Dice probability

I've played both, and I'm making that statement of fact.

Individual rolls are more variable. Within the scope of a session and a campaign, they average out about the same.

If you think the average is the only thing that matters you are absolutely fucking retarded

I'm not saying that.

I'm saying that, over the course of a game, how often you succeed and fail, that sense of competence and capability, will be roughly the same.

In a bell curve system, it'll be quite predictable, as you're very likely to succeed easier rolls, and very likely to fail harder rolls.

In a d20 system, it's less certain, with more chances for sudden failures or unexpected successes to take things in different and unusual directions.

But overall, they plot out pretty similarly.

It doesn't matter if the d20 "averages out the same," because that theoretcial average has aboslutely no bearing on the present, immediate game and roll. The d20 generates one number between 1 and 20 on a flat curve, every roll. The 3d6 generates one number between 3 and 18 on a bell curve, every roll. The d20 is much more swingy, and thus, its effects more pronounced. You're either an idiot or a poe if you think people play games on the 1,000 roll level.

...Over the course of a game, you think a thousand rolls is a big number? A single D&D combat, four characters, four enemies and four turns, would have 32 rolls for all their attacks, 40 counting initiative, not counting any AoE's, saves or extra abilities that might spur a roll.

A combat often doesn't take a full session, and you're still getting plenty of skill rolls outside of that. Even a moderately long campaign, twenty sessions or so, will blast past a thousand rolls in no time.

So you completely ignore the message and get hung up on technicalities. Alright. I guess you'll also ignore the fact that saying both "average out in the end" completely invalidates any "the d20 is more dramatic" argument because you can't have your cake and eat it, too. The moment to moment drama is completely fake if it averages out in the end.

Nice reddit spacing too.

No? It makes perfect sense.

Each individual roll is more variable, so in the moment it's a more tense and dramatic event, with a less certain outcome.

That the results even out overall doesn't retroactively stop the roll being exciting because its uncertain. You can't predict how things are going to even out, only that they will.

Do you actually have a point?

Not him, but "more dramatic" and "averages out" aren't mutually exclusive. Each roll is swingy and random, therefore, dramatic. In the long run, it still averages out to normal. So, feel free to get mad, but bear in .Ind that you're just as guilty of glossing over the message as he is.

What possible point could be made from saying that both average out? Even if a character's rolls with a d20 does average out to the same as 3d6, that character's competence does not. The character can easily have been wildly incompetent in things the sheet said they were good at, and competent in things they had no reason to be good at because of how swingy a d20 is. Saying that doesn't mean that the character was actually competent in what they were made to be competent in, or incompetent in what they were made to be incompetent in, simply that there was competence. That isn't tense or dramatic, that's the game invalidating your character concept that you wanted to play because it uses shitty RNG.

Nope.

Assuming the system is badly designed doesn't invalidate the strength of the d20 as a dice.

And, again, it evens out. You might have those sudden failures at what you're meant to be good at, or surprising successes outside of your sphere of competence, but they'll still be the exception, not the rule. They're more common than in a bell curve system, sure, but your modifiers will still mean you tend towards, overall, succeeding at your strengths and failing at your weaknesses. It just makes the individual bits and pieces getting there more interesting and fun.

>because it uses a completely fabricated equivalency for the d20 percentages
What does that even mean?

>Assuming the system is badly designed doesn't invalidate the strength of the d20 as a dice.
The system is badly designed if it's using 1d20, full stop. You can try to mitigate the disasterous effects the d20 has on your character's ability to perform, like FantasyCraft does with a minimum skill result of 20+CL and Action Dice and very low DCs, but that's compensating for a shitty RNG.

Calling failures and surprises exceptions is disingenuous as it will happen far more often than it would with any RNG with a non-flat curve to it. It isn't more "interesting" or "fun" to have your character fail at things they should be good at and succeed at things they should be bad at. It's bad design, except when used in comedic games, where the swinginess is a benefit because it will lead to hilarious situations, but it has no staying power outside of that because of how destructive it is to characters and stories.

If you look at the average and the standard deviation of each distribution, 3d6 and 1d20 are NOT equivalent. 3d6 is equivalent to 1d10+5. (I haven't looked at 1d20.)

Your opinion isn't fact.

It's perfectly possible to design a good system around a d20, especially since you're ludicrously exaggerating how inconsistent it is.

Those divergent results are interesting, and can often lead to fun moments, but they're still relatively uncommon.

I don't even like D&D that much, you're just really, really mad about d20s.

>It's perfectly possible to design a good system around a d20
Like?

D&D 4e

And how does D&D 4e achieve this?

