A search for an optimal resolution mechanic

Lago PARANOIA · Post by **Lago PARANOIA** » Mon Mar 19, 2012 4:34 pm

erik wrote:And... fuck, did I fall for being trolled? I read up the page on this thread and I still feel played.

I was being serious. I like how the d10 does probability, but as for how the die is actually rolled... honestly, I think that it sucks. This just might be my imagination, but it doesn't feel like it rolls correctly. And the shape irks me. I'd love to find ways to get around that, but I'm not sure if it's possible short of doing clunky things like 'ignore the 10s digit on the d20' or 'always reroll 11s and 12'.

Previn · Post by **Previn** » Mon Mar 19, 2012 5:00 pm

FrankTrollman wrote:
Previn wrote:Are there any examples of a dice pool with counted hits that increase the size (number of faces) of some or all of the dice?
Yes. This is a terrible mechanic because it makes all other modifications to the system (dice number, target number, hit threshold, explosions) incoherent.

-Username17

What? Do you mean it makes the ability to calculate odds incoherent?

If I have a TN of 5+, and I'm rolling 5d6 along with 2d8, I've just got better odds of hits with those two d8. I can't generate more hits than if I was rolling 7d6, the TN didn't change and I'd just as soon drop exploding anyways.

Lago PARANOIA · Post by **Lago PARANOIA** » Mon Mar 19, 2012 5:08 pm

FrankTrollman wrote:That would give you the same range as 2d10, but be much harder to culculate. Specifically, it would give you a bar of identical probabilities between 9 and 13, and then curve off slowly after that.

-Username17

How much harder to calculate? Is there some kind of rule of thumb you can use to determine how much less (or more) additional modifiers affect the outcome like with 2d10s or 3d6s?

tussock · Post by **tussock** » Wed Mar 21, 2012 3:15 am

As a rule of thumb, d8+d12 is the same as 2d10. You'll never notice the difference unless you keep a tally of every result, unless maybe if you have a special result on an 11.

...You Lost Me · Post by **...You Lost Me** » Wed Mar 21, 2012 6:22 am

I like d8+d12, but it's even more awkward to roll than 2d10 IMO.

Username17 · Post by **Username17** » Wed Mar 21, 2012 12:07 pm

When you're rolling 2dN, then the middle number comes up 1/N times. That is: no matter what you roll on the first die, the second die has one number that will make it come out to the middle number. Each number you move away from the most likely number reduces your chances of rolling it by 1/N^2. That is, there is one less number on the first die that would put you in striking distance and if you are in striking distance there is still one number that you could roll on die two that would deliver the result in question.

So for example: on 2d6, you get a 7 one time in 6. You get a 6 or an 8 five times in 36 (1/6 - 1/36). On 2d10, you get an 11 one time in 10. You get a 10 or 12 nine times in 100 (1/10 - 1/100). And so on.

With mismatched dice, it's more complicated. On d8+d12, every number between 9 and 13 is equally likely, because no matter what you roll on the d8, there is exactly one roll on the d12 that would deliver it to you. So 9, 10, 11, 12, and 13 all come up 1/12th of the time. Thereafter, the chances drop by 1/8*1/12 each time. So 8 or 14 comes up 7/96 of the time (there are 7 numbers on the d8 that would put you in striking distance and only 1 number on the d12 that would seal the deal). A 7 or 15 comes up 6/96 of the time, a 6 or 16 comes up 5/96 of the time, and so on until a 2 or 20 comes up 1/96 of the time.

-Username17

Lago PARANOIA · Post by **Lago PARANOIA** » Tue Apr 10, 2012 12:32 am

This is probably going into crazytown incalculability shenanigans, but, what would be the merits of mixing a curved + linear modifier RNG with more dice? For example, for an untrained skill check you roll 2d6 + mods, but if you have relevant training you roll 3d6 + mods and if you have master training it's 4d6+mods.

echoVanguard · Post by **echoVanguard** » Tue Apr 10, 2012 5:45 am

Lago PARANOIA wrote:This is probably going into crazytown incalculability shenanigans, but, what would be the merits of mixing a curved + linear modifier RNG with more dice? For example, for an untrained skill check you roll 2d6 + mods, but if you have relevant training you roll 3d6 + mods and if you have master training it's 4d6+mods.

