A search for an optimal resolution mechanic

[wotmaniac]

Has there ever been a good resolution mechanic that used playing cards?

Well, I don't know if this counts, but Savage Worlds uses playing cards to determine initiative ... every round.

I understand their thinking: "hey, give players something tactile to draw their attention and break-up any monotony -- they love that shit" ... but it fails hard because it's a completely random thing that has absolutely nothing to do with the rest of the game -- it's rather intrusive.

[Previn]

You can make the effectively different sections of a dicepool bigger by making the dice hit more often. If you hit on a 5+, your difficulties can go up about 1 per three dice of awesome. If you hit on a 4+, difficulties can go up about 1 per two. If you hit on a 3+, then difficulties can go up about 2 every 3.

What that essentially means is that by lowering the TN, you can increase the threshold at which you need auto-hits to maintain sanity. Personally, I think that rolling more than 12 dice for a "normal" test is bullshit. But at the same time I see real value in people rolling 18 dice on specialist tests to show that they are super awesome. 24 dice is even OK to roll for "boss fights" and similar shenanigans.

So a major badass PC might need auto-hits if he is supposed to be attempting a task with a difficulty of more than 6 if his TN is 5+. But the cutoff for requiring autohits for the same badass PC would be more like 12 hits if his TN was 3+.

-Username17

Two questions:

Could you use the lowering of the TN to indicate tiers? So Dirt Farmers use a TN of 6+, PCs and NPCs they interact with use TN 5+, Legendary PCs and NPCs use 4+ and Elder Dragons and Gods use 3+?

What is the average size of a dice pool in Shadowrun? I was under the impression that you should have between 8-12 dice in anything you actually expect to do?

[Username17]

Could you use the lowering of the TN to indicate tiers? So Dirt Farmers use a TN of 6+, PCs and NPCs they interact with use TN 5+, Legendary PCs and NPCs use 4+ and Elder Dragons and Gods use 3+?

In theory you could do something along those lines, but in practice I don't think it works out. People have done a lot of stuff with trying to make variable TNs work for dicepool games and the results aren't good. Variable TNs make the value of individual dice vary, which makes the value of dicepool modifiers and the value of TN modifiers hard to predict. The net result has been system after system that outputs just really weird results.

What is the average size of a dice pool in Shadowrun? I was under the impression that you should have between 8-12 dice in anything you actually expect to do?

For SR4, yeah. A PC gets between 8 and 12 dice in anything they expect to do, and up to 18 dice in anything that they invest heavily in specializing in. And that really does work pretty well.

The issue is that SR4 doesn't handle vehicles or rocket launchers well at all. Once things get bigger than "very skilled man with a sub machine gun and some cyberware" the game simply falls apart.

-Username17

[Lago PARANOIA]

Has there ever been a good resolution mechanic that used playing cards?

Depends on how far you want to take 'resolution'. There have been a few, but they've been mostly confined to video games because, well, shuffling cards sucks and is slow.

I can imagine a system where they'd be really worthwhile for a theoretical game engine where you don't want a result to necessarily be strictly inferior or superior to every result not itself. For example, a fantasy mass combat game where you draw cards that do things like 'Your officers promise the men loot if they capture the next town. Atrocity + 1 <= 5; Morale + 1 <=7.' or 'Your engineers figure out a way to optimize the siege engines. Siege Engines + 2 <=5' or 'A wander necromancer places a curse on your men to have them rise from the dead. Morale - 2, if this unit dies it turns into Enemy Skeleton Troops. If the morale is 6 or higher upon death, it remains under your control.'

[Lago PARANOIA]

In theory you could do something along those lines, but in practice I don't think it works out. People have done a lot of stuff with trying to make variable TNs work for dicepool games and the results aren't good. Variable TNs make the value of individual dice vary, which makes the value of dicepool modifiers and the value of TN modifiers hard to predict. The net result has been system after system that outputs just really weird results.

What if you make changing TNs:

1.) Unidirectional: they can only go down, not up.

2.) Universal: it's impossible for you to be an epic-level character and not have a base TN of 3.

