The New School Manifesto

[Kemper Boyd]

Do you really plan to roll such scenes 1000 times each, to work out if it's easy?

Well, in this case, the chance for success is a bit lower than without a target number so I think the chance of success is easy enough to intuit, eyeball or approximate, given that you got the base percentage of 85% and only matches of 1's and 2's will be affected. Close enough for government work!

Actually, a friend of mine just got interested in crunching the numbers at work, so we're going to have sample sizes of one million rolls per possible default roll, for a given total of 9 million rolls. That should give us a nice amount of data to analyze.

[Fuchs]

Fix your quote tags please.

[John Magnum]

Boyd, your pathological fear of math is incredibly bizarre.

So far, all I've ever seen you intuit is basic correlation. If you add more dice, it makes your odds better by some nebulous amount. If you muck around with target numbers, it makes your odds worse by some nebulous amount. That's seriously not enough to work with.

In d20, the DM and the system writer can be very precise about how bonuses and DCs affect odds of success. You know that raising the DC by 4 drops your odds of success by 20 percentage points (barring situations on either side where someone's fallen off the RNG).

Even in dice pool systems counting hits, probability calculation is a little easier. It's more harder than uniform distributions, but there's still a simple heuristic. Given the number of dice and the target for success, it's really easy to figure out how many successes you'll probably get. And you know that the possibility of getting more or fewer is decent, but it rapidly drops off since the number of successes is an approximately normal distribution.

This actually gives people a lot more to work on in a way that's a lot easier to intuit than the matching system.

As a designer, do you have any guidelines for your playtester DMs to adjust the difficulty of challenges? Or are you going to playtest by letting them randomly assign bonuses and penalties until they get results that "feel right"?

It's seriously stunning to me that you refuse to get even the most basic understanding of how your resolution system actually works.

[erik]

GM says that the cliff has got a bit of an overhang, so the target number is three. Now you got all that fun climbing equipment, so you avoid that nasty penalty this time, your chance of a success is a bit lower than in the first example, but not by much, can't really bother to work out the actual percentage difference.

As other said, THIS is why you need to know the math, and why having a complicated system is not a good solution for you (and the math behind this can get much more complicated).

It does not just lower your chance of success a bit in that example.

The chance of getting doubles or better on 6d10 is 85%
The chance of getting triples or better on 6d10 is 16%

You just flopped your percentages basically from very likely to succeed to very likely to fail with that one change... and you thought it was only a tiny change.

This clearly is not intuitive, even for you who is supposed to be designing this game, so imagine how it will be to the gamers who do not have time to crunch a million scenarios in their head?

[edit: forgot to end a]

[Stormgale]

It's seriously stunning to me that you refuse to get even the most basic understanding of how your resolution system actually works.

Well at the most basic level it's a set of D10's matching we already know how those work, as that table has been posted at least twice

The main problem that has been brought up is that It is hard to have an exact statistical knowledge of a given die roll if more successes or target numbers are needed.

I think the argument then becomes A) Why does it matter (If you can easily state that a given roll A is harder or easier than a given roll B does the exact percentage matter, in the middle of a game of any type I have never seen a player give me an exact probability of their given chance of success))

But if we want to tackle this head on, sure:

Assuming 2d10 there are 10 possible matching sets out of a possible 100

Assuming 3d10 there are 280 possible matching sets out of a possible 1000

If we remove 1's from the equasion then you it becomes

2d10 = 10-1=9%

3d10 = 280/1000-(1*10+1*10+1*10+1)=280-31=251=25.1%

Both roughly a 10% loss in probability per value removed

Thus a 4d10 (must be at least a 5) is about as likely as getting a success on 3d10 (any available)

Apologies if my math is flawed I did do this in my head

Edit: hey erik can you break out the math on your above example, Im curious

[John Magnum]

Actually, I thought when he said "the target number is three" he meant "pairs of 1s and pairs of 2s don't count". Which has a smaller probability penalty in the specific example, but in the general would mean that he's bolting a dicepool system onto his dicematch system and creating a juddering abomination.

Which do you actually mean, Kemper?

[Kemper Boyd]

Actually, I thought when he said "the target number is three" he meant "pairs of 1s and pairs of 2s don't count". Which has a smaller probability penalty in the specific example, but in the general would mean that he's bolting a dicepool system onto his dicematch system and creating a juddering abomination.

Which do you actually mean, Kemper?