For each point of mods, shift the value to the right by 1.

As far as merits, that would depend greatly on how you set your success and failure conditions - for example, if the average mod is +3 and you fail on a 10 or lower, untrained users will succeed about 50% of the time, while trained users will succeed about 90% of the time and specialized users will succeed about 99% of the time. However, if you're doing stuff like setting 'critical success thresholds' at the midpoints of each graph (normal success at 11+, extra success at 14+, and tremendous success at 18+), you pretty much just map a 50% success rate for that threshold onto the appropriate category while making it effectively impossible to lower tiers (sans huge modifiers).

It should also be pretty obvious that whatever you do, the value of modifiers will grow exponentially, and the effect will be compounded at each mastery tier.

echo

Lago PARANOIA · Post by **Lago PARANOIA** » Mon May 28, 2012 2:03 am

So. 5E D&D's nascent advantage/disadvantage system applied to dicepools. Something like that would be rerolling one or more failure (or success) dice to your advantage.

On the one hand, I like it because it fucks the RNG less and unlike for a d20 allows you to have a range of advantage of disadvantage rather than an all-or-nothing. On the other hand, it can very quickly reach the point where your dicepool size is your result, especially if you use a low TN.

So personally, I'm wondering about the merits of doing an integrated approach to dicepool fuckery. Some game affects change the size of the dicepool. Some game affects allow positive or negative rerolling. And other game effects cause certain die rolls to explode (or implode; that is, on a failure you remove a hit and reroll that dice). And then very strongly segregating them such that CAN is the ONLY way to temporarily increase your dicepool size. So on.

How do you think that would work out for the overall goal of controlling dicepool bloat?

Username17 · Post by **Username17** » Mon May 28, 2012 4:36 am

The 5e Advantage/Disadvantage system has existed for dicepools for years. It's called a "roll and keep" system. Roll and Keep is kind of fun to play, because the actual act of rolling a pile of dice and selecting winners from the pile is itself kind of fun. But it's completely shit to design for, because the probabilities are all over the place. I don't think it's any accident that every roll and keep system ever made has turned into hot garbage the moment people started to pick up modifiers.

-Username17

Lago PARANOIA · Post by **Lago PARANOIA** » Mon May 28, 2012 4:55 am

You know, I've always wondered for awhile whether people are really that offended by asymmetric probability (like in Roll and Keep or Advantages/Disadvantages) that's 'on the fly'. People get very offended if bonuses from buffs or magical items or class features don't work correctly, but a penalty from trying to fight underwater or a bonus from fighting behind cover doesn't seem to grind peoples' gears as much, even though the probability is probably ineffable. Or take Edge. No one really minds that using Edge to turbocharge a roll creates really funky probabilities because it's not expected -- all people know that it's good and it's not a good that they're supposed to count on in normal situations.

That said, you're probably right that even if you tried to implement it stringently the probability would just be way too hard to divine.

Username17 · Post by **Username17** » Mon May 28, 2012 5:00 am

Lago PARANOIA wrote:You know, I've always wondered for awhile whether people are really that offended by asymmetric probability (like in Roll and Keep or Advantages/Disadvantages) that's 'on the fly'. People get very offended if bonuses from buffs or magical items or class features don't work correctly, but a penalty from trying to fight underwater or a bonus from fighting behind cover doesn't seem to grind peoples' gears as much, even though the probability is probably ineffable. Or take Edge. No one really minds that using Edge to turbocharge a roll creates really funky probabilities because it's not expected -- all people know that it's good and it's not a good that they're supposed to count on in normal situations.

That said, you're probably right that even if you tried to implement it stringently the probability would just be way too hard to divine.