3.) Inviolable: TNs only change if you enter a new tier. There is no effect in the game possible that will change your TN except for entering a new tier. If anyone publishes a Prestige Class or feat that does this, no matter how narrow the effect is, they get laughed out of the room.

4.) Intentionally non-linear in effect: even though 'using cover' always adds a 1 to your attackpool modifier, Vash the Stampede simply gets more out of it than Captain Picard.

5.) Between tiers, the dicepool size increase is small.

The output of this system would be:

A.) If you completely tank or neglect a skill, you don't become much better in it as you gain in levels. Sure, your epic-level wizard with a dicepool of 2 for stealth sneaks slightly better than a peasant with a dicepool of 3, but a newly trained scout recruit will still outclass him.

B.) However, due to the shifting TN, higher-tier generalists are about on the same level as lower-tier specialists because they're still increasing their dice pool size. While I think people are offended by the idea of late-series Parn (mid-tier, no stealth) sneaking better than James Bond (low-tier stealth specialist), they're not offended by Obi-Won Kenobi (mid-tier stealth generalist) sneaking better than James Bond.

C.) The boost in power to jumping to a higher tier is very significant without having to rewrite large sections of the character sheet.

D.) If you construct the numbers properly, it stealth-renormalizes the RNG without requiring much input from the players. I'm a fan of renormalizing the RNG between tiers but I've been very hard-pressed to find a solution with linear/bell curve RNGs that doesn't become obvious and intrusive.

[DrPraetor]

Lago - so instead of having a TN of 4, epic characters have a TN of 2 in order to roll fewer dice? Rolling a smaller pile of dice is always good, but that's a lot of *work* in order to reduce the number of dice, and it isn't good for what you care about, which is the *variance*.

Also I'm not sure why you want to split characters up into these tiers of awesome - there are settings in which it would make sense (for example, Superheroes. Anyone who is "In Heroic ID" has a TN of 2 instead of 4 for whatever it is they do) but in any vaguely-realistic setting, it's going to be a broken mechanic. And anyway, you're better off giving the superheroes reduced thresholds/free hits, as I'll explain below.

But other than that, let's talk - what do we want out of die rolling mechanics *besides* quick resolution.

First, a quick comment on how dice-pool systems work, which I don't want to repeat again and again below. A dice-pool system is a draw from a binomial distribution (http://en.wikipedia.org/wiki/Binomial_distribution). You can set the threshold (the number of hits, minimum value of "k") wherever you want, so what matters isn't the expected value of "k" as a function of the number of dice, it's the *variance* in "k" as a function of number of dice. It's easy to lower the variance (roll fewer dice), it's getting *more* variance which is difficult; and the variance is maximized by having a TN of 4. So since the only reason to roll dice *at all* is to increase the variance of the outcome, to make a long story short - if you're going to use dice pools, the number of the target shall be 4. 2 is right out.

Finally, I'm assuming that doing algebra is out of the question. So the only alternative to making a draw from the above-mentioned binomial distribution is to make a draw from a Uniform distribution (that is, a 20-sided or % die.) When I was a kid (before I got my PhD) I thought it was fun to come up with game systems where the different tasks below were accomplished by sometimes rolling a backgammon die, sometimes rolling a fixed number of D6, and so forth. This is a major mistake that just wastes time and confuses people.

In order to answer this in a concrete fashion, and because I find the civil turn this conversation has taken deeply disturbing, let me posit an example scenario, based on this thread (http://www.tgdmb.com/viewtopic.php?t=53097):
SpaceLem's Mom is the biggest, ugliest Ogre in the trailer park. Because SpaceLem's Mom is gobbling up all the available cock, leaving none to be used as a medium of exchange, the trailer park economy has crashed. Our Heroes are dispatched by The High Pimp of the Elves, to discover what is going on, and put a stop to it.

