I´m wondering about succes-probabilities with a "roll high under" mechanic. I believe this is common in late BRP-systems.
Let´s say the attacker rolls to hit, and the defender rolls to parry. If both make their rolls (roll a number under or equal to their skill%)
then the one who rolled the highest number wins (if the attacker then he hits, if the defender then he managed to parry).
Not bothering with critacals/special hits, I´d like to know the probabilities for the outcome (hit, parry, miss) with different skill% for attacker and defender.
If there´s a chart like that somewhere I´d like to find it.
The skill-levels doesn´t have to be %, 1-20 of course works just as well.
Any help would be appreciated.

I understand the mechanic you describe; but if the goal is to roll equal to or under, I think lower should always be better.

There, now the world is a better place...

Quote from: Razor 007;1114295I understand the mechanic you describe; but if the goal is to roll equal to or under, I think lower should always be better.

There, now the world is a better place...

I´ve been thinking in the same line myself, which is part of why I posted the question. I would think that if the system is´nt broken, then "high wins" means that theres is a better probability for the higher skill to win. If you get my point - I realise that my english isn´t good.
I just cant bother to calculate the math for this. The only way I know how to is by putting up a chart for all possibilities, and that would take forever.
I was hoping that someone had already caculated this, or knew an easier way.

Ok, let's assume that the attacker's skill A is higher than the defender's skill D. The attacker will miss if he rolls higher than A. If the attacker rolls lower than A but higher than D, then he hits regardless of the defender's roll. If both the attacker and the defender roll less than the D, then it's a 50/50 chance that either will win.

So, the attacker chance to miss is equal to 100-A + (A * 1/2 of D). If the skills are A=60 and D=40, then the attacker will miss 100-60 (40%) plus 60% * 1/2 of D (20%) so the attacker will miss 100% -40% - 12% or 52% of the time.

If the defender's skill is higher than the attackers it's a bit more complicated because parrying a miss has no effect, the attacker's chance to miss is equal to 100-A [A straight miss] plus the chance of parry which is A * ((D - A) + 1/2 A). If A=40% and D=60% you end up with the chance to miss as 100-A (60%)  plus 40% * ((60%-40%) + 1/2 40%)) or 60% + 40% * (20% + 20%) or 60% + (40% * 40%). So he'll miss 76% of the time.

Quote from: Razor 007;1114295I understand the mechanic you describe; but if the goal is to roll equal to or under, I think lower should always be better.

There, now the world is a better place...

I'm not a fan of "roll under" systems, but something I like even less is "roll under, the lower the better". That kind of mechanic tends to weirdly favor low abilities, cuz the lower your ability, the lower you have to roll to succeed. And since Low = Better that means with low abilities your success rate might be low, but every time you succeed you hit the ball right out of the park--which makes zero sense for someone with low abilities. That's why "Roll Under, the higher the better" is more sensible.

As for the OP's question, I've never run into anything like that. It's kind of a weird mechanic to measure probabilities for, since you have to account for each opponent's success rate, then pin it against each other.

Quote from: VisionStorm;1114316I'm not a fan of "roll under" systems, but something I like even less is "roll under, the lower the better". That kind of mechanic tends to weirdly favor low abilities, cuz the lower your ability, the lower you have to roll to succeed. And since Low = Better that means with low abilities your success rate might be low, but every time you succeed you hit the ball right out of the park--which makes zero sense for someone with low abilities. That's why "Roll Under, the higher the better" is more sensible.

I don't necessarily disagree with your sensibilities here (that is how Heroquest Glorantha works), but there is also the GURPS option of comparing Margin of Success i.e. my skill is 17 and I roll an 11, success by 6, you have a skill of 12 and roll an 11, success by one (I win); so it shakes out that lower is better. Crit ranges also shift with skill, and below a skill value of 3 you simply auto-fail.

I personally prefer the feel of roll-under in general, but that's neither here nor there... :cool:

I think the idea of opposed roll--with one nullifying the other as a binary outcome--is not best expressed in such a roll under percentage system.  Let's say that you do the math.  What it essentially means is that we've still got a binary, pass/fail outcome, but the higher the defender's ability the lower the chance of success.  Look at the extremes:  Attacker 100%, defender 0%.  Attacker has 100% chance.  Whereas, if both are at 100%, then it's who rolls the highest, which means Attacker has a 50% chance (maybe give or take 1% depending upon how you handle ties).  You could go to Anydice.com, generate a spreadsheet with the possibilities, and study the curve generated.  I doubt it will be very interesting, since essentially as a defender's ability increases the attackers chances go down.  You don't need opposed d100% rolls to do that.  

