opposed roll dice probabality analysis

[radmonger]

I did this previously for questworlds, and now here it is for RQ:G.

RQ;G has a core mechanic for opposed rolls, described on p142. in short, both sides roll, and the one who gets a better degree of success wins. A critical beats a special, and so on down to a failure beating a fumble. This is adapted for combat by the 'attack versus parry' and 'attack versus dodge' tables, which contain more specific details about each case.

Working out the chance of success when a skill of 40% is opposed by a resistance of 70% is actually suprisingly tricky, as there are lots of special cases like 'a roll of 1 is always a criticial'. and doesn't necessarily produce intuitive results. So i wrote a simple java program to do the calculations. This produced to following table:

 

 

in it, rows are the skill or weapon attack percentage, and the columns the opposing skill or parry percentage. Both numbers go up to 250%; the 'abilities over 100%' rule from p144 is used.

for example, a sword skill of 30% opposed by a parry of 10% has just over a 30% chance of landing a blow, based on combining:

- chance of successful attack and failed parry

- chance of special or critical attack and normal parry.

- chance of failed attack and fumbled parry

 

 

Edited December 24, 2023 by radmonger

[radmonger]

A couple of conclusion stand out from that table:

• for values less than 100, the table is irregular, over that is changes structure and repeats.
• because the the hard-coded '5 is success, 96 is a failure' rule, even extreme skill disparities have a chance of not ending the way you would expect. 
• as there is no WQ/Pendragon-style 'tiebreak rule', any given roll has a non-zero, and sometimes large, chance of producing no decisive result

For example, a contest between 90 and 80% skill has about 30% chance of being won by the higher skill, 205 by the lower, with 50% of a draw.

 

Edited December 24, 2023 by radmonger

[Ian Absentia]

This is enlightening.  Thank you!  I saw your QW version; have you done one for (albeit slight) variation for the generic BRP rules?

!i!

[French Desperate WindChild]

hello @radmonger thanks for the sharing :)

however ,as i was surprised by some results (for example the irregularity seems to me not "enough" 0.6385 for example from 130 vs 80, 140 vs90, etc..)

i tried some tests and have not the same results

 

the most obvious (I did not see it before all my tests ^^ ) is your 10 vs 10 result :

if Att has only 10% chance of success its roll, it is not possible to be the winner with 13.42% (> 10) once you compare with a potential success of the defense.

 

see what i did (i may have made mistake, by the way, I'm not sure at all)

row Att :  the skill (1.3 = 130%) then the crit chance = 5% of this and round. As special = 20% of skill but the first 5% are critical, it means 15% of "pure" special, then the "rest" of success chance. So for 130%, you have 7% crit, 20% special,  68% of normal success (68+20+7 = 95, 96+= failure)

row Def: same than row  Att.

row s: it is the % of "win" for the column. for example, with our 130 vs 70 : if Att crit, Att doesn't win only if Def obtains a crit (70 -> 4%) =>96%. If Att obtain a special, it doesn't win only if Def obtains crit (4%) or special  (11%) => 85%

 

row S : it is the final probability to win when Att obtains a result. For example, with 130, Att has 7% to obtain a critical roll, then against Def, 7% x 96% = 6.72% to win

last cell gives the full chances of win = chance of win with a crit (6.72%) + chance of win with a special (17%) and chance of win with a normal success (20.4%)

so 44,12%

 

10 vs 10 = 9,23% chance of "win" (seems better than 13,42%)

 

I share my excel if you find any issue

rq opposition.xlsx

[Mugen]

On 12/24/2023 at 6:53 PM, radmonger said:

A couple of conclusion stand out from that table:

(...)

• as there is no WQ/Pendragon-style 'tiebreak rule', any given roll has a non-zero, and sometimes large, chance of producing no decisive result

For example, a contest between 90 and 80% skill has about 30% chance of being won by the higher skill, 205 by the lower, with 50% of a draw.

That, and the fact failed rolls have no impact on the result of the contest whatsoever. But it's also true in Pendragon.

[radmonger]

58 minutes ago, French Desperate WindChild said:

if Att has only 10% chance of success its roll, it is not possible to be the winner with 13.42% (> 10) once you compare with a potential success of the defense.

There is a 5% chance of the opposition fumbling, as they only have 10% skill too. In the table on p199, a failed attack versus fumbled parry results in normal damage being dealt, as well as a roll on the fumble table. 

Note that this rule means if you have a skill of less than 30%, it is actively a bad idea to attempt to parry or dodge and opponent with lower skill.

One thing is I think there are different possible ways to interpret the 'over 100%' rules. The code assumes:

• The adjusted chance is used as the basis for calculating criticals and specials for both sides.
• the opposition skill only needs to be reduced to 0; any excess after that still adds to the chance of scoring a special/critical.

 

 

 

Edited December 25, 2023 by radmonger

[French Desperate WindChild]

59 minutes ago, radmonger said:

There is a 5% chance of the opposition fumbling, as they only have 10% skill too. In the table on p199, a failed attack versus fumbled parry results in normal damage being dealt, as well as a roll on the fumble table. 

oh I did not follow this point

ok I understand the difference. However there would be two ways

the one where you can win even if you fail (your option then) and the one where you must succeed to win.

For example if you are greek in Marathon and must run to Athens, and some persian pursuers try to prevent you, even if they fumble you must succeed to reach the city. If not, noone would know how was the battle.

[radmonger]

For an opposed roll, I would interpret a failure versus fumble to mean the goal is accomplished, even though you failed at the task. For example, you collapsed on the road 5 miles from Athens, but the runners the Persians sent themselves got captured and revealed their plan. 

[French Desperate WindChild]

9 hours ago, radmonger said:

For an opposed roll, I would interpret a failure versus fumble to mean the goal is accomplished, even though you failed at the task. For example, you collapsed on the road 5 miles from Athens, but the runners the Persians sent themselves got captured and revealed their plan. 

That’s karma ! For me not this case but our rules may vary 😀

but i would follow the « fumble » rule when someone try to unlock a door (the locksmith did a fumbled so it helps the thief)

 

 I would apply the fumble when the fumbled action create a direct opportunity / help / bonus to the opposite action (as a defense fumble offer opportunity for a better attack)

that s just choice and taste

 

un all cases interesting job

[Brian Duguid]

I did a similar analysis a few weeks ago, although I ignored fumbles so some of my results differ from yours where low skill levels are found:

 

[Akhôrahil]

Opposed rolls is perhaps the weakest part of BRP. There are ways to handle it or fix it, like the brilliant fix in Pendragon, but it is something that has to be handled or fixed.

[RandomNumber]

My group dropped the RQG opposed skills roll RAW in favour of the version in the Quickstart, which is similar to Pendragon.  It does run counter to the "lower is better" dice roll philosophy.  However, it is less likely to yield a draw.

[DreadDomain]

19 hours ago, RandomNumber said:

My group dropped the RQG opposed skills roll RAW in favour of the version in the Quickstart, which is similar to Pendragon.  It does run counter to the "lower is better" dice roll philosophy.  However, it is less likely to yield a draw.

Yes, that version is much better. At the very least, adding "highest roll wins" as an option when a tie does not make sense would have been a good compromise for RQG. Much cleaner.

By the way, I also prefer the attack/parry interactions from the quickstart rather than the matrix in RQG.

Edited December 28, 2023 by DreadDomain

[Runeblogger]

Having the highest skill win in case of a draw would be another option. 
As in Call of Cthulhu.