Well, what do we want to happen, and how can we set up quick-resolving mechanics to achieve these goals?
* En route to the trailer park, our heroes are attacked by eunuch bandits. They're meant to think this is filler but of course it'll be a clue later on. At the beginning of the fight, the players charge on horseback, which is a somewhat-risky manoeuvre.
- Skilled characters have a real (but diminishing) chance of failure.
- However, even poorly-trained characters will *probably* succeed in staying on horseback.
So we want a *low* margin of success (so even characters with low skills probably succeed) and a *high* variance (so even characters with high skills sometimes fail.) In a dice pool system, this is actually easy to achieve - set the threshold high and give people bonus dice to compensate.
Fixed RNG systems generally fail at this - either there's a fixed chance of failure (1% or 5%, whatever) which you run up against no matter your skill level, or no chance of failure for skilled characters; and, you need to give unskilled characters some bonus. Mostly games like D&D you just don't roll for this kind of stuff, it's assumed to be automatic if you have any ranks in Ride at all.

* Our Heroes are captured by Ogres, and chained to big heavy logs to prevent them from running away. The characters see a chance to escape, if they can pick up their logs and haul them 15 feet quickly.
So, in this case, a sufficiently strong character just does it, weak characters can't do it, and intermediate characters need to test their pith and vigor.
This is vary hard to do with a draw from a fixed-range RNG. On % dice you can give people some fixed % penalty, but presumably then even super-strong people fail sometimes. You can do it by switching die sizes (so this test gets a D6 instead of a D20) but this works clunkily for only a few cases.
Again, though, with dice pools it's easy. You set the threshold to be Str dependent and people roll say 3 dice. Super-strong people need 0 hits (so succeed automatically), really-strong people need 1 hit (7/8 of success), kinda strong people need 2 hits (50/50) and average people need 3 hits (1/8 succeed).

* One of our heroes tries to convince SpaceLem's Mom to spare his life. Even for a super-bard this is unlikely to work, but then a low charisma character ought to have some shot at making a plea for mercy that she finds amusing, so what do we do?
Well, the fixed length RNG completely dies here. If there's a fixed number penalty, the unskilled character has no chance at all, and if not then the highly skilled character is practically guaranteed to succeed.
But, with dice pools it's easy, you can see this coming - we set the threshold *and* the variance very high. So you need a lot of hits but you roll a lot of dice. You probably still fail but you've got some chance at least; and of course charismatic characters have a noticeably bigger (but still small) chance of success.

***
TADA!

So, dice pools with a TN of 4 are the optimal resolution mechanic.

Next time: degrees of success? How much *variance* do you want in the degree of success between a skilled and unskilled character? You can probably write this one yourself.

For future reference - that is the level of detail required to win an argument with Frank. Do not bring lesser shit than this.

[Username17]

So since the only reason to roll dice *at all* is to increase the variance of the outcome

I disagree with this premise. The purpose of rolling dice is to fit a variance of outcomes within an acceptable range, not merely to increase it. If we just wanted to increase the variance, we'd roll dice in series. If percentile dice didn't have enough variance for our tastes (despite already having an expected variance greater than the actual number of potential outcomes), we'd roll d1000 or d10000. If that wasn't enough, we'd just keep adding extra d10s to the end until it was.

We roll dice pools because it gives us access to a number of potential options while still clustering numbers around average values. Basically because it gives the illusion of variance (which is required to keep people interested in the game) while still giving us actual predictability (which is required to keep the player characters alive and thus keep the story from ending despite all the "risks" they are taking).

The fact that TN 3 or 5 have less expected variance than TN 4 is actually an advantage.

-Username17

[DrPraetor]

So you've been whoring yourself out and running Shadowrun games for people who don't have even a single advanced degree in a quantitative discipline? For shame.

This is doubtless true, people "feel" that rolling 6 dice and hoping for at-least-2-5s is "risker" than rolling 6 dice and getting at-least-3-4s, even though the opposite is true.

But is it worth rolling the extra bales of dice, taking longer to count those extra bales of dice, and so forth? I don't think it is. I think you get better benefit in terms of seeming-risk from setting the TN at 4, and letting people roll extra dice on 1s and 6s (this ends up being the same number of dice you'd end up rolling on average with a TN of 5, assuming the same threshold), which has the double benefit of being the absolute best possible RNG because it's open ended.

