily means that you have to change the rules or accept stupid results when you bring out walls or tanks or something that are supposed to be able to simply sit there without harm while hobos break bottles on them.

-Username17

DrPraetor wrote:Stubbazubba - the problem with no-botches is that then you can't have no-guaranteed-hits, without guaranteed successes.

Consider this fundamental flaw with non-botching/non-exploding dice:
If you want to average 2 successes, you have to roll 6 dice, which gives you 2 +/- sqrt(2/3) hits.
If you want to average 4 successes, you have to roll 12 dice, which gives you 4 +/- sqrt(4/3) hits. There is *no way* to generate 4 +/- sqrt(2/3) hits!
How would you try? Well, you could generate 2 hits + 6 dice, which would give you 4 +/- sqrt(2/3) hits, but it would also mean you have zero chance of failing anything that takes 2 hits to succeed. Consider - 3 hits below expectation (1) is impossible, but 3 hits *above* expectation (7) is going to happen 2% of the time.

Maybe I'm just not math savvy enough (in fact that's definitely true regardless), but this seems like the odds of a no-frills TN 5 dicepool system, which is not what I suggested in my post (correct me if I'm wrong, as I can't quite see where you're getting your ranges from, either). I don't want to have to roll three times the number of Hits I want in order to have a 50/50 chance of success. What I proposed was a TN 5 dicepool where a 5 on the die is 1 Hit and a 6 is 2. AFAIK, that would indicate that your mean Hits would be equal to #dice/2. I agree that something important, the ability to very occasionally fail tests that you otherwise have enough Automatic Hits for, is lost without botches, though.

This gets worse and worse as dice pools get larger - that is, everything breaks down when the tanks come out.

I'm totally OK with using Automatic Hits to push the distributions into different tiers like that, but to keep Orc Warrior #5 on the radar at all, this necessitates having botches, which I'm also OK with, so long as they can be mitigated with OOC resources a la Fate Points. I don't like exploding dice, though, so I proposed my first system, a TN 4 system where 1s just botch and 6s give you two successes. The expected value remains #dice/2, but you have a slim possibility of getting negative Hits up to the number of dice you're rolling. If you have 5 Automatic Hits and you're rolling 6 dice, you have a 1/46,656 chance of ending up with -1 Hits total. At the same time, you have an equal chance to end up with 17 Hits total. So as you roll more dice, your range of values increases in both directions at different rates. This only happens when you have botches and you can get more than one Hit per die. Depending on how your system works, this may or may not be acceptable. I can't really see a reason to go with exploding dice and such when one of these two systems will do the job. If you're opposed to botches, use TN 5, 6s = 2 Hits, if you're not, use TN 4, 6s still = 2 Hits.

A more mathy explanation - with the spreadsheet with the exact probabilities of different outcomes geared to match the 65/80/90 vs. 2/9/21 that Frank says he wants - is forthcoming but work has been a bitch.

Looking forward to it.

FrankTrollman wrote:This part I will agree with. When your game system is based around John McClane having a real (albeit small) chance of getting injured by a drunkard with a broken bottle while still being able to drive a car off the roof of a parking garage into an enemy attack helicopter and leap to safety, then it's not going to support tanks very well. Very tough characters in a dicepool system can't just stand there while Palestinian children hit them with sticks. And for purposes of representing the heroes of these stories, that's good emulation. But it necessarily means that you have to change the rules or accept stupid results when you bring out walls or tanks or something that are supposed to be able to simply sit there without harm while hobos break bottles on them.

-Username17

Why is Damage Reduction not a valid solution here?

echo

echoVanguard wrote:

FrankTrollman wrote:This part I will agree with. When your game system is based around John McClane having a real (albeit small) chance of getting injured by a drunkard with a broken bottle while still being able to drive a car off the roof of a parking garage into an enemy attack helicopter and leap to safety, then it's not going to support tanks very well. Very tough characters in a dicepool system can't just stand there while Palestinian children hit them with sticks. And for purposes of representing the heroes of these stories, that's good emulation. But it necessarily means that you have to change the rules or accept stupid results when you bring out walls or tanks or something that are supposed to be able to simply sit there without harm while hobos break bottles on them.

-Username17

Why is Damage Reduction not a valid solution here?

echo

Strict numeric shifts are in fact a valid solution. They just aren't dice pools. You can solve many mechanical problems with a system by using a completely different system.

You could also solve the problem of players having a fairly bad idea of what their exact chances are to complete tasks by rolling percentile dice instead.

-Username17

FrankTrollman wrote:You could also solve the problem of players having a fairly bad idea of what their exact chances are to complete tasks by rolling percentile dice instead.

-Username17

Do the players really need to know the exact chances? Heck, what's the minimum chance in the % of success that's noticeable? 2% on d100 isn't going to be seen as noticeable for hundreds of rolls.

If I'm rolling dice in Shadowrun and I've got 10 dice, I expect 3, maybe 4 successes. It would be nice to know that I've got around a 70% chance for 3 or more succes and only a roughly 45% for 4 or more, but I'm not sure how much it actually adds to play durring the game. When rolling a lot of the time you're rolling you don't know the exact DC you're trying to beat anyways so guessing the exact chances of succeeding are impossible.

This seems more like something where it would be nice, but it pretty low on the list of needs so long as the players can guesstimate and have it line up roughly with what they actually experience when rolling.

All you would need would be a chart showing the odds of getting X Hits when rolling Y dice, numerical shifts wouldn't even need to figure into that.

Previn wrote: Do the players really need to know the exact chances?

No. They don't. But the difficulty of calculating those chances is a flaw with dicepools in general.

I don't think it is an insurmountable flaw, but it's a definite drawback of dice pools. And because it already exists, I don't think that dicepools respond well to the kinds of "epicycles" that Dr. Praetorius is talking about. Botches and explosions make guesstimating odds considerably more difficult, exacerbating a problem dicepools already have to be, well, considerably worse.

-Username17

Stubbazubba wrote:I don't want to have to roll three times the number of Hits I want in order to have a 50/50 chance of success. What I proposed was a TN 5 dicepool where a 5 on the die is 1 Hit and a 6 is 2. AFAIK, that would indicate that your mean Hits would be equal to #dice/2. I agree that something important, the ability to very occasionally fail tests that you otherwise have enough Automatic Hits for, is lost without botches, though.

I'm aware of the arguments for a d6 pool based on the ubiquity of the d6 and better ability to roll cleanly, but is there an inherent mechanical benefit as opposed to d10?

It seems a d10 would allow for (relatively) easier ability to determine odds, and using Stubbazubba's example, you could have a greater choice of successes and better ability to fiddle with the final output as opposed to the d6 due to the increased range.

Is there something obvious I'm missing?

Previn wrote:Is there something obvious I'm missing?

The ease of calculating d10 based odds is very real when you are rolling one or two dice. The math comes out in percents, which means that you're basically done once you have the equation set up properly.

For larger piles of dice, that's just not true any more. Very few people can do combinatorials with teen thousand in the denominator in their heads, meaning that you're going to use a calculator or a piece of paper regardless. And once you do that, it simply doesn't matter any more whether the denominators are base 10 or base 6.

So d% and 2d10 both have "easy to calculate odds" as a real advantage that must be considered when deciding whether you want to use that system. But Dicepool d10 doesn't.

-Username17

For the average player, just how important is it for them to need to be able to actually know/compute actual probabilities? For most people, I would think that simply being able to quickly discern qualitatively meaningfulness at the margins is good enough.
It's not really fair to use the demands of Denners as the baseline of expectations -- most people just can't be bothered to care that much.