To see, what you might try is map it out as if the system will use a d10, but otherwise work the same way.  That's easy to do even without the math, and will give you a similar curve (albeit with bigger jumps).

This might be a more interesting system if it isn't attacker/defender, but an exchange where the higher roll within skill becomes the "attacker" for that round.

Or you could do what I'm trying to develop, which is both attacker and defender are rolling, with "effect" generated on success (that is, not binary outcomes, since it is possible for a defense to be partially successful or an attack to accomplish nothing directly, but set up another attacker to succeed).  It is funny, because I generally do not enjoy roll under systems of any type (having an irrational prejudice against them), but was more or less forced into using one for my design due to various reasons (likely not relevant to this discussion).

Quote from: Antiquation!;1114317I don't necessarily disagree with your sensibilities here (that is how Heroquest Glorantha works), but there is also the GURPS option of comparing Margin of Success i.e. my skill is 17 and I roll an 11, success by 6, you have a skill of 12 and roll an 11, success by one (I win); so it shakes out that lower is better. Crit ranges also shift with skill, and below a skill value of 3 you simply auto-fail.

I personally prefer the feel of roll-under in general, but that's neither here nor there... :cool:

Oh, yeah. Going by Margins of Success is definitely another way to do it. Since it skews things in favor of the opponent with the highest ability, which is what a simple "Roll Under; lower is better" fails to do. That's really the main issue with that mechanic. I think going by Degree of Success might also work as well, which is how Alternity did it, since higher abilities still have a better chance of scoring high success than lower abilities. Though, in Alternity you still had the issue of "lower is better" (to an extent), but it was mitigated by adding Degrees of Success into the mix.

The issue with "roll under" systems is that they complicate opposed rolls and tend to favor high Attributes/Ability Scores above actual skill (which is the opposite of real life)--specially in old D&D, where you could get a 90% success rate just by getting lucky during character creation and scoring an 18.

In my own book the system was roll =/<. It works in stages. The attacker had to actually hit. So say they hit on a 50% or less then a roll of 47 hits, 51 misses. The defender had the option to either evade with agility or deflect with armour. Same system. Roll =/<. Applicable skills, stats or gear actually add a negative modifier to the rolls. -1 for every 5 points over 50. The modifier also acted as a sort of passive threshold. So that roll of 47 to hit vs someone with a passive armour or dodge mod of 5 would be a hit still, but half damage for example.

The whole system was like that as to me it was easier to gauge probabilities. Modifiers and Thresholds simply slide the % chance of success/fail up or down. I just applied the modifiers in reverse to get a probability if needed. So the 50-5/threshold5 roll equated to a 55% chance of success, 5% chance to only ping because you hit on a roll of 55 or less and any roll of 51-55 pinged.

Probability 'windows' might be viewed much the same. YMMV on that.

Quote from: zx81;1114309I´ve been thinking in the same line myself, which is part of why I posted the question. I would think that if the system is´nt broken, then "high wins" means that theres is a better probability for the higher skill to win. If you get my point - I realise that my english isn´t good.
I just cant bother to calculate the math for this. The only way I know how to is by putting up a chart for all possibilities, and that would take forever.
I was hoping that someone had already caculated this, or knew an easier way.

If by "later BRP" you mean CoC 7E, you don't really need to calculate the probabilities, the higher skill will always be harder to defend against. You'll notice on the sheet that each skill has two lower numbers next to the base level, representing the chance of a "hard" success for the number that is half your base skill, and an extreme success that is 1/5 your base skill. Once the numbers are rolled, the degree of success is what is compared, not the actual number rolled.

To Fight Back/Parry, you have to beat their level of success. you can't Fight Back against an extreme success as you can't roll better than that. To Dodge, you have to equal the level of success.

So for example the attacker with an 80% (80/40/16) Brawling goes up against a defender with 50% Brawling (50/25/10). The attacker rolls a 39 (hard success) and the defender rolls a 11 when trying to Fight Back (hard success), and fails to defend himself, even though he made a much better roll.