Also, for any fixed number of dice in your box, the TN 5 RNG breaks down in a narrower range, which is an issue as soon as people start popping out tanks and rocket launchers.

[PhoneLobster]

But is it worth rolling the extra bales of dice, taking longer to count those extra bales of dice, and so forth? I don't think it is....

...I think you get better benefit ... letting people roll extra dice on 1s and 6s ... which has the double benefit of being the absolute best possible RNG because it's open ended.

Inconsistency detected!

Also. Exploding dice? Really. Now I hate dice pools on many levels for good reasons more than thoroughly explored. But exploding dice. I think it bares mentioning they are one of the most hateful baddy bad bad bits of a potential dice pool mechanic, and that simply NOT having exploding dice makes your dice pool mechanic significantly LESS horridly complex, unpredictable, opaque and just plain physically finicky to roll/resolve.

I mean if you cared about those things you probably wouldn't be rolling dice pools to start with, but even if you have a high margin of tolerance at SOME point you need to say enough is enough and exploding dice by all rights should be that point.

[DrPraetor]

Inconsistency how?

Personally, I like an open-ended results space. If you set the TN at 4, which means for a shadowrun-like dice pool space, you are rolling like 5-12 dice, then exploding dice on 1/3 results require you to roll 5-12 + 1/3(5-12) = up to 18 dice or so, tops. Very managable.

In exchange, you tend to roll the fewest dice possible given the variance on the test, and yet on each and every test you roll, the outcome is *actually* open-ended.

Anyway, by the only *objective* measure, which is variance, you are best off rolling piles of dice with a 50% chance of success each.

If you want to say "people *feel* like the variance is higher when rolling a bigger pile of dice, even though this isn't actually true", well, I'll grant that's correct. So play rolemaster, and enjoy how your critical hits cause holes in the space time contiuum, you bloody wanker.

[PhoneLobster]

But is it worth rolling the extra bales of dice, taking longer to count those extra bales of dice, and so forth? I don't think it is.

...5-12 dice, then exploding dice on 1/3 results require you to roll 5-12 + 1/3(5-12) = up to 18 dice or so, tops. Very managable.

You know. Before we even get into how bad wrong open ended mechanics are from a design and consistency standard. There is the thing where you complain about rolling "bales of dice" and taking longer to count them THEN going on about how 18 dice are "very managable" especially when it's approximately 2/3rds as many dice which then determine a variable number of extra dice which will be about 1/3rd as many dice that you then roll in an additional roll step.

And knowing exploding dice systems and the fondness for "open ended roll" fanatics for endless regressive explosion mechanics, then probably add another 1/3rd of 1/3rd and so on until you reach a small enough number that you don't roll another fucking explosion which theoretically MIGHT be NEVER.

No really you don't like rolling fiddly "bales of dice" but ~18 to potentially INFINITY dice (with multiple regressive separate additional dice pool rolls) is NOT a bale of dice too fiddly for you?

[Username17]

Open ended gaming is good. Open ended random number generators are bad. They are bad for two important reasons. The first is that black swan events where your PC ultra-succeeds on a test are pretty cool and fairly memorable (people remember the grand slams more than the strikeouts), but black swan events where your PC gets ultra-killed by Skeleton Henchmen #12 are game endingly horrible. The second, and possibly even more damning reality is the Take 20 situation. The thing where if you can repeat a task and you have time to kill, you can just try and try again until you succeed. When the RNG is literally open ended, every task no matter how stupid can be attempted this way. You get into the "I don't have any lockpicking skill, but if I default to my intelligence I figure I can open the vault in no more than ten thousand attempts. You might want to get yourself some popcorn..." situation. And that is horrible.

Note that both problems are neatly cleaved by tying open ended results to Edge or Action Points or some other player character resource. Then players can't take 20 on open ended rolls because they have a limited number of open ended rolls. And open ended rolls don't threaten to ultra-murder player characters in random and story-ending ways because Skeleton Henchman #12 doesn't have any Edge points to spend.