>If you look at the average and the standard deviation of each distribution, 3d6 and 1d20 are NOT equivalent. 3d6 is equivalent to 1d10+5. (I haven't looked at 1d20.)
Exactly. The standard deviation of 3d6 is closest to that of 1d10. The standard deviation of 1d20 is 1.94 times as large. Which is why you need to use modifiers twice as big to achieve the comparative results, as suggests.

Tight mechanical balance and knowing how to accommodate for the variability of the dice? Y'know, designing it well around the d20?

There are others, btw, Mutants and Masterminds springs to mind. That mecha game that showed up the other day, Lancer, seemed kinda neat too, although it needs more time in the oven.

>Tight mechanical balance and knowing how to accommodate for the variability of the dice?
Be specific.

What more do you want? If you want to learn about 4e's dice mechanics, go open the book and read them yourself.

If you can't be specific, you don't know enough about the system to make those claims. If you can be specific but refuse to, you harm no position but your own.

By giving players solid boosts to start out with, having numbers used on d20s scale proportionately with each other, and the devs actually had a clue what a player's numbers would look like at any level.

And it did this without fetishizing small numbers like 5E does.

Alternatively, I have no idea what hoop you want me to jump through and no real incentive to attempt to answer such a vague and pointless question.

>By giving players solid boosts to start out with, having numbers used on d20s scale proportionately with each other
Such as and how?

It's not vague or pointless. I'm asking you to specifically explain how 4e D&D gets the d20 right. Saying that it does isn't explaining it. Be specific.

why post anime with that?

Or to put that another way: "OMG, look at how much more swingy rolling a single die is than rolling three dice! The difference is so stark, it's difficult to even compare them."

We're on an anime imageboard.

If you compare the 3d6 and the 1d20 columns, you will see the 1d20 column has repeated numbers and then skips amounts in order to make it "fit". Essentially forcing the numbers into a false equivalency by altering the scale.

Did you read the text at the bottom? It skips numbers because it's demonstrating how +1 on 3d6 approximates +2 on 1d20. That's the entire point of the entire thing.

The 1d20 repeats numbers because it has hit the ceiling or the floor. That's assuming there's always a chance for failure or success. Otherwise, it would cap out at 100% and 0%, but that would actually bring the percentages closer to what they are on 3d6.

Some more data for you bois.
This one compares the concentration of results for 3d6 and 1d20.

Yeah 3d6 over 1d20 only really impacts the extremes and diminishes the range when you use it extensively in a single session. People that waffle on about bell curves usually seem like the least informed. Not to mention it increases the steps necessary to determine an action. It would make more sense if you had a much larger or smaller range or if your mean result over all games wasn't the same.

It's still absolutely shit math. Anyone can make numbers fit by adding shit into a variable or making them up. It's much better to spread out or compress the values of one curve to fit the other like I did here This way, you can see the true difference in how each curve affects the likelihood of giving you an extreme result.
3d6's 50% range is half as big as 1d20's, and so is it's 25% range. Essentially, you're more than twice as likely to get an extreme result (in the top 1/4 or bottom 1/4 of possible results) from 1d20 than from 3d6.

>It's still absolutely shit math. Anyone can make numbers fit by adding shit into a variable or making them up.
The standard deviation of 1d20 is roughly twice that of 3d6, so you need steps twice as large on the 1d20 to make a comparison. The only thing this is doing is "scaling" things so you can compare them. It's the same reason you can't conclude that d% are way more swingy than 2d10 because adding +8 to the average result practically assures success on 2d10 while doing comparatively little on d%.

>It's much better to spread out or compress the values of one curve to fit the other
A compressed curve does not demonstrate real world usage. You can't roll on a compressed 1d20.

>3d6's 50% range is half as big as 1d20's, and so is it's 25% range.
In other words, +1 on 3d6 is roughly equivalent to +2 on 1d20.

It's not better, you don't contribute any real information. If your only point is that the numbers aren't exactly precisely the same then you lose the discussion by default. In the end the likelihood of an extreme result doesn't need to result in an extreme mechanical impact.

Crapping the bed over such small change is entirely a self imposed life style choice.

Here's another way of thinking about it, with 1d20, you will roll a number between 1 and 5 1/4 of the time. Based on how d20 games are balanced, die rolls below 6 will almost always result in failure of a task that you on average should be able to do. A character will almost never have 6 points or more above what is expected of him for his level.
1d20 means that you will absolutely fail at things 1/4 of the time. Meanwhile with 3d6 you reduce the chance of getting a result in the bottom quarter (an auto-fail) to just 10%.

>A compressed curve does not demonstrate real world usage. You can't roll on a compressed 1d20.

