Oppsed Rolls-Roll low

[Mister Apocalypse]

Long ago I asked about the merits of low roll wins in opposed resolution rather than high roll wins. The conventional wisdom has it that low roll wins is overly biased towards the lower skilled character.

I did up a spreadsheet that does the math and gives the percentages of character A or B winning an opposed roll, and the math behind low roll wins, isn't nearly as biased as conventional wisdom. Yes, the lower skilled character's chances of success improves, but where or not this is an unfair bias remains to be seen.

For the spreadsheet, I defined the conditions of the contest as follows:

Character A: the lower skilled character's skill%

Character B: The higher skilled character's skill%

Condition 1: Both Succeed [%=AxB]

Condition 2: A succeeds, B fails [%=Ax(1-]

Condition 3: A fails, B succeeds [%=Bx(1-A)]

Condition 4: Both fail [%=(1-A)x(1-]

Ignoring critical,special successes, and fumbles (the inclusion of which would favor we wind up with:

A winning condition 2, B winning condition 3, both splitting condition 4.

The only difference between roll low and roll high is in condition 1 (both succeed).

We can break down codition 1 into:

Condition 1a: the cases where both players roll under A%, where the odds are even [%=AxA]

Condition 1b: the contested region, where both succeed but B rolls higher than A. [%=AxB-(AxA)]

So since we are ignoring specials, both players would split Condition 1a, and the only difference between the two methods is with Condition 1b.

In a nutshell, the difference between roll low and roll high is in who win during condition 1b. With roll low, A wins, while with roll high B wins.

Here are some results at various skill ratings for A and B to show the differences between the two methods:

1) A: 10%, B:90%

Low Wins: 14%/86%

High Wins: 6%/94%

2) A: 40%, B: 80%

Low Wins: 38%/62%

High Wins: 22%/78%

3) A: 20%, B: 50%

Low Wins: 38%/62%

High Wins: 32%/68%

4) A; 30%, B: 70%

Low Wins: 36%/64%

High Wins: 24%/76%

5) A: 40%, B: 50%

Low Wins: 47%/53%

High Wins: 43%/57%

Now in theory the breakdowns for opposed rolls should probably match up to the relative % in skills. That is if B is twice as good as A, he should with twice as many contents, (for a 33%/67% breakdown). Likewise a case where one character has a slight edge (40 vs 50) should result in a slight advantage (44%/56% breakdown)

According to the results, roll low is closer to that result, and roll high is unfairly biased towards the character with the higher skill.

Once you start to factor in for criticals, special successes and fumbles, the odds will shift even further towards B, with B's superior special and fumble range, giving B significant more wins during cases where both contestants succeed or both fail.

For roll low, this just about sets things to right, but for roll high, it heavily biases the results towards the higher skilled character. For example, in the A: 10, B:90 scenario A will win practically none of the cases where both succeed or both fail, as B's special success range overlaps As win range (so A must roll and 01) and A's fumble range costs him most of the both failed cases. As a result with roll high, A:10, B:90 comes out with A having a less than 5% chance of winning.

So, if anything roll high is unfairly biased, not roll low.

[Pete Nash]

So, if anything roll high is unfairly biased, not roll low.

I think it all comes down to personal interpretation of how much the % reflects the actual skill or capability. As the system stands a 20% skill difference represents a major increase in competence.

I prefer roll high, with the increased bias, because if using the suggested Skill Ratings a neophyte should realistically have no chance of overcoming a master, and an amateur should be regularly overcome by a professional. I also find it helps me predict the outcome of a challenge better, rolling high giving a more consistent result. But that's just my preference and I don't have any conceptual difficulties with roll high/differing levels of success.

[Atgxtg]

I think it all comes down to personal interpretation of how much the % reflects the actual skill or capability. As the system stands a 20% skill difference represents a major increase in competence. I prefer roll high, with the increased bias, because if using the suggested Skill Ratings a neophyte should realistically have no chance of overcoming a master, and an amateur should be regularly overcome by a professional.

That will happen either low roll as well. Looking at roll roll for neophyte vs master a 14% (before criticals, etc.) is hardly much of a chance. After crticals, it drops down under 5%. As far as amatuer vs. professional goes, it would depend on how you rate them skill wise. I've seen a couple amateur programmers code circles around a professional software engineer.

I also find it helps me predict the outcome of a challenge better, rolling high giving a more consistent result.

I don't follow you here. Mathematically either result is "consistent". If you mean that roll high throws the contest to the higher skilled character-yes it does. Nut if that is what you want, you don't need to roll for it.

It also skews the combat system. Only the current incarnation of BRP uses opposed rolls for combat. Not ever MRQ does so. I think it is bad to use opposed rolls for everything except combat. I think the same basic method should be used for all task rolls in the game.

But using opposed rolls in combat would take a lot of the fun out of the game. A slight edge in skill would be an almost insurmountable obstacle.

Especially in conflicts that last more than one roll.

But that's just my preference and I don't have any conceptual difficulties with roll high/differing levels of success.

Either method will "work" mathematically. That is either method will give a result (barring the occasional tie). I think that the roll high method is too skewed and goes against the initial core system.

However, my point is that the math does disprove the belief that "low roll wins" is too biased towards the lesser skilled character. The difference between the too is never more than 20%, and usually much, much less.