Exactly what you said here. Except that I don't see it as a juddering abomination, but you got it right.

[John Magnum]

It's not a HUGE deal if the players can't give good probabilistic estimates of their levels of success, although if a single subtle change can flip their probability of success from 80% to 20% then that actually is a huge fucking problem because you still want to have some basic idea that you're likely or unlikely to succeed. A success chance of 70% and a success chance of 0% are both smaller than a chance of 80%. If you can't tell which of the first two your applied modifier produces, it seriously fucking isn't enough to go "Well this lowers your chance of success."

It's a bigger deal if the MCs don't have access to good probability information. They're the ones deciding how difficult tasks are, so they need to be able to make informed choices about the effect of any given penalty or bonus. If you're an MC who wants to make a challenge that the party wizard has a 30%ish chance of succeeding, how do you do that? The Kemper Boyd Solution is "keep turning knobs and pulling levers on my giant black box until playtesters shrug and say they're happy."

It's an ENORMOUS deal if the designer has no clue whatsoever about how the various knobs and levers of his resolution mechanic affect probability of success. This is fundamental information that needs to be used when writing character ability, determining character progression, writing MC advice, and basically every aspect of the content. If you don't have this information, then the dice mechanic isn't just a black box to the players and MC, but the designer, which means that the entirety of the system's mechanics are just random guessing that will be randomly tweaked until he accidentally shits out a satisfactory playtest.

Incidentally, by now the idea that dicematch systems ever have intuitiveish probabilities should be thoroughly debunked because so much shitty math has been flung around.

[erik]

Well at the most basic level it's a set of D10's matching we already know how those work, as that table has been posted at least twice

*sigh*
I brought up that table because he didn't even know that much.

I think the argument then becomes A) Why does it matter (If you can easily state that a given roll A is harder or easier than a given roll B does the exact percentage matter, in the middle of a game of any type I have never seen a player give me an exact probability of their given chance of success))

Because if the players and game designers don't know how much harder you are making a challenge, then by what basis do you make it harder?

Kemper thought that making a little change from needing 3 dice instead of 2 was only a small shift, when in fact it was a huge shift in his scenario.

A player might not need to know the exact probability, but here a supposed expert player cannot even intuit a remotely accurate general possibility.

At this moment I cannot provide the calculations for the 6d10's. I just got my 1 year old up and am gettin him breakfast/ready for the day. For ease of use I just went once again to wolfram alpha and tallied the percentages of 3 matches on up. I'm pretty certain I could do it given time, but I've been taking the easy way on math here since I am provided a tool that can assist me.


[edit: AH! I thought we were talking target number of 3 matches. Going from needing to match doubles on 3+ is a less significant change certainly. I think the math on that is just take 80% your 85% to give you 68% which is closer to his expectations.]

[edit 2: gah, doing math is harder with a 1 year old eating an eggo in your lap. I somehow lapsed into thinking I was dealing with d20s. fixed math in my above edit.]

[John Magnum]

Did we ever get a definitive answer to how triples are counted? To me, if you get dice A, B, and C all turning up the same, that's three matches since A-B is a match, A-C is a match, and B-C is a match. That method is probably the easiest to figure the probabilities for, because seriously one of your basic most fundamental tools is "Given that I'm rolling X die, what is the expected number of matches I will get?" because if you can't answer that then your system is broken so hard that I can't even comprehend it. We haven't actually answered that question.

If I roll 10d10, how many matches will I probably get? That's actually a lot more important to know than the probability of at least one match on Xd10 for X = 1..10. As a player, I'll probably end up with some fixed number of dice I'm tossing around, and the MC is adjusting difficulty by adjusting the number of successes required, right? For that to be even slightly meaningful to anyone, we need to know how many successes I'm likely to get, even just so the MC can decide if my odds of success are more or less than 50%. At this point, even that BARE MINIMUM level of control over the resolution mechanic has not been provided.

Anyway. Answering this question will probably be easier if you count triples as three matches, quadruples as 12 matches, and so forth, because I think that makes the combinatorics turn out nicer. Of course, that turns the actual counting of "how many successes did I get?" into a much harder task. You either tell your players to calculate the combinatorics in their head, or you provide a lookup chart of "Pair = 1 success, Triple = 3 successes, Quad = 12 successes, Quint = 60 successes, you're not getting six of a kind you cheating fuck" in which case stop being a doucher because when step 2a of "How do we actually tell how well I did on this roll?" is "LOOK UP TABLE 1-6" then your entire system is a nonstarter.