Are you this dense? Of course you can't. That's not the point. It's a demonstration of how ridiculously spread out the results of 1d20 can be. Yes, you can try to fix this with increasing the size of bonuses, but it still means giving a fuckton of bonuses to everything everywhere. It means more bookkeeping, more avenues for min-maxing, more difficulty in maintaining balance across levels.

>It's the same reason you can't conclude that d% are way more swingy than 2d10
Except all things being equal they are because it's a flat die compared to something with a curve. Stop with this bullshit sophistry.

Not necessarily true unless you play in a static system where you always maintain the same proportion of bonus to your rolls.

If a system has more opportunities to increase bonuses this changes. On a check that has a 50/50 success chance at one point then with a +9 bonus at another point it will always succeed for a d20, for 3d6 the bonus only needs to be +7.

>the likelihood of an extreme result doesn't need to result in an extreme mechanical impact

And yet it does with 1d20. 1d20 increases the likelyhood that a combat will end up with extremely unlikely outcomes. In a game that involves lots of strategic choices, it sucks to have everything thrown to to shit because your dice decided to roll in the bottom quarter 3 times in a row. It also sucks for DMs when a player triple-crits an important character that wasn't supposed to die. Randomness should make a game exciting, not insane or frustrating.

Do you think low bonus systems are better? They're usually worse. Balance isn't synonymous with good nor with fair.

Not it doesn't unless you design it that way. I'm beginning to think guys like you are so fixated on this you just can't see the forest through the trees.

Balanced is in fact synonymous with fair.

3d6 is probably better if you're concerned about the game breaking(hello, diplomacy rules), but 1d20 is clearer. Keep in mind that 3d6 only has a 15 point range, though, so it maps poorly for a conversion, and is best used for new games. If you must convert, roll 2d10, and roll high /low on 20 to check for ones. It doesn't get the same level of result, but it does get the result you're looking for, and it balances pretty well into preexisting systems. It might make things a bit slower though.

Its confirmation bias. He can't remember the actual rate, so he just remembers it happening, and equates the two.

Never underestimate the power of a lazy, lazy brain that's not being forced to actually do the work.

>Hey my name is tim and i work ten hours a day and have 500$
>Hey my name is drake and i work five hours a day and have 100$
>This isn't balanced, let's take 200$ from Tim and give it to Drake
>The amount of money they have is now balanced, therefore robbing drake was fair

I bet you're a commie too.

Robbing tim, fuck me, i shouldn't stay up this late after a long shift.

>Yes, you can try to fix this with increasing the size of bonuses
Okay, now you're arguing about scale rather than the effect of a bell-curve on "swinginess". If you want smaller bonuses and shit, then preferring something with a smaller standard deviation makes sense, but then we're back to the fact that the proper single die to compare 3d6 to is 1d10, not 1d20.

Nice editing on that sentence, bro.

This.

Pathfinder, and specially the recent versions of D&D, all have very carefully limited ways to increase the bonuses to your rolls to maintain level balance with monster challenge ratings.
This means that you can't just say that you can offset the chances with a large bonus, because even with a bonus the size of what is expected of a character for a certain level, they will usually fail a check if you roll in the lower quarter of results. And the probability of that happening with 1d20 is a huge 25%. The probability of that happening twice in a row is still a sizable 5%. It's simply how these games are designed.

You shouldn't bother to reply at all.

>the proper single die to compare 3d6 to is 1d10, not 1d20.

We are talking about the differences between 1d20 and 3d6. You are using 1d10 literally as a strawman. Nobody would use 1d10 for roleplaying because the number of results is too small (10 in 1d10 vs 16 in 2d6 vs 20 in 1d20).

cont.

If you use 3d6 instead, the chances of rolling in the lower quarter of possible results is only 10%, with the possibility of it happening twice in a row being 1%. Much more manageable odds for concurrent failure. Nothing will stress out a player more than two or three back-to-back shit rolls. They know they are good players, they know the strategy necessary to beat the encounter, it's just that this piece of shit extreme randomness is getting in their way.

lol wut
people use even d6s for rpgs

2d10 always struck me as the table top best system.

Double ones and double tens are uncommon but not infrequent.

The average of two d10s roll would be the ideal number distribution and range but would be irritating for most people to do.

A lot of time could've been saved in this thread if people just used anydice.
anydice.com/program/508

>Yes, you can try to fix this with increasing the size of bonuses, but it still means giving a fuckton of bonuses to everything everywhere. It means more bookkeeping, more avenues for min-maxing, more difficulty in maintaining balance across levels.
It inherently means none of that.

Veeky Forums has trouble understand what +10% means in percentile games.

