My solution for Opposed Skill checks (over or under 100%)

[duncan_disorderly]

I proposed a version of this in one of the other threads (to complete indifference), but this is a bit more complete and thought out

Opposed tests are made as normal skill checks - so critical and fumble rules are in effect. Characters with a skill over 100% roll as normal with the reduced chance to fail and the increased chance to critical.

Results:

• character A criticals, B fumbles or fails - A gets a (critical) success
  character A criticals, B succeeds - A gets a (normal) success
  character A succeeds, B fumbles - A gets a (critical) success
  character A succeeds, B fails - A gets a (normal) success
  Both characters succeed or both critical - the highest roll wins
  • - If Rolls are tied and both succeed or both critical then work down this list
    (1) If one character has a skill of > 100 and the other doesnt, then he wins
    (2) If "temporary stalemate" is an option, roll again next round**
    (3) The highest skill wins - if skills are tied and a "temporary stalemate" is not an option*** roll again immediately
  Character A fails, B fumbles - work down this list
  • (1) If "both fail" is an option, then both fail*
    (2) If "temporary stalemate" is an option, roll again next round (B tkes a -10% penalty)**
    (3) A gets a normal success
  Both characters fail or both fumble (including tieds rolls) - work down this list
  • (1) If one character has a skill of > 100 and the other doesnt, then he wins
    (2) If "both fail" is an option, then both fail*
    (3) If "temporary stalemate" is an option, roll again next round**
    (4) The highest skill wins

* eg an attempt to pick a pocket - the thief does not get anything, but the victim does not notice the attempt

** eg an attempt to sneak past a guard - the sneak gets part way, but then has to wait as the guard appears suspicious

*** eg a contest to be the first character to grab the Rune...




Some examples.

Character A has a skill of 60%, B has a skill of 40%
A will critical on 1-6, succeed 7-60, fail 61-99, fumble 00
B will critical on 1-4, succeed 5-40, fail 41-99, fumble 00

If A rolls a critical (6%)
- he will achieve an overall critical 60% of the time (B fails or fumbles)
- he will achieve an overall success 36% of the time (B succeeds) + ~2.3% (B crits but rolls less)
- he will lose 1% of the time (B crits and rolls higher)
- there will be a tie ~0.7% of the time (both roll the same value in the range 1-4) - A will win if a result is required this round

If A succeeds (54%)
- he will achieve a critical 1% of the time (B fumbles)
- he will succeed 59% of the time (B fails) +~24.8% (B succeeds but rolls less)
- he will lose 4% of the time (B criticals) +~10.4% (B succeds & rolls more)
- there will be a tie ~.8% which A will win if a result is required

If A fails (39%)
- He will succeed 60% of the time, but only if a result is required this round and B fumbles (1%) or fails (59%)
- he will fail 36% of the time (B succeeds)
- he will fail to a critical 4% of the time (B Criticals)

If A fumbles (1%)
- he will fail to a critical 40% of the time (B criticals or succeeds)
- he will fail 59% of the time if a result is required this round (B fails)
- he will succeed 1% of the time if a result is required this round (B fumbles too)

Total chances for A in this contest
Critical - 4%
Success - 71%
Fail - 22.5%
Lose to Crit - 2.5%



Character A has a skill of 110%, B has a skill of 90%
A will critical on 1-11, succeed 12-95, fail 96-99, fumble 00
B will critical on 1-9, succeed 10-90, fail 91-99, fumble 00

If A rolls a critical (11%)
- he will achieve an overall critical 10% of the time (B fails or fumbles)
- he will achieve an overall success 81% of the time (B succeeds) + ~5.8% (B crits but rolls = or less)
- he will lose ~3.2% of the time (B crits and rolls higher)
- there will be no tie as a is >100% and B isn't

If A succeeds (84%)
- he will achieve a critical 1% of the time (B fumbles)
- he will succeed 9% of the time (B fails) +~44.5% (B succeeds but rolls less)
- he will lose 9% of the time (B criticals) +~36.5% (B succeds & rolls more)
- there will be no tie as a is >100% and B isn't