So I don't have an objection to "Spend an Edge, make this roll open ended". But as a standard mechanic on normal tests, it doesn't work.

-Username17

[DrPraetor]

I'm perfectly happy with fixed-availability open ended rolls. You can also go the Ars Magica route, and have open ended rolls only apply in "stress" situations; so your lockpicking isn't open ended. But the capacity to *sometimes* do open ended rolls is good, and it's better to be able to do so with the same variance with 8/9 as many dice.

Most shadowrun-type games don't have "literal death" as a result of being stabbed by Skeleton Henchmen #12, but if you want to keep the game interesting, at the very least, Skeleton Henchmen #12 ought to have some capacity to drop you; or make you spend an edge pip to avoid.

Trying to trick the players into paying attention to the fight with skeleton henchmen because:
1) the players are stupid
and
2) dice are shiny

Doesn't cut it, sorry.

[DrPraetor]

No really you don't like rolling fiddly "bales of dice" but ~18 to potentially INFINITY dice (with multiple regressive separate additional dice pool rolls) is NOT a bale of dice too fiddly for you?

I want to keep those bales of dice as small as possible; thus avoiding the *extra* bales of dice; emphasis on the extra; you are already rolling a bale of dice.

I do like open-ended die systems, and they do particularly well at addresses the problem Frank claims to see with TN 4 dice pools - giving the characters an irrational illusion of risk of uncertainty. Nothing does that better than exploding dice pools! You could get 30 successes, might as well try it!

[Username17]

Trying to trick the players into paying attention to the fight with skeleton henchmen because:
1) the players are stupid
and
2) dice are shiny

Doesn't cut it, sorry.

That is why 4e D&D is stupid, yes. You can't make fights with skeleton henchmen matter in those ways, no. But neither can you make fights with skeleton henchmen matter by giving them real risk, because iterative probability being what it is the chances of actual PCs making it out alive through dozens of conflicts with even minuscule real risks are vanishingly low.

If you want to have skeleton henchmen, then you have to make those battles matter in terms of resources expended, time lost, alarms raised, and so on. Things that your actual dice resolution system don't matter for at all. You also want a certain number of these encounters to contrast weak and strong opponents so that the bigger enemies feel bigger than something, and so that the Players have a chance to test their abilities and learn tactics in battles with lower stakes. And let's face it, most die systems can fit those frames as well.

The dice are just there to ensure that however many results your dice could generate, that the result where the skeleton henchmen score a couple of big crits at the beginning of the battle and then the story ends on a downer note during the trivial establishing shots of the narrative.

Dice Pool systems generate a lot of Black Swan events, especially if the TN is relatively rare. The higher the TN, the more extreme the Black Swan events get. The average number of hits is simply the chance per die times the number of dice. But the maximum number of hits is the actual number of dice being rolled. Shadowrun and After Sundown use TN 5, which means that a Black Swan crit is actually three times as many hits as the average. If the TN was 4, a Black Swan event would only be twice as many hits as average, and at TN 3, a Black Swan event would be only 50% more than an average roll.

Frankly, TN 3 is looking better and better to me.

-Username17

[tussock]

Let's talk about damage for a bit. Rolling 1d20+6 (3E monk unarmed strike damage) is lame, but not experience-ruiningly lame. I just don't care for that amount of swinginess. However, rolling 1d6+24 is so lame that it's barely worth talking about.

The thing is, damage rolls on a linear/bell-curve range have several competing interests.

You seem to be loving on Standard Deviation at about 1/5 of the average or a bit more, from your further examples.

For XdY the StDev is SQRT(X * (Y^2 - 1) / 12).

At 20% of average for StDev ... we get

1d6+5, 2d6+5, 3d6+4, 4d6+3, 5d6+2, 6d6+0, and we don't want to subtract.
1d12+11, 2d12+11, 3d12+10, 4d12+9, 5d12+6, 6d12+3. Looks like a pattern.