This is an incredibly bad way to illustrate the difference. Just do a fucking probability density graph.

I prefer d20, because addition is hard for me.

d100 is the best probability distribution and for some reason it isn't used very often.

>Yes, you can try to fix this with increasing the size of bonuses, but it still means giving a fuckton of bonuses to everything everywhere. It means more bookkeeping, more avenues for min-maxing, more difficulty in maintaining balance across levels.
First, it's not a fix. Just because +4 on a d20 is roughly equivalent to +2 on 3d6 doesn't mean you would otherwise have applied a +2 and are now having to scramble to match 3d6 by doubling it. Whatever dice you're using, you apply the appropriate size bonus for the difficulty of the task at hand. The size of that bonus varies according to the dice, but that doesn't mean you're having to correct one system because the other's better.

Second, even with double the bonus size on 1d20, there's going to be more math on 3d6. For 1d20, you might have a roll of 12 plus a bonus of 4, while on 3d6, you might have rolls of 2, 5 and 4, plus a bonus of 2.

Third, I don't know what the fuck any of this has to do with min-maxing or balancing.

because accurate d100s are more useful at the driving range than the gaming table, and autists (present company included) can't help their instinct to roll ersatz d20s first and declare which one is the tens second.

electronic rolls would solve this, but the userbase is composed of people with an exceptional hate for vidya and anything similar or they'd already be playing those instead, so good luck getting that to take off.

*actual d100s
*ersatz d10s
it's 29:00 friday night, i don't need an excuse

That's why you get those dice with two digits on them so one can be the tens unit

>Such as and how?

By having +1/2 level to stuff and having offence and defence scale to a roughly equal degree.

It also gets to play about with that rather swingy nature with stuff like the Avenger, who's mechanical trick is 'Roll twice and take the better'. Which is much more effective thing with 1d20.

Multiple dices vs d20s does get interesting when it comes to bonuses. Due to the tighter range of average results on multiple dice, static bonuses become a lot more powerful. It's something I learned with Battletech, where +1 is a huge bonus.

Quite interesting that they took a feature of a 4e class and made it the core gimmick of 5e (advantage/disadvantage).
And short/encounter and long/daily rests (specially when looking at the variant rule of short rests in 5 minutes), hit dice/healing surges and so on... while at the same time they claim 5e is more akin to other editions than to 4e

5e's hit dice are not REALLY the same imo. 4e's healing surges were a limitation (Even magical healing drew from them), 5e's are a bit more like what people said 4e's were like (Extra free healing).

I'm very curious as to why you guys don't just use percentile dice. Why are you fucking with probabilities that are difficult to understand at the table?

I think it'd would be interesting to compare 1d20 to 3d6 by calculating the expected value and variance of (1d20 - 3d6)^2. That should be a good measure of how different the distributions really are.

Additionally, I'd like to see 2d20 take highest (or lowest) compared to 3d6, if any user could check that. I'm unable to at the moment.

Either way, I think that user's preferences rely on their own utility function, and the only way to compare utility functions is with yet another utility function. At least in general. I think.

All in all, 3d6 has a more centric roll. You'll often roll between 5 and 16 and have a lot of 8~13s. It's way less swingy, and works best when people have abut the same modifiers - that means, usually you yon't try to roll against anything much stronger than you in any field. A human-centric campaign where almost no one is above level 6, for example, is perfect for 3d6 as modifiers don't explode. This is true because you usually get rolls inside the main 10-number gap with a tendency for the middle ones, so modifiers are way stronger than dice here.

When you have a wide range of modifiers though, d20 is obviously superior. The d20 gives more swing to the rolls - a bad roll and a good roll can be 14 numbers apart and your result can vary wildly on that. As noted in the OP, a +8 in d20 is always +40% chance of success, while in 3d6 it can be as much as 80%. 3d6 is very bonus-sensitive.

>probabilities that are difficult to understand at the table
Not everyone is american. Most countries have a pretty decent education system. I'm from a 3rd world country and laugh every time someone says "b-but probability is hard!" regarding TTRPGs.

I prefer 1d20 (or 1d100 if possible) to be able to make easy probability math or to convert stuff and ideas to rpg

1d0-9+1d10 is better

2000 byte no fullwidth is a bitch
the tl;dr is that 2d20 drop averages slightly over 15, is more common 15- and 4-, and is super-poor for games because it clumps everything at one end. from a game design perspective it's good mostly for dealing with degrees of success on a roll-under table.

Competence in d20 games comes from the growing list of what you can take 10 on.

Track the difficulties of skill checks from the book, and you will know most of what tasks you can auto succeed at.

Now that we've got that particular insecurity out of the way, would you mind answering my question?