[Mugen]

I know that, mathetically speaking, roll low is interesting. But yet, the method doesn't sound right to me.

I don't like the idea that if A (the character with the highest skill) 's roll falls between B's skill and his own skill and B succeeds at his skill roll, advantage is given to B.

I mean, the range between both skills reflects A's better mastery of the situation, and in such a case it sounds like a disadvantage to him : if he succeeded because of the things he knows and B doesn't, the final word is given to B.

Note that I do know that A still has a better chance of success than B, even with roll low. It's only a psychological point of view...

[Atgxtg]

But consider the psychological impact of an opposed roll increasing a character's chance of success!

With the high roll wins method that's what happens. For example a character with a 90% skill has a better chance of succeeding against a low skilled (27% or less) opponent than if the roll were unopposed.

And keep in mind the chances of both characters making the roll, but B rolling higher than A's success chance is very slim.

I don't like the idea that with roll high, B at 90% could put in a lackluster 89 roll and beat A's fairly decent roll of 06.

By the way things have worked for BRP up 'til MRQ/now, the idea was that would have barely made the roll where as A roll was a solid success. High wins flies contrary to the way criticals and fumbled work too. For a character with 90% skill it means rolling a 90 is better than a 19, but an 18 is better than a 90!

[RosenMcStern]

So, if anything roll high is unfairly biased, not roll low.

I fail to see how this should be unfair. The high skill character is supposed to have the upper hand, after all. Favouring the better one is realistic, not unfair.

[RosenMcStern]

I've seen a couple amateur programmers code circles around a professional software engineer.

Hackers are all amateurs, and it is well known that they code better than professional programmers.

Only the current incarnation of BRP uses opposed rolls for combat. Not ever MRQ does so.

Er, Loz and Pete have not stressed this fact so far to avoid premature complaints, but in fact MRQ2 has a combat system that is very similar to BRP - with the addition of manoeuvers and a couple of other touches of genius.

The point is that there are two kinds of 'opposed rolls': the one that only checks if you have different levels of success and considers all equal levels of success as ties, and the one that looks for a winner even in case both contestants achieve the same level of success. BRP uses the first method for everything, including combat, with the second method as an option if you like - but an option that cannot be applied to combat. Note that a tie here means that the defender wins - either he was not hit, or he parried.

Pendragon and HeroQuest use the second approach. Contestants never tie there, unless they roll the same number.

MRQ1 had serious existential doubts about whether it wanted to use method one or method two. MRQ2 has grown up and chooses option 1, at least for combat.

[Pete Nash]

That will happen either low roll as well. Looking at roll roll for neophyte vs master a 14% (before criticals, etc.) is hardly much of a chance. After crticals, it drops down under 5%. As far as amatuer vs. professional goes, it would depend on how you rate them skill wise. I've seen a couple amateur programmers code circles around a professional software engineer.

Yes, but it happens less for roll high. As for amateurs beating professionals, that should be the exception, not the rule.

I don't follow you here. Mathematically either result is "consistent". If you mean that roll high throws the contest to the higher skilled character-yes it does. Nut if that is what you want, you don't need to roll for it.

Ah, what I meant was that the result is more predictable. Don't get me wrong, I still like some randomness... I just like to see a decent advantage for having a higher skill.

Either method will "work" mathematically. That is either method will give a result (barring the occasional tie). I think that the roll high method is too skewed and goes against the initial core system.

Whereas I prefer it to be more skewed as it gives more value to each percentage point of the higher skill. It suits my interpretation of skill values in the real world.

As Paolo implicates, its not a question of fairness - merely a question of how biased you want the probability outcome to be. :thumb:

[pulpcitizen]

Stepping aside from 'bias' and 'fairness' for a moment, I prefer the high roll for two reasons:

1. the perception it creates.

2. that it doesn't compound (possible) special or critical successes.

[Atgxtg]

Leon,

you're actually bumping an old thread, with much missing but...

1. What perception are you talking about?

2. It doesn't compund the specials and critcs. That's part of the problem. It adds a low wins/high wins element.

[pulpcitizen]

Leon,

you're actually bumping an old thread, with much missing but...

1. What perception are you talking about?

2. It doesn't compund the specials and critcs. That's part of the problem. It adds a low wins/high wins element.

Sorry - I am still coming to terms with the changes the board has undergone. :shocked:

1. The perception that I mention is not in mechanics, but in personal perception (ie my own). Whilst I am comfortable with the low success roll often meaning special or critical success, a high-roll success for opposed rolls creates an illusion (and I know it is an illusion really) for me of reward for the more skilled participant; which is something I agree with.

2. I feel low-roll compounds the benefits of special and criticals to a degree, in that in terms of low rolling you veer towards the range at which they come into effect.

[Atgxtg]

Sorry - I am still coming to terms with the changes the board has undergone. :shocked:

1. The perception that I mention is not in mechanics, but in personal perception (ie my own). Whilst I am comfortable with the low success roll often meaning special or critical success, a high-roll success for opposed rolls creates an illusion (and I know it is an illusion really) for me of reward for the more skilled participant; which is something I agree with.

Well, at least you know it is an illusion. It's your game an your choice.

2. I feel low-roll compounds the benefits of special and criticals to a degree, in that in terms of low rolling you veer towards the range at which they come into effect.