If A fails (4%)
- He will succeed 10% of the time, but only if a result is required this round and B fumbles (1%) or fails (9%)
- he will fail 81% of the time (B succeeds)
- he will fail to a critical 9% of the time (B Criticals)

If A fumbles (1%)
- he will fail to a critical 90% of the time (B criticals or succeeds)
- he will fail 9% of the time if a result is required this round (B fails)
- he will succeed 1% of the time if a result is required this round (B fumbles too)

Total chances for A in this contest
Critical - 2%
Success - 55%
Fail - 42%
Lose to Crit - 1%


Character A has a skill of 160%, B has a skill of 140%
A will critical on 1-16, succeed 17-95, fail 96-99, fumble 00
B will critical on 1-14, succeed 15-95, fail 96-99, fumble 00

If A rolls a critical (16%)
- he will achieve an overall critical 10% of the time (B fails or fumbles)
- he will achieve an overall success 76% of the time (B succeeds) + ~7.3% (B crits but rolls less)
- he will lose ~5.9% of the time (B crits and rolls higher)
- there will be a tie ~0.8% of the time (both roll the same value in the range 1-4) - A will win if a result is required this round

If A succeeds (79%)
- he will achieve a critical 1% of the time (B fumbles)
- he will succeed 4% of the time (B fails) +~40.5% (B succeeds but rolls less)
- he will lose 14% of the time (B criticals) +~39.7% (B succeeds & rolls more)
- there will be a tie ~.8% which A will win if a result is required

If A fails (4%)
- He will succeed 5% of the time, but only if a result is required this round and B fumbles (1%) or fails (4%)
- he will fail 81% of the time (B succeeds)
- he will fail to a critical 14% of the time (B Criticals)

If A fumbles (1%)
- he will fail to a critical 95% of the time (B criticals or succeeds)
- he will fail 4% of the time if a result is required this round (B fails)
- he will succeed 1% of the time if a result is required this round (B fumbles too)

Total chances for A in this contest
Critical - 2%
Success - 49%
Fail - 47%
Lose to Crit - 2%

Character A has a skill of 160%, B has a skill of 40%
A will critical on 1-16, succeed 17-95, fail 96-99, fumble 00
B will critical on 1-4, succeed 5-40, fail 41-99, fumble 00

If A rolls a critical (16%)
- he will achieve an overall critical 60% of the time (B fails or fumbles)
- he will achieve an overall success 36% of the time (B succeeds) + ~2.9% (B crits but rolls less)
- he will lose ~1.1% of the time (B crits and rolls higher)
- there will be no tie as A is >100% and B isn't
this round

If A succeeds (79%)
- he will achieve a critical 1% of the time (B fumbles)
- he will succeed 59% of the time (B fails) +~31.7% (B succeeds but rolls less)
- he will lose 4% of the time (B criticals) +~4.3% (B succeeds & rolls more)
- there will be no tie as A is >100% and B isn't

If A fails (4%)
- He will succeed 60% of the time, but only if a result is required this round and B fumbles (1%) or fails (4%)
- he will fail 36% of the time (B succeeds)
- he will fail to a critical 4% of the time (B Criticals)

If A fumbles (1%)
- he will fail to a critical 40% of the time (B criticals or succeeds)
- he will fail 59% of the time if a result is required this round (B fails)
- he will succeed 1% of the time if a result is required this round (B fumbles too)

Total chances for A in this contest
Critical - 10%
Success - 81%
Fail - 8.8%
Lose to Crit - 0.2%

 

[simonh]

So basicaly the rolls are made using the existing rules for determining success level, and the level of success of the winner is the difference in their levels of success? One rank better = success. 2 ranks better = critical, with highest roll wining on a tie?