You MIGHT be able to come away with something that's SLIGHTLY VIABLE if you decided to make one match your fixed target number and fiddled with probabilities by adding bonus dice to the player pool and taking away penalty dice. As we saw earlier, this gives you a crappy distribution of possible odds of success, but it might be at least sort of functional.

The funny thing is, in the new "You need a match at least this high for it to count" system, the ONE lever on your resolution system's black box with a reasonably predictable behavior is the one that's actually just the standard dice pool "number of hits" mechanic. The only remotely successful bit of your entire mechanic is the part that isn't actually your mechanic at all, but Shadowrun's mechanic glued onto your crappy framework.

Incidentally, I HAVE tried to play a game of Cthulhutech and use the Framewerk resolution system, and it's painful. Even with a mere 5d6, the process of figuring out how good any given roll was is a lengthy operation. The probabilities are completely opaque to player and MC, and probably to the designers as well. It's a nightmare.

[erik]

Did we ever get a definitive answer to how triples are counted?

Three of a kind is three of a kind, four of a kind is four of a kind. How many of a kind you have tells you how well you do. In certain situations (I don't really feel like going into too much detail right now) rolling multiple matches of various numbers is good.

Triples are not treated as two potential pairings, just as one set. That's how it is in the One Roll Engine, which I'm pretty sure is being adhered to here. I don't think you ever break up sets of the same number (this goes out the window when you start adding dice with funky properties).

To return to Kemper's quote, if your amount or size of matches is relevant, and the MC is supposed to use this data in a meaningful manner, then ought they not know roughly how probable it is to get those multiple or larger matches? How can an MC meaningfully set a difficulty if both the MC and players don't know how hard something just became?

Oh, and god help us when we get to intuiting probabilities of multiple matches.

[edit: oh noes! I just realized my 80% of 85% is off because I forgot about taking into account multiple matches. Shit, we are already there.]

[John Magnum]

So four of a kind counts as four matches? I'm trying to wrap my head around the resolution mechanic. It goes "roll a big pile of dice, count the number of matches, the number of matches is your Number that gets compared to other shit", right? And so rolling 1 1 1 2 2 3 counts as...four matches? 1 1 1 1 2 2 counts as five?

Or is he saying that "three of a kind" is literally some additional category, where you separately count pairs, triples, quads, etc.? I don't know One Roll Engine, so just figuring out how to convert any given pile of dice into the number I rolled is tricky for me.

This is important to know. Kemper has made it sound like 10d10 isn't out the window, you might actually be rolling 10d10. Once you have that many dice, according to Wolfram it's actually more likely to get a triple or better than to get just pairs or worse.

[RadiantPhoenix]

So, just fyi, I think that counting the number and size (number of matching dice) of each match on XdY is still only an O(n) operation --

You just bin-sort X dice into Y piles based on what was rolled (X read operations, X move die operations), then count the size of each of the Y piles (Y count operations).

[erik]

So four of a kind counts as four matches? I'm trying to wrap my head around the resolution mechanic.

No no no.

Or is he saying that "three of a kind" is literally some additional category, where you separately count pairs, triples, quads, etc.?

Literally an additional category. But a three of a kind will do if all you needed is two of a kind. Basically having more dice means you do better? How much better you ask? Get out your tea party set. That's how much better!

Once you have [10] dice, according to Wolfram it's actually more likely to get a triple or better than to get just pairs or worse.

Indeed.

To digress a bit, I played a Wild Talents (which uses a matching d10 system with even more extra confounding variables mixed in!) session at Gencon one year where I think Greg Stolze or another high uppity actually ran the session. There was a podcast of it, but I won't bother tracking it down to provide the awful crowd with masturbatory material. The entire session nobody seemed to know what they were doing or even what they could do. It was total MTP with a black box that was referenced on occasion. Now, that's a lot like any time you play a new game I imagine so I cut it some slack back then.

[Username17]

ORE fiddles around with the following information:

• The number of dice in a single match
• The total number of matches
• The difference between the highest and lowest number
• The literal value of a match

Computing any of these is fucking awful, and the author doesn't seem to have bothered at any point in the creation of the game. Kemper here is probably doing the same.