The thing is: Edge really isn't that hard to divine. If you are going to reroll your dice, you succeed on 5/9 of dice instead of 1/3. If you are wondering how pulling a reroll is going to affect your roll right now, it's just an amount of bonus dice equal to your misses. It's big, but it's not ineffable.

Effing the addition of a rolled or kept die in Seven Seas is ineffable. Because the odds change so massively based on how many dice are already rolled or kept.

-Username17

Lago PARANOIA · Post by **Lago PARANOIA** » Mon May 28, 2012 5:12 am

I'm not a probability or statistician person at all, so I present to you the following scenario:

For example, you're trying to flank a target with your buddy and the target is also blinded. The TN is 4 on a d6 and your dicepool size for attacks is 8. Your advantage rating is one. Flanking nor blinding shifts either of your dicepool sizes.

Your buddy uses an ability that lets you throw out an off-turn melee basic attack, and your advantage rating lets you reroll one failed die one time only. Afterwards your buddy shifts and flanks, giving you an advantage rating of 2 thereafter.

You take your normal turn and attack. getting to reroll two failed die. Afterwards, you make an iterative attack at dicepool size 5. You still get to reroll two failed die.

What would be the quick and dirty odds on all of those attacks?

Username17 · Post by **Username17** » Mon May 28, 2012 5:28 am

In a scenario like that, rerolls are not really different from just rolling more dice. With five dice in the pool, a rerolled die is no different from an extra die if you have at least one die that is a miss - something that happens 31 out of 32 times at TN 4 and 242 out of 243 times at TN 5.

For the 5 die, TN 4 scenario, a reroll is exactly the same as rolling a 6th die except that you lose the 1/64 chance of getting 6 hits. The maximum doesn't move, but the odds otherwise are almost wholly indistinguishable from rolling more dice. For the 8 die scenario it's even more silly - it'll only be different from just rolling a 9th die one time in every five hundred and twelve rolls. And even then you could just get the same exact curve by just rolling 9 dice and capping hit potential at 8.

Rerolls are only really different from rolling more dice if the dice they reroll can have negative utility in and of themselves. If you are making botches go away, then your reroll scheme matters. Otherwise, not so much.

-Username17

Lago PARANOIA · Post by **Lago PARANOIA** » Mon May 28, 2012 11:18 am

Actually, that honestly doesn't sound very bad. Except for extreme edge cases it doesn't sound all that different from adding an extra die. So you can have a 'virtual' dicepool that's a bit larger than what you intended but it still caps the maximum result. Also while the work needed to reroll 2 failures out of a size 14 dicepool is actually slightly more work than just rolling a size 16 dicepool, I still maintain that people a priori derp out over just the size of the dicepool once you get past the 14-16 range so that's helpful.

wotmaniac · Post by **wotmaniac** » Wed Mar 06, 2013 1:20 am

Sorry to necro, but this seemed at least as good as starting a new thread .....

I'm curious about you guys' thoughts on the following:

So, me and a friend of mine had a conversation that touched tangentially on Savage Worlds, and something occurred to me in regards to SW's step-up -vs- step-down:
* step-up = diminishing rate of improvement with each step
* step-down = increasing rate of improvement with each step
While the 2 extremes of each mechanic are basically the same (with the only real difference being variance), the climb from one end to the other is vastly different.

Solely as it pertains to rate of improvement, I'm gonna have to side with step-up, in relation to that which is being modeled.

Thoughts?

Dean · Post by **Dean** » Wed Mar 06, 2013 4:32 am

I'm gonna be honest. I don't know what you're talking about. Clarify?

wotmaniac · Post by **wotmaniac** » Wed Mar 06, 2013 6:17 am

okay:
I'm talking about inverting the Savage Worlds die-improvement scheme -- start with d12 and work down to d4, and instead of "roll at least a 4", it would be "roll under a 4". (obviously, some other base modifications would need to be made, but this is the basic concept).

When you start with d4, your base success % is 25%, working your way to d12 gets you 75%.
if you start with d12 (roll under), you start with 25% success chance, working your way down to d4 gets you 75%.

