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Anything but rolling a ton of dice, needing X successes, a la Shadowrun and Storyteller, but particularly Shadowrun because of d6's.  A 1 point target number shift is big;  2 points, enormous.

Any linear-distribution roll has the advantage that any adjustments have consistent impact, until you get to the fringes.  Not true with 3d6.

The nice thing about 3d6 is the bell curve is built into the dice.  With 1d20 you have to build the probabilities into the system and I have yet to see a system do that very well.  And if we're using linear dice I'd prefer percentiles for granularity reasons.

Exploding dice in the vein of Shadowrun always really annoyed me because it makes it impossible to guess what the actual odds are of any success, not to mention the weird step distribution of outcomes.  Shadowrun specifically also screwed up the implementation by adding exploding dice to 6 instead of 5, so there was functionally no difference between a target number of 6 and 7, or 12 and 13.

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1 hour ago, Old Man said:

The nice thing about 3d6 is the bell curve is built into the dice.  With 1d20 you have to build the probabilities into the system and I have yet to see a system do that very well.  And if we're using linear dice I'd prefer percentiles for granularity reasons.

Exploding dice in the vein of Shadowrun always really annoyed me because it makes it impossible to guess what the actual odds are of any success, not to mention the weird step distribution of outcomes.  Shadowrun specifically also screwed up the implementation by adding exploding dice to 6 instead of 5, so there was functionally no difference between a target number of 6 and 7, or 12 and 13.

Well, if a 5% granularity isn't good enough...3d6's granularity is far worse.  Between 7 and 13, the difference between is just under 10%, up to 12.5%...so it's VERY coarse.

Why is a bell curve better than a uniform distribution, in your opinion?

Yeah, percentiles are more granular...for tables, you likely want that.  But for making hit rolls or skill checks?  5% granularity is probably plenty good enough.

Shadowrun exploding dice...remember that Shadowrun (at least the editions I played) was counting number of successes.  There wasn't much totaling.  I think there was some in 1st Edition...but that got dropped.  The uneven distribution of outcomes WAS a huge problem, and as you note, there was no difference between 6 and 7.  And not much difference between 6 and 8....even 6 and 9.  But you can work out the probabilities easily.

Target 2:  5/6

Target 3:  2/3

Target 4:  1/2

Target 5:  1/3

Target 6:  1/6

Target 7:  1/6

Target 8:  1/6 * 5/6 = 5/36

Target 9:  1/9

Target 10:  1/12

Target 11:  1/18

Target 12:  1/36

So you're only losing about 5% going from target 6 to target 9.  I don't think many GMs really understand that any target number over 5 is becoming a fishing expedition, especially if more than 1 success is needed.  And when you hit 10, 11...it hardly matters.  12?  It doesn't matter, it's Fat Chance.

If you explode on a 5...the probabilities are

Target 5:  1/3

Target 6:  1/3

Target 7:  5/36

Target 8:  1/9

and so on.  So you make a really funky looking  distribution.  It might *sound* better but I don't think it is.

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My issue with flat probability distribution functions coupled to game mechanics is that catastrophic failure is, as a practical matter, far more frequent and you are much more subject to the tyranny of the dice.  In 3d6, assuming fair dice, you hit the most adverse possible roll an order of magnitude less frequently than you do with 1d20 ... but GMs more or less invariably assign the same life-threatening severity of consequence to worst rolls in both systems.

Attempting to build a character that is less subject to the whims of the dice may or may not be possible in a given system.  In HERO's 3d6 center-peaked system, you can try building fewer powers/abilities than your compatriots but build those with more skill adds, so to speak, so that as long as you don't step on the "natural botch" of the dice, you can have a reasonable expectation of successes.  Square-distribution systems tend to be more granular and have caps on the maximum number of skill adds, and with the flat p.d.f., in fact your success is dominated by your ability to roll in the top half of the distribution, and there is nothing you can do about it.

You must understand: the adversarial relationship between me and my dice is legendary in our gaming group, which is a large one.  The large size of the group exacerbates the frustrations of the unlucky player, because working around the table for a single turn takes longer for the big group, and for a four-to-five hour session it makes for fewer turns around the table when you have seven players compared to when you have three.  Depending on the complexity of the game mechanics and how much time is spent in story-telling, description, and explanation, a given player doesn't make that many rolls over the course of a gaming session.  Small-number statistics dominate the player experience.

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Well, if a 5% granularity isn't good enough...3d6's granularity is far worse.  Between 7 and 13, the difference between is just under 10%, up to 12.5%...so it's VERY coarse.