I mean seriously, once you have matches of a certain type not count, things get really intractable. Remember that nice little "1-({9!/N!}/10^N)" equation? Yeah, forget that shit, because now you have alternate cases where numbers land in the "don't count" numbers and then don't reduce the chances of future dice coming up non-matching. Which means that you don't actually save any time subtracting out the chances of no matches.

So, just fyi, I think that counting the number and size (number of matching dice) of each match on XdY is still only an O(n) operation --

You just bin-sort X dice into Y piles based on what was rolled (X read operations, X move die operations), then count the size of each of the Y piles (Y count operations).

For piles of dice that are considerably smaller than a hundred, it's still faster to run comparisons, and that's O(n^2). Bucket sorting all the dice and then running ten counting operations is indeed O(n), but the linear operator is much bigger than running a simple compare. And by "much bigger" I mean like ten times bigger. So if you have ten dice or less, it's still going to take you less than half the time. Of course, if you had enough dice, the compare function is O(n^2) and it will eventually take longer than a ten flavor bucket sort, but it's not relevant to the available dice range of 2-10 dice.

-Username17

[TheFlatline]

Did we ever get a definitive answer to how triples are counted? To me, if you get dice A, B, and C all turning up the same, that's three matches since A-B is a match, A-C is a match, and B-C is a match. That method is probably the easiest to figure the probabilities for, because seriously one of your basic most fundamental tools is "Given that I'm rolling X die, what is the expected number of matches I will get?" because if you can't answer that then your system is broken so hard that I can't even comprehend it. We haven't actually answered that question.

If I roll 10d10, how many matches will I probably get? That's actually a lot more important to know than the probability of at least one match on Xd10 for X = 1..10. As a player, I'll probably end up with some fixed number of dice I'm tossing around, and the MC is adjusting difficulty by adjusting the number of successes required, right? For that to be even slightly meaningful to anyone, we need to know how many successes I'm likely to get, even just so the MC can decide if my odds of success are more or less than 50%. At this point, even that BARE MINIMUM level of control over the resolution mechanic has not been provided.

Anyway. Answering this question will probably be easier if you count triples as three matches, quadruples as 12 matches, and so forth, because I think that makes the combinatorics turn out nicer. Of course, that turns the actual counting of "how many successes did I get?" into a much harder task. You either tell your players to calculate the combinatorics in their head, or you provide a lookup chart of "Pair = 1 success, Triple = 3 successes, Quad = 12 successes, Quint = 60 successes, you're not getting six of a kind you cheating fuck" in which case stop being a doucher because when step 2a of "How do we actually tell how well I did on this roll?" is "LOOK UP TABLE 1-6" then your entire system is a nonstarter.

You MIGHT be able to come away with something that's SLIGHTLY VIABLE if you decided to make one match your fixed target number and fiddled with probabilities by adding bonus dice to the player pool and taking away penalty dice. As we saw earlier, this gives you a crappy distribution of possible odds of success, but it might be at least sort of functional.

The funny thing is, in the new "You need a match at least this high for it to count" system, the ONE lever on your resolution system's black box with a reasonably predictable behavior is the one that's actually just the standard dice pool "number of hits" mechanic. The only remotely successful bit of your entire mechanic is the part that isn't actually your mechanic at all, but Shadowrun's mechanic glued onto your crappy framework.

Incidentally, I HAVE tried to play a game of Cthulhutech and use the Framewerk resolution system, and it's painful. Even with a mere 5d6, the process of figuring out how good any given roll was is a lengthy operation. The probabilities are completely opaque to player and MC, and probably to the designers as well. It's a nightmare.

Let's get even better. Let's say I roll two 6's, three 4's, and two 8's. How many "successes" do I get from that result? Do I get one three of a kind? Three pair? Is only the best portion of the roll counted, like hold 'em poker?

[PoliteNewb]

I can answer that, at least as far as the ORE system in Godlike worked.

A match of high numbers (the two 8's) is considered a "tall" set. This indicates a high level of success (better than the two 6's). So if you were doing something that required you to do really well, or you wanted to do your best work, you would take the 8's.

A large match (the three 4's) is considered a "wide" set. This indicates a higher degree of speed. So if you didn't care how good the job was, just that it got done faster, you would take the 4's.

Keep in mind that if the task is, say, running a race, you would want the wide set! Even though "beating the other guy" is what most people would consider "a high degree of success", they take it to mean "running without passing out from exhaustion", and the width determines speed. This is seriously an example in the book.