However, as you work up from d4, your % goes .25->.5->.625->.7->.75. each step up gets you smaller increases.
when you start with d12 and work down, ... well, just flip that last line.

so, the question is basically what is more preferable, increasing returns or diminishing returns?

Username17 · Post by **Username17** » Wed Mar 06, 2013 6:38 am

wotmaniac wrote:okay:
I'm talking about inverting the Savage Worlds die-improvement scheme -- start with d12 and work down to d4, and instead of "roll at least a 4", it would be "roll under a 4". (obviously, some other base modifications would need to be made, but this is the basic concept).

When you start with d4, your base success % is 25%, working your way to d12 gets you 75%.
if you start with d12 (roll under), you start with 25% success chance, working your way down to d4 gets you 75%.

However, as you work up from d4, your % goes .25->.5->.625->.7->.75. each step up gets you smaller increases.
when you start with d12 and work down, ... well, just flip that last line.

so, the question is basically what is more preferable, increasing returns or diminishing returns?

Both of those are fucking terrible. There's no rhyme or reason to any of the improvements or penalties you could have, and it doesn't support events being particularly rare under any circumstances. That is super double fucked.

Savage Worlds has an objectively shitty system. No idea why you'd want to copy anything at all from their action resolution mechanics.

-Username17

Prak · Post by **Prak** » Wed Mar 06, 2013 7:27 am

There's an rpg that just went through Kickstarter called Alas, Vegas. It uses a fairly unique resolution mechanic:

Basically, you're playing a kind of modified version of Blackjack using Tarot cards. There are two levels of skill, no relevant ability, and having a relevant ability.
If you don't have the ability relevant to the action you're attempting, a major arcana card will always be a failure, and the action can't be retried.

When you're doing a non-contested action, the Dealer (gm) assigns a difficulty from 3-12, and you flip over a card. If it's a minor arcana that meets or exceeds the diff, you succeed. If it's lower than the diff, you fail. If you have a relevant ability and get a major arcana, you succeed.
There's an option for "how long does it take" in which the character is basically assumed to succeed, and you just need to figure out how long they're at it. Dealer specifies seconds, minutes or hours, and flips a card. If it's a major arcana and you have the relevant ability, you flip a second card and add 10 to the value. Double major arcana fails, even with a relevant ability.

In contested actions, you're literally playing blackjack with all involved characters.

AV is more of a story game with RP aspects, and the picture on the cards revealed influence the story.

Lago PARANOIA · Post by **Lago PARANOIA** » Thu Oct 24, 2013 6:46 am

http://anydice.com/program/2c64
So yeah. I'm on a dicepool kick again.

I've been trying to create a dicepool resolution mechanic that:

A.) Can cover a wide range of results.
B.) Never has you roll more than 10 dice at once.
C.) Minimizes extra calculations.
D.) Can still generate outlying results like all hits on a 13-die pool -- which is a problem I have with autobuying hits.
E.) Still have some of the functionality of autohits where it provides a hard limit on how low your check can get. So while Spider-Man and even Wonder Woman will still need to worry about hordes of mooks with machine guns, Superman doesn't.

Of course, there are a couple of weaknesses with my approach.

A.) It assumes that you buy special dice. It will still work with bog-standard d6s and d8s, but you have to memorize an additional single-digit subtraction step that depends on the size of your dicepool.
B.) It's still flat-out impossible to generate absolute min results at all or max results with dicepools of >16 even though the curves still map very closely to rolling them by hand. However, even the raw dicepool has less than a 1/500 chance of generating the maximum result, so I'm not too worried. If for some reason people are making that kind of longshot I can see the table making a one-time exception. I'm just not cool with people rolling 12+ die pools as a matter of course.

I'm even less worried about the inability to generate 0 results. You got at least 10 dice in your pool, you deserve to have a backstop.

The Extra Dice are specially marked dice used just for this game.
1d3 Extra Dice are 1d6s which have two faces each of -1, 0, and 1.
1d4 Extra Dice are 1d8s with two base designs. One has a -1, 0, 1, and 2 for two faces each, the other has a -2, -1, 0, and 1. They're always rolled in pairs, so don't worry about using the wrong one.