Why is a bell curve better than a uniform distribution, in your opinion?

Yeah, percentiles are more granular...for tables, you likely want that.  But for making hit rolls or skill checks?  5% granularity is probably plenty good enough.

Shadowrun exploding dice...remember that Shadowrun (at least the editions I played) was counting number of successes.  There wasn't much totaling.  I think there was some in 1st Edition...but that got dropped.  The uneven distribution of outcomes WAS a huge problem, and as you note, there was no difference between 6 and 7.  And not much difference between 6 and 8....even 6 and 9.  But you can work out the probabilities easily.

Target 2:  5/6

Target 3:  2/3

Target 4:  1/2

Target 5:  1/3

Target 6:  1/6

Target 7:  1/6

Target 8:  1/6 * 5/6 = 5/36

Target 9:  1/9

Target 10:  1/12

Target 11:  1/18

Target 12:  1/36

So you're only losing about 5% going from target 6 to target 9.  I don't think many GMs really understand that any target number over 5 is becoming a fishing expedition, especially if more than 1 success is needed.  And when you hit 10, 11...it hardly matters.  12?  It doesn't matter, it's Fat Chance.

Thanks for working out the probabilities, although it really shows the bizarre long-tail distribution that exploding dice give.  And there's added complexity from throwing multiple dice in the pool.  In our SR2 campaigns we were fairly routinely throwing 8 dice at a time trying to hit targets in the 8-10 range, which succeeds something like 50-60% of the time, but my math skills weren't good enough to work out those odds at 11pm without using a calculator or slowing the game down.

If you explode on a 5...the probabilities are

Target 5:  1/3

Target 6:  1/3

Target 7:  5/36

Target 8:  1/9

and so on.  So you make a really funky looking  distribution.  It might *sound* better but I don't think it is.

You're right, but that isn't what I meant.  If Shadowrun explodes on a 6, then the value of that die should be a 5, and the next die added on.  That way sixes are not equivalent to sevens.

Problem solved.

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11 hours ago, Cancer said:

My issue with flat probability distribution functions coupled to game mechanics is that catastrophic failure is, as a practical matter, far more frequent and you are much more subject to the tyranny of the dice.  In 3d6, assuming fair dice, you hit the most adverse possible roll an order of magnitude less frequently than you do with 1d20 ... but GMs more or less invariably assign the same life-threatening severity of consequence to worst rolls in both systems.

It's one reason why I dislike catastrophic failure...in general, barring making it very rare.  (Like rolling a 1 on a d20 is a potential catastrophic...then roll d100.  Another 1?  Oh dear.  But that's 2000 to 1.)  And, that said...catastrophic failure is fine in some campaigns, where the tone fits, or where maiming or dying is temporary.

I'll also grant that D&D's "1 always fails, 20 always succeeds" can become darn near tactical, compared to Hero's "3 always succeeds, 18 always fails."  There was a school of thought, back in 3.0, where you just use the insta-kills against the BBEGs...because the damage from most spells, where they'd make their saves most of the time, just never cut it.  A 5% chance of ending the fight was STILL better than what you'd get otherwise.  The damage system became broken with the big 3.0 Con changes.

That actually points out an advantage of a WIDE uniform distribution...d100 to even d1000.  It's less about the granularity in the middle, and more about letting you assign auto-success or auto-failure to the remote tails...on d1000, perhaps 1-4 and 997-1000.  1 in 250.  But 1000-sided dice would be...awkward at best, so you're generally rolling 3 d10s.  Which one is which digit?  It opens the door to cheating...and I saw it with certain players.  At times, too, in the heat of the game...players can get too into it.  Be that as it may, the math side gives you a better practical framework.

8 hours ago, Old Man said:

Thanks for working out the probabilities, although it really shows the bizarre long-tail distribution that exploding dice give.  And there's added complexity from throwing multiple dice in the pool.  In our SR2 campaigns we were fairly routinely throwing 8 dice at a time trying to hit targets in the 8-10 range, which succeeds something like 50-60% of the time, but my math skills weren't good enough to work out those odds at 11pm without using a calculator or slowing the game down.

No reason to work these out at the table.  The math's not bad, if one took a class in probability anyway.

A quick and dirty approach is to go with the expected number of successes.  This is simple, as long as you know the probability of success on 1 die, P.  The expected # of successes is simply P * N, where N's the number of dice.  So rolling 9 dice with target number 9...you expect 1 success on average.  That doesn't mean you'll always get 1...sometimes you'll get 2.  But it's a general gauge.  If your expected number of successes is, say, 0.5...9 dice with target number 11...you can recognize your chances are bad.