For simplicity, aim for the die size or a bit under for up to 4 dice, and no mods for 5+ dice. As you don't really want to throw and add more than 12d6 or 4d(other), damage totals over about 50 points per attack aren't allowed. Scale your game to suit, maybe with damage multipliers.

[DSMatticus]

Frankly, TN 3 is looking better and better to me.

I think people would find the lack of variability unexciting. They will just say "things seem easy," especially if they have any experience with Shadowrun or other more traditional d6 die pools. And yes, that's totally a problem of human psychology, but you're dealing with human players, so the shittiness of their psychology is relevant.

[DrPraetor]

Frankly, TN 3 is looking better and better to me.

I think people would find the lack of variability unexciting. They will just say "things seem easy," especially if they have any experience with Shadowrun or other more traditional d6 die pools. And yes, that's totally a problem of human psychology, but you're dealing with human players, so the shittiness of their psychology is relevant.

It also messes up the exploding dice, if you ever want to do that. TN 4 does exploding dice *very* elegantly:
* On a 6, roll an extra die (+1/2 hit on average)
* On a 1, lose a hit and roll an extra die (-1/2 hit on average)

You can make this work with TN 3, but it gets weird:
* Roll an extra die for every *2* 6s (which is +1/3 of a hit for every 6, give or take rounding)
* Lose a hit, and roll an extra die for every 1 (which is -1/3 of a hit for every 1)

Yuck.

@tussock - yes, you can have people roll mixed piles of polygonal dice, and backgammon dice, and hey you can go the WFRP 3rd ed. route and throw in some dice with skulls and comets and an AC-DC logo. Not only do you stab the ogre warlord in the chest, you rock hard while doing so! Uh-oh, you rolled the Jonas Brothers, sucks to be you.

Or, hey use a couple of these:
http://dicegamers.com/16mm-math-dice-numerals

With sufficient study, you could absolutely build a working game out of this stuff (the people who may WFRP 3rd ed. *chose not to do so*, because even in the gritty world of Hello Kitty you do not chop your own leg off like an eighth of the time, but that's not an intrinsic failure of using funny dice), however I see no way this could be the "best possible mechanic". It's clunky, it's hard to remember the parameters of different tests well enough to keep them remotely consistent, or to have different skills and attributes for your character scale in a meaningful way - for example, suppose that I make my character strong instead of dextrous? Well, if the tests for strength are on a completely different scale with wholly different piles of dice from the tests for dexterity, it's very hard to judge how much of a difference this is going to make. Not good.

[Username17]

It also messes up the exploding dice, if you ever want to do that. TN 4 does exploding dice *very* elegantly:
* On a 6, roll an extra die (+1/2 hit on average)
* On a 1, lose a hit and roll an extra die (-1/2 hit on average)

You can make this work with TN 3, but it gets weird:
* Roll an extra die for every *2* 6s (which is +1/3 of a hit for every 6, give or take rounding)
* Lose a hit, and roll an extra die for every 1 (which is -1/3 of a hit for every 1)

Yuck.

What the hell are you talking about? All target numbers explode exactly the same way. You could have dice explode on more or less numbers. Hell, you can have more explosions than you have hits on each die. The equation for average results on exploding dice is simply:

(H-B)/(D-X)

Where H is the number of numbers that you score a hit on, B is the number of numbers you score a negative hit on, D is the number of faces on each die, and X is the number of numbers that explode.

What this means is that from an averages standpoint, there is nothing protected at all about things exploding on a 1 or on a 6. You could have dice explode on a 4 or on a 2. While it's more random, it's not actually different in the long run from simply using a smaller die. Just as handing out botches on a 1 is not really different from just giving out less numbers that provide hits.

Your D6, 1s Botch, 4+ Hits, Explode on two numbers scheme is on average the same as just giving people an equal number of coin flips - it's just more complicated. "(3-1)/(6-2)" reduces to "1/2". You're just adding fiddly bits to disguise the essential coin flippiness of the process.

