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Opposed Rolls and Success Levels


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... I got a lot of complaints about BRP's convoluted "roll low, lower is better unless its contested, then higher is better if you are both within the same success level". All my players hated it and it was a big barrier towards getting them to accept BRP.

Which is one of the main reasons I have no truck with the blackjack method, and simply use: roll under, roll low - if success levels are tied and we still need to distinguish who did better, I use the margin by which you rolled under to determines who did better. Mathematically it's identical to black jack's (highest roll under skill) but maintains the consistency of BRP basic dice paradigm (roll under, roll low). And it comes up so rarely, and even then it's incredibly rare to need to ACTUALLY do the (trivial amount) of maths involved that I've never found a group that find it hard work. And I cannot say the same for the black jack method, which I have seen several times frustrate / annoy some players to the point of them switching system / mechanic at the first opportunity...

Cheers,

Nick

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Rather than using die roll as a proxy for higher skill on a tie, why not use higher skill wins on a tie?

Well the answer is that it is pretty brutal.

It is a system I have used for a while (largely because of the newbie unfriendly nature of the blackjack and levels and success hybrid as outlined by others) and like but it is unforgiving.

i.e. I face off against the weirwolf in a sprint.

With my measly 10percent skill I have some small chance of rolling a critical to get the perfect start, whilst he traps his fingers on the wheel rim (fumble). However if we both race our best race ever (critical) or both seasons best (special) or a good performance (success) then he will whup me.

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Rather than using die roll as a proxy for higher skill on a tie, why not use higher skill wins on a tie?

Well the answer is that it is pretty brutal.

I like it. No calculations, just result.

I would add though, that a special success beats success, and critical beats special success, in a tie.

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I like it. No calculations, just result.

I would add though, that a special success beats success, and critical beats special success, in a tie.

Yes absolutely. Sorry I wasn't clear. A tie is the same level of success.

I.e. crit beats spec beats success beats fail and highest skill wins a tied level of success

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Rather than using die roll as a proxy for higher skill on a tie, why not use higher skill wins on a tie?

Well the answer is that it is pretty brutal.

And horribly unfair. A guy with a 90 skill looses to a guy with a 91 skill more often that a guy with 05% skill loses to a guy with 25% skill!

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Naw, you could still have success levels.

If I had a skill of 70%, a special success would occur on a roll of 56-69. A roll of 70 = critical.

I like the table, but wish you kept the skill based crits as opposed to the 1% crits.

BTW, how do you handle skills over 100%?

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Which is one of the main reasons I have no truck with the blackjack method, and simply use: roll under, roll low - if success levels are tied and we still need to distinguish who did better, I use the margin by which you rolled under to determines who did better. Mathematically it's identical to black jack's (highest roll under skill) but maintains the consistency of BRP basic dice paradigm (roll under, roll low). And it comes up so rarely, and even then it's incredibly rare to need to ACTUALLY do the (trivial amount) of maths involved that I've never found a group that find it hard work. And I cannot say the same for the black jack method, which I have seen several times frustrate / annoy some players to the point of them switching system / mechanic at the first opportunity...

Sounds good.

I've been thinking of using multipliers of the skill chance, which amounts to about the same thing.

Cheers,

Nick

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And horribly unfair. A guy with a 90 skill looses to a guy with a 91 skill more often that a guy with 05% skill loses to a guy with 25% skill!

Brutal in enforcing 'better guy wins more of the time' certainly and I've liked the way its worked for a long time but ........ the whole point of fora is to pick other people's brains so: you've obviously spotted/internalised a statistical or mathematical artefact here would you be kind enough to talk me through it (slowly and patiently since its obviously jumped out at you fairly immediately so it must seem pretty darned obvious to yourself)?

Ta

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Brutal in enforcing 'better guy wins more of the time' certainly and I've liked the way its worked for a long time but ........ the whole point of fora is to pick other people's brains so: you've obviously spotted/internalised a statistical or mathematical artefact here would you be kind enough to talk me through it (slowly and patiently since its obviously jumped out at you fairly immediately so it must seem pretty darned obvious to yourself)?

Ta

Sure. First off it's not "better guy wins more of the time" but that the "better guy wins nearly all the time" - a slight edge in skill (as low as 1%) has a overwhelming impact on the outcome.

My example of 90% cs. 91% works as follows:

Both roll the same success level 62.73% (.05x.05+.13*.13+.77*.78+.09*.08+01*01) of the time. So the majority of cases are ties, and automatically given to the 91% guy. The remaining 37.27% is almost, but not quite an even split, so the total breakdown is about 19%/81% in favor of the 91% guy. That's a huge and a horribly unfair advantage for a 1% difference in skill. And that is about a close a distribution as you can get with high skill wins on tied success levels..

With 5% vs. 25% it works out as:

Both rolls the same success level 64.06%(.01*.01+.04*.20+.90*70+.05*.05)) of the time. So agains, the majoirty of cases are ties (in this case failures, but still ties). The remaining 35.94% breaks down in about a 5:1 advantage for the 25%er. So the final breakdown is about 6%/94% in favor if the 25% character.

Now, okay, 90 vs 91 is not worse that 05 vs 25, but it's not much better. In fact, with high skill winning on ties, the actual difference in skill has little effect on the outcome. Compare 5% vs. 90%

Both roll the same success level 11%(.01*.05+.04*.70+.90*.09+.05*.01) of the time. The remaining 89% break down at about 18:1 in favor of the 90%er, for a 05%/95% outcome- only a 1% shift from 05 vs 25%, so all that extra skill doesn't matter much. All that matters is having a higher skill that the other guy.