Speed of task resolution is never more granular than vague units...rounds, minutes, hours, days.

And to make it even more confusing, in combat you completely ignore the "height determines success level" rule, because raw damage is based off of width (height determines hit location).

As for having multiple sets (like in the example), that allows you to do multiple things at the same time. So you could assign your three 4's to punching a guy, your two 8's to dodging, and your two 6's to some other damn thing.

I have no idea how KB's system compares to this, because he won't fucking tell us.

[erik]

[edit while posting: ah, cool. PoliteNewb ninja'd me on explaining the height/width rolls and probably did a better job. duh-leted!]

I found a site where a guy went through a lot of the work plotting out probabilities for width (specific number of dice that match) and height (specific number on die). Note that this guy apparently has more than basic math know-how and he wanted to do this because he couldn't intuit it. Also note, his analysis does not even touch on the more complicated crap like the die types Frank mentioned, nor cases where height and width matter.

And it certainly doesn't address stuff like backlash dice. Honestly those backlash dice are the worst feature of your adaptation of this system, Kemper. As written, they make it so that for anyone who attempts that task being better makes you do worse in a very dramatic fashion. Which should at the very least it should be toned down some if not reversed all-together.

I know that in Deadlands the Huckster spellcasters cast hexes by drawing cards to make a poker hand, and the stronger casters can draw more cards increasing chances to cast a more powerful spell, but also the more likely you are to draw a black joker which will give you backlash. Similar enough in that better casters have a greater chance of betting backlash, except some key differences.

There is not nearly the disincentive in probability of that backlash since at most you are probably drawing an 8 card hand with a 15% chance of backlash, as opposed to Lion's... damn I don't even know how likely it is since the math is more complicated but it's way worse than 15%. And then the severity of backlash is not as dire- most make the hex fail and are temporarily inconvenient, some rare ones are permanent inconveniences and/or really bad. Death by backlash requires some seriously bad luck piled higher and deeper. And the more skilled hucksters generally take an ability to stop drawing cards if they wish, which cuts down on your backlash odds.

If backlash were worse in Deadlands either in frequency or severity, then it would basically be a trap option and only soon-to-be-unhappy players would ever invest in using hexes (which is a large character building investment on top of it all)... which is basically what you have proposed so far as I can tell.

[Leress]

So if Kemp wanted to keep the backlash it should be tie to getting multiple 1s with the more 1s the more severe?

[PoliteNewb]

So if Kemp wanted to keep the backlash it should be tie to getting multiple 1s with the more 1s the more severe?

That would be significantly less horrible, yes. But it would also require a change to the mechanic, because as it stands right now, multiple 1's are a match, thus success.

[erik]

If it was set to something like Difficulty above 1, and all the 1's rolled were backlash dice that would be better than all unmatched dice, I'd think.

Still, your chance at getting five 1's on a 10d10 is about 0.15%, but if there are other ways to mitigate backlash a bit, as he implied, then that's not the end of the world. If you're really consistently tempt fate attempting something with a higher difficulty, then you can get smacked down hard, which I think is what he wants to go for.

Using your method suggested, spellcasting is still hella-hard to do effectively without generating some backlash, but it isn't nearly guaranteed. Nor does this method punish you for being proficient at your craft and reward you for being really bad at it.

[edit: 0.15%, not 1.5% Oy!]

[Avoraciopoctules]

If it was set to something like Difficulty above 1, and all the 1's rolled were backlash dice that would be better than all unmatched dice, I'd think.

Still, your chance at getting five 1's on a 10d10 is about 0.15%, but if there are other ways to mitigate backlash a bit, as he implied, then that's not the end of the world. If you're really consistently tempt fate attempting something with a higher difficulty, then you can get smacked down hard, which I think is what he wants to go for.

Using your method suggested, spellcasting is still hella-hard to do effectively without generating some backlash, but it isn't nearly guaranteed. Nor does this method punish you for being proficient at your craft and reward you for being really bad at it.

[edit: 0.15%, not 1.5% Oy!]

Sounds decent to me. Definitely an improvement.

[Milkmaid79]

I realize this thread is ancient but I found a quote from Greg Stolze that proves what several posters mentioned. He didn't do any sort of math in coming up with his One Roll Engine- he designed it by 'instinct'. His was the last message in the thread.

http://forum.rpg.net/showthread.php?381 ... babilities