-Username17

[tenuki]

Your D6, 1s Botch, 4+ Hits, Explode on two numbers scheme is on average the same as just giving people an equal number of coin flips - it's just more complicated. "(3-1)/(6-2)" reduces to "1/2". You're just adding fiddly bits to disguise the essential coin flippiness of the process.

-Username17

It's elegant.

The fact that the dice explode does not affect the mean but increases the variance. It allows you to make some rolls exploding and some not without changing the expected result. I like it.

In a TN 3 system, the mean changes when you toggle exploding dice on/off. That's even messier than DrP's solution for it.

As for exploding coin flips... dunno. I've got this vague hunch that it might not work very well.

[Username17]

The fact that the dice explode does not affect the mean but increases the variance. It allows you to make some rolls exploding and some not without changing the expected result. I like it.

In a TN 3 system, the mean changes when you toggle exploding dice on/off.

But as previously noted, the game gets shitty if you go open ended on die rolls without spending something. If the open endedness doesn't favor the person rolling inherently, you have to come up with some other bonus to go alongside it (probably extra dice). Indeed, since everything else being equal more randomness is bad for the PCs, what you've set up in that instance is that the dicesplosion is an extra payment on top of spending Edge (or whatever) to get a pile of extra dice.

It is actually desirable for the diceplosion to be a good thing inherently, so that players will buy it on purpose.

-Username17

[K]

Every time someone says "it's elegant," it seems like they really mean "it duplicates a much simpler mechanic, but does so in a very complicated way that makes it hard for the average gamer to calculate the odds."

Personally, I don't want to do more than two operations. I can count out dice pools, count successes, count botches, and count exploding dice, but at no point do I want to do more than two of those things.

In the realm of repetitive calculations performed by slightly buzzed or fatigued humans, elegant and perfect rarely trumps simple and pretty good.

[tenuki]

Every time someone says "it's elegant," it seems like they really mean "it duplicates a much simpler mechanic, but does so in a very complicated way that makes it hard for the average gamer to calculate the odds."

Actually the opposite is true. For TN 4, the equity for a single die always remains +1/2. I'd call that easy to calculate indeed.

On the other hand, calculating the value of an exploding d6 with TN 3 in the first place involves the limit of an infinite product series.

Of course you can always simply tell your players that explosiveness improves the expectation for each die from +2/3 to +3/4, or 1 extra success per 8 dice on average, which looks like a very workable amount for a fate point mechanic.

Doesn't make it easier to calculate though.

[Username17]

Every time someone says "it's elegant," it seems like they really mean "it duplicates a much simpler mechanic, but does so in a very complicated way that makes it hard for the average gamer to calculate the odds."

Actually the opposite is true. For TN 4, the equity for a single die always remains +1/2. I'd call that easy to calculate indeed.

On the other hand, calculating the value of an exploding d6 with TN 3 in the first place involves the limit of an infinite product series.

Of course you can always simply tell your players that explosiveness improves the expectation for each die from +2/3 to +3/4, or 1 extra success per 8 dice on average, which looks like a very workable amount for a fate point mechanic.

Doesn't make it easier to calculate though.

You could tell them crap like that, but you'd be wrong. The equation is:

(H-B)/(D-X)

H is number of numbers on the die that are hits
B is number of numbers on the die that are botches
D is total number of numbers on the die
X is number of numbers on the die that explode

It's very easy to calculate new averages. Adding 6s explode to a 4+ TN shifts it from 3/6 to 3/5 hits per die. Adding 1s that botch to 4+ TN shifts it from 3/6 to 2/6. Adding both shifts it from 3/6 to 2/5. Adding 6s explode to a 3+ TN shifts it from 4/6 to 4/5. Adding 1s that botch shifts it from 4/6 to 3/6. Adding both shifts it from 4/6 to 3/5.

The thing is: botches are stupid and make calculations much longer than they need to be. Also they perversely make new dice bad for you sometimes which is counterintuitive and also horseshit in general.

If you were going to do negatives at all, you'd use standalone penalty dice, which would be evaluated on their own in a separate pool.

-Username17

[tenuki]

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?