Mathematically precise...the probability of 1 or more successes is 1 - (the probability of NO successes).  If P(success) is 1/9, then P(failure) = 1 - P(success) = 8/9.  The probability of no successes on N dice is simply P(failure) ^ N.  So this kinda thing can be worked out.  OK, don't do this by hand, but it's easy to write a spreadsheet.

 5 6 7 8 9 10 11 12 0.333 0.167 0.167 0.139 0.111 0.083 0.056 0.028 1 0.667 0.833 0.833 0.861 0.889 0.917 0.944 0.972 2 0.444 0.694 0.694 0.742 0.79 0.84 0.892 0.945 3 0.296 0.579 0.579 0.639 0.702 0.77 0.842 0.919 4 0.198 0.482 0.482 0.55 0.624 0.706 0.796 0.893 5 0.132 0.402 0.402 0.473 0.555 0.647 0.751 0.869 6 0.088 0.335 0.335 0.408 0.493 0.593 0.71 0.844 7 0.059 0.279 0.279 0.351 0.438 0.544 0.67 0.821 8 0.039 0.233 0.233 0.302 0.39 0.499 0.633 0.798 9 0.026 0.194 0.194 0.26 0.346 0.457 0.598 0.776 10 0.017 0.162 0.162 0.224 0.308 0.419 0.565 0.754 11 0.012 0.135 0.135 0.193 0.274 0.384 0.533 0.734 12 0.008 0.112 0.112 0.166 0.243 0.352 0.504 0.713 13 0.005 0.093 0.093 0.143 0.216 0.323 0.476 0.693 14 0.003 0.078 0.078 0.123 0.192 0.296 0.449 0.674 15 0.002 0.065 0.065 0.106 0.171 0.271 0.424 0.655 16 0.002 0.054 0.054 0.091 0.152 0.249 0.401 0.637 17 0.001 0.045 0.045 0.079 0.135 0.228 0.378 0.619 18 0.001 0.038 0.038 0.068 0.12 0.209 0.357 0.602 19 0 0.031 0.031 0.058 0.107 0.191 0.338 0.586 20 0 0.026 0.026 0.05 0.095 0.175 0.319 0.569

First row is target number.  Second row is P(Success) for that target number, on 1 die.

The far left column is the number of dice.

The other columns are then the probability of FAILURE...of not getting any successes.  Getting 1 success is...plausible.  But in Shadowrun in many cases, you need more than 1...and that's when life gets HARD.

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4 hours ago, Logan.1179 said:

Straya!

Everything wants to kill you.

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All the hoons and the wazzas.

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53 minutes ago, L. Marcus said:

All the hoons and the wazzas.

And Bazzas.

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Ah, they're alright. They just want to philosophize you.

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6 minutes ago, Cygnia said:

Let's hope it's not mistaken for a giant mouse by a father and son team of cats.

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I actually sampled kangaroo meat in a taco during Origins this past June.  Reminded me of skirt steak.

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7 hours ago, L. Marcus said:

Ah, they're alright. They just want to philosophize you.

Do the horrors of that continent know no limits?

3 hours ago, Cygnia said:

I actually sampled kangaroo meat in a taco during Origins this past June.  Reminded me of skirt steak.

Never had kangaroo, but ostrich also tastes like beef, gator tastes like chicken, and escargot tastes like bicycle tube in garlic sauce.

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5 hours ago, Cygnia said:

We had an escaped wallaby here in Pierce Couny, Washinghton many years back. The Tacoma News Tribune had fun with it. Big headline: "Wallaby Watch: Day 2!" IIRC the wallaby was recaptured less than a week later, though.

Dean Shomshak

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1 hour ago, Logan.1179 said:

But MC Hammer don't hurt 'em.

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2 hours ago, DShomshak said:

We had an escaped wallaby here in Pierce Couny, Washinghton many years back. The Tacoma News Tribune had fun with it. Big headline: "Wallaby Watch: Day 2!" IIRC the wallaby was recaptured less than a week later, though.

Dean Shomshak

The wallabies here are one of the few examples of an invasive species that didn't wreck the local ecosystem.

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4 hours ago, Old Man said:

Do the horrors of that continent know no limits?.

You say that like groking the external world using reason & intellect, and to remind our public officials to behave for the public interest, is a bad thing.

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