That will certainly work, but it means that once your skill goes over 100% your relative ability rises excruciatingly slowly. This is because critical chances rise so slowly, only once every 10% skill. Every skill increase you get between whole 10s of percent makes no difference.

I've done the calculations for a character with 160% versus one with 90%. The workings are at the end of this post.

Compare to the results you did for character A with 110% versus B with 90%. A's skill has gone up by 50% points which you'd expect to make a huge difference.

In fact, the odds have hardly moved. At 110% skill A had an agregate chance of a success or crit (a win) of 57%. At 160% he has an agregate chance of a win of 59%. That's only a 2% improvement in his overall chance of beating a character with a 90% skill, despite the 50% improvement in his ability!

Please check this because I'm no maths genius, but I think you can see that the improvement rate slows to a crawl.

160% vs 90%
A crits 16%)
Crit 10%
Success 87%
Lose 3%
Tie 0%

A Succeeds (79%)
Crit 1%
Succeed 53.5%
Lose 45.5%
Tie 0%

A Fails (4%)
Succeed 10%
Fail 81%
Fail to Crit 9%

A Fumbles (1%)
Fail when B succeds or Crits 90%
Fail when B Fails 9%
Succeed, B fumbles 1%

Total chances for A in this contest
Crit 2.4%
Success 56.6%
Fail 40%
Lose to Crit 1%


Simon Hibbs

 

[JohnLokiBeard]

I use the same method as Duncan, because skill ratings are not really % values!
I remember an RQ2 article from White Dwarf about 15-20 years ago, where the author mentioned that if two opponents with sword skills of 75 and 25 were to face off, the betting wouldn't be 3/1 in favour of the more skilled opponent, it would be more like 30/1.
The fact that the success of skills are rolled on d100, and have always been referred to as 'xx%', leads to the confusion, as does the fact that with a skill of 06 to 95 does actually correspond to the % chance of success; but the oft-repeated "no, you don't have to roll 'speak own language' every time you try to talk" is a clue that we should stop thinking of RQ skill ratings as % and instead treat them as qualification levels.

Using First Aid as an example, rough competence levels might be:
25 = cub scout badge
50 = eagle scout badge
75 = paramedic
100 = E.R. doctor
[Or again we could referrence Language skills, the famous RQ3 "How many moneys for leg of lamb?"]

Yes, improvement slows to a crawl at over 100, but that's how it works in the real world with top athletes. Besides which, skill levels also offset difficulty modifiers - the 160 vs 90 becomes 80 vs 10 on a narrow ledge at night during a storm.

 

[simonh]

I use the same method as Duncan, because skill ratings are not really % values!
I remember an RQ2 article from White Dwarf about 15-20 years ago, where the author mentioned that if two opponents with sword skills of 75 and 25 were to face off, the betting wouldn't be 3/1 in favour of the more skilled opponent, it would be more like 30/1.

Actualy in MRQ your odds of winning in this situation, in a streight opposed roll contest are... drum roll... 74.75%, with a 0.5% chance of a tie.

The article was, I'm sure, refering to earlier versiosn of RQ, and probably combat over a series of rounds and I'm sure it was accurate in those circumstances.

However opposed ocntests resolved in a single roll, or onw roll for each side, is different from combat where it generaly takes half a dozen to a dozen rolls. The more rolls there are, the more the results will be statisticaly averaged out, in favour of the more highly skilled character.

Yes, improvement slows to a crawl at over 100, but that's how it works in the real world with top athletes. Besides which, skill levels also offset difficulty modifiers - the 160 vs 90 becomes 80 vs 10 on a narrow ledge at night during a storm.

That's true, and it's a useful effect, but it's essentialy the only effect that rasising skill over 100% would give under this system. Relative to characters with around about 90% skill in a streight contest, you will remain essentialy as effective as you were at 100% skill (about 55% to 60% chance of winning in a single opposed roll contest) forever.

The rate of improvement is actualy worse than it was under RQ2 or RQ3.

Simon Hibbs