Quote from: VisionStorm;1114316I'm not a fan of "roll under" systems, but something I like even less is "roll under, the lower the better". That kind of mechanic tends to weirdly favor low abilities, cuz the lower your ability, the lower you have to roll to succeed. And since Low = Better that means with low abilities your success rate might be low, but every time you succeed you hit the ball right out of the park--which makes zero sense for someone with low abilities. That's why "Roll Under, the higher the better" is more sensible.

As for the OP's question, I've never run into anything like that. It's kind of a weird mechanic to measure probabilities for, since you have to account for each opponent's success rate, then pin it against each other.

Lots of people love d20 Roll High; and the higher the result, the better.  But then, Ability Scores Modifiers are added....  With d20 Roll Under, you don't need to bother with Modifiers.  The higher your score is, the easier it is to roll under.  It's simple.  You don't have to consider opposing rolls for everything.  A failed roll can encompass all types of failures / misses.

Quote from: Razor 007;1114377Lots of people love d20 Roll High; and the higher the result, the better.  But then, Ability Scores Modifiers are added....  With d20 Roll Under, you don't need to bother with Modifiers.  The higher your score is, the easier it is to roll under.  It's simple.  You don't have to consider opposing rolls for everything.  A failed roll can encompass all types of failures / misses.

Adding a modifier is not exactly a Herculean task either. It's not like you're calculating THAC0 or anything. And unlike Roll Under without opposed rolls, using Roll+Mod as a core mechanic can (easily) handle 100% Every. Single. Possible ability related roll that could ever come up in a TTRPG without exception whatsoever.

Skill checks, Combat (which is essentially a type of skill), Defenses (basically a type of opposed skill), Perception/ Detection/ "Listen" rolls (also opposed skill if used to detect someone's actions), Resistances/ "Saving Throws" (more opposed skills), application of force (i.e. bend bars/lift gates and break doors in older D&D), etc. And all without having to resort to specialized mechanics for every tiny thing that's not an unopposed skill roll (at least if we use OD&D as a benchmark).

Additionally, going with D&D at least (this may vary with other systems), Roll Under can be heavily reliant on having high Ability Scores (which in OD&D never improve, except via Wish spell) just to have a decent chance of success at anything. Yet conversely, if you have really high ability scores you get inflated chances to succeed at everything.

An OD&D character with a 18 score has a whopping 90% chance to succeed at anything tied to that score (assuming an unpenalized roll, representing average difficulty). Conversely that same character would get a +4 bonus in D&D 3e+, which translates as a 70% chance against DC 10 (average difficulty). Which is not as high for an untrained ability and still leaves more room for growth.

TL;DR/Conclusion: Roll Under is more simple as long as you're willing to deal with its flaws and limitations. But the moment you want it to do more than simple Knowledge checks or similar ability checks that can be rolled unopposed its simplicity starts breaking apart. And it tends to rely too much on high Attributes/Ability Scores over actual training, which undermines skills and assumes natural ability as the overriding factor to perform all actions.

I haven´t got time to read all the answers before going to work, but I´ll try to be clearer:
I just want to see the probabilities for the roll-under-mechanic, so that I can compare it to the system we´re using now.
We´re playing a version of BRP closer to the one from the Worlds of Wonder-box (and, I believe, early Stormbringer and CoC).

Quote from: Razor 007;1114377Lots of people love d20 Roll High; and the higher the result, the better.  But then, Ability Scores Modifiers are added....  With d20 Roll Under, you don't need to bother with Modifiers.  The higher your score is, the easier it is to roll under.  It's simple.  You don't have to consider opposing rolls for everything.  A failed roll can encompass all types of failures / misses.

pre 3e D&D had a roll under mechanic for things like stat checks. And Roll under in absolutely no way eliminates modifiers.

Quote from: zx81;1114391I haven´t got time to read all the answers before going to work, but I´ll try to be clearer:
I just want to see the probabilities for the roll-under-mechanic, so that I can compare it to the system we´re using now.
We´re playing a version of BRP closer to the one from the Worlds of Wonder-box (and, I believe, early Stormbringer and CoC).

What sort of dice are being used? Same as in BRP or something else?