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Why not just use that lowest roll wins within a success level? So that critical, beats special success, and special success beats success, and so on. But if for example both have success, the lowest roll win.

The highest skill still have an edge because of greater chance of success, special success and critical.

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Why not just use that lowest roll wins within a success level? So that critical, beats special success, and special success beats success, and so on. But if for example both have success, the lowest roll win.

The highest skill still have an edge because of greater chance of success, special success and critical.

Some people, (I'm not one) believe that low roll wins is unfair to the higher skilled character, becuase thier skill doesn't matter much when the other guy rolls low. But, it is debatable. Mathematically, low roll wins still favors the character with the greater skill. Just not quite so much. But the difference between low roll wins and high roll wins is not a lot, percentage-wise.

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a very useful analysis.

Thanks for that. Very thorough. Not gonna make me stop using that algorithm. But can see why it worries you. You are dead right my ruling 'highest skill wins on tie' does indeed mean that highest skill wins nearly all the time. And I suppose it's simplicity causing a simplistic result - higher skill wins margin not so important should not surprise me!

Ta

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Some people, (I'm not one) believe that low roll wins is unfair to the higher skilled character, becuase thier skill doesn't matter much when the other guy rolls low. But, it is debatable. Mathematically, low roll wins still favors the character with the greater skill. Just not quite so much. But the difference between low roll wins and high roll wins is not a lot, percentage-wise.

Sorry, I got a bit nerdy about this, trying to understand the math. I have an example here I think illustrates how fair the roll-low-wins rule is to the higher skill holder.

For simplicity I use only two success levels: success and failure. Higher skill win when same number is rolled within a success level.

A has skill of 75

B has skill of 25

Chance for A to win by own success and opponent failure is 0,75*(1-0,25) = 0,5625

Chance for B to win by own success and opponent failure is 0,25*(1-0,75) = 0,0625

Other rolls possible are success success: 0,75*0,25 = 0,1875

And fail fail: (1-0,75)*(1-0,25) = 0,1875

These are all rolls possible (0,5625+0,0625+0,1875+0,1875=1)

So, how many of these fail-fail or success-success situations will A win? Not so many:

If both roll success, A will win only on 25 to 01, if B rolls higher. That is 25 numbers of 75 numbers possible rolled, and only half of which will be lower than B´s roll:

25/75*0,5=0,1666...

Similarly, if both roll failure, B succeed on 75 to 26 (50 numbers) and half of the time when rolling 99-76 (24 numbers). Person A then succeed at a rate of:

1-(50/75 + 24/75*0,5)=0,16

Of all rolls, A will then win: 0,5625+(0,1875*0,167)+(0,1875*0,16)=0,6237..= appr. 62%

Person A will then have a 62% chance of beating anyone with skill 25, when using lowest-roll-wins.

I´m not sure about this math, but it seems right. The question is then if a 62% chance of beating anyone at skill 50 points lower is fair...

I think this can go on forever =|

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Thanks for that. Very thorough. Not gonna make me stop using that algorithm. But can see why it worries you. You are dead right my ruling 'highest skill wins on tie' does indeed mean that highest skill wins nearly all the time. And I suppose it's simplicity causing a simplistic result - higher skill wins margin not so important should not surprise me!

Ta

No problem. We can all choose our own rules variants.

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Sorry, I got a bit nerdy about this, trying to understand the math.

Don't be sorry. There was an older thread around here where somebody (name witheld to protect the guilty) did just that.

I have an example here I think illustrates how fair the roll-low-wins rule is to the higher skill holder.

I´m not sure about this math, but it seems right.

It looks about right.

The question is then if a 62% chance of beating anyone at skill 50 points lower is fair...

Yup. Hence the post I did wondering what people think the odds of winning should be. Should the odds be set by the difference?, by the ratio? Or what.

Should 27 vs 75 be treated the same as 50 vs 150, or the same as 100 vs 150?

Plus you happened to have picked a contest where the skills add up to 100, so the results would be the same with either low roll or high roll wins!

But in most cases there is a slight shift in the odds between roll low and roll high. I wish I could find the old thread, since I think we worked out a worst case situation.

I think this can go on forever =|

Yup. THose who like a particular method will use it regardless of the math, because they like it.

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Nope. not in combat. Even MRQ1 didn't use opposed rolls for combat (although I'd bet money it was supposed to, it would have made more sense that way).

As a matter of fact, the last playtest document used opposed rolls in combat (I think it had been edited by Ken Hite).

In case where the defender tried to parry and he had the same success level, the amount of damage blocked varied on which roll was highest :

-APx1 if the attacker's roll was higher.

-APx2 if the defender's roll was higher.

In case of a dodge, the defender had to give ground if he had lowest roll, or chose hit location if he had the highest roll.

I don't know why mongoose changed this before they released MRQ1.

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From what I've read, it seems Matt Sprange changed it after it was released. On the Mongoose forums people who were at the convention where MRQ was released were shown one way to play in the demo, and then MAtt posted on the forums that it was wrong, and so were the printed MRQ rules. Things rapidly got stranger after that. He tried to patch problems with the rules that were cuased by the changes in the system. RQ rules were (and still are, as are the rules in BRP) interdependent of each other. So any radical change to one aspect of the game system will have a domino efffect on other aspects of the system. I don't think Matt Sprange every really understood that. He would come up with quick fixes to problems in response to complaints and the quick fixes would lead to even worse problems. Like when he submitted an alterate damage table with higher weapon damages in response to complaints that MRQ combat was not very deadly. Upping the weapon damages did indeed make the game more deadly, but it also reduced the effects of armor and parrying.

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