If you don't have extra dice, you can make them out of regular dice easily enough. Just roll the dice, divide the result by 2, round up to the nearest integer (this is a specific exception to the round down rule), and subtract 2 for each d6 and 5 for each pair of 1d4s (or 1d8s divided by two, rounded up, if you don't have d4s but have d8s).

To calculate your hits, roll your 'regular' dice denoted by your dicepool size and then perform the extra dice calculation. Then add your automatic hits.


Dicepool	Base	Auto	Extra Dice
7	4	2	(1d6/2) - 2 / 1d3
8	5	2	(1d6/2) - 2 / 1d3
9	6	2	(1d6/2) - 2 / 1d3
10	4	4	2 of ((1d6/2) - 2) / 2d3
11	5	4	2 of ((1d6/2) - 2) / 2d3
12	6	4	2 of ((1d6/2) - 2) / 2d3
13	4	6	[2 of 1d4] - 5 / 2d4
14	5	6	[2 of 1d4] - 5 / 2d4
15	6	6	[2 of 1d4] - 5 / 2d4
16	4	8	[2 of 1d4] - 5 / 2d4
17	5	8	[2 of 1d4] - 5 / 2d4
18	6	8	[2 of 1d4] - 5 / 2d4
19	4	10	(1d6/2) + [2 of 1d4)] - 7 / 2d4 + 1d3
20	5	10	(1d6/2) + [2 of 1d4)] - 7 / 2d4 + 1d3
21	6	10	(1d6/2) + [2 of 1d4)] - 7 / 2d4 + 1d3
22	4	12	2 of (1d6/2) + [2 of 1d4)] - 9 / 2d4 + 2d3
23	5	12	2 of (1d6/2) + [2 of 1d4)] - 9 / 2d4 + 2d3
24	6	12	2 of (1d6/2) + [2 of 1d4)] - 9 / 2d4 + 2d3

You can fiddle with the results in the link at the top. I could have it scale even further but for a TN:3 game which is supposed to cover, say, PL15 Mutants and Masterminds I think that's more than good enough.

Dean · Post by **Dean** » Thu Oct 24, 2013 7:04 am

I'm sorry Lago but I just don't understand the basics of what you are posting. I understand it is a resolution mechanic but I can't make heads or tails of it. Not to mention Statement B says you have a 10 die absolute maximum and then you talk about die pools of 13, 16, and 24.

Im lost man

PhoneLobster · Post by **PhoneLobster** » Thu Oct 24, 2013 7:23 am

Lago PARANOIA wrote:So yeah. I'm on a dicepool kick again.

I'm just going to flat out ask.

Lago, your proposed dicepool mechanic, it's bad satire right?

deaddmwalking · Post by **deaddmwalking** » Thu Oct 24, 2013 9:13 am

As I take it, his system allows you to take a 15-dice pool, and resolve it with rolling fewer dice. So, if you would have a 15-dice pool, instead of rolling 15 d6s, Lago would have you roll two 'special dice' and two regular dice. You achieve similar results to the 15-dice pool with only 4 dice.

Clearly, what he has created is not easier or more intuitive than just rolling large fistfuls of dice.

PhoneLobster · Post by **PhoneLobster** » Thu Oct 24, 2013 9:24 am

deaddmwalking wrote:Clearly, what he has created is not easier or more intuitive than just rolling large fistfuls of dice.

At least then at some level he seems to have recognized that large variable fistfuls of dice are a problematic cost and should be streamlined in some form.

Nice to see the pro dice pool crowd making SOME sort of progress over time.

But not really seeing it being a particularly sane mechanic yet. I mean. When you base mechanic is so bad it needs a complex table based shortcut that tells you which custom dice to use instead to get an approximation of the same results you have a bit of a problematic base resolution mechanic.

And I'm utterly unclear. This is 2013. If your insane mechanic needs a short cut/accounting assistant because it's just that bad why the hell aren't you making your phone do the work?