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Task Rounds

Task Rounds

Postby DigitalPagan » Wed Oct 19, 2016 11:54 am

So something that has confused me for a while now. Per the rules for Task Rounds (Mythras page 66) it states a competent worker will usually accomplish the work in 4 rounds. Per my math the chances of actually getting 100% in 4 rounds is rather slim even for those with higher skill values. For example, with a skill of 75% the chance of getting 4 successes in 4 tries is only 31.6%, .75*.75*.75*.75 = .31640625. Is my math way off, or did I miss understand that statement/mechanics? I'm sure the chance of criticals skews those results a bit but I don't think that would make up that much of a difference.
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Re: Task Rounds

Postby Belgath » Wed Oct 19, 2016 12:16 pm

DigitalPagan wrote:So something that has confused me for a while now. Per the rules for Task Rounds (Mythras page 66) it states a competent worker will usually accomplish the work in 4 rounds. Per my math the chances of actually getting 100% in 4 rounds is rather slim even for those with higher skill values. For example, with a skill of 75% the chance of getting 4 successes in 4 tries is only 31.6%, .75*.75*.75*.75 = .31640625. Is my math way off, or did I miss understand that statement/mechanics? I'm sure the chance of criticals skews those results a bit but I don't think that would make up that much of a difference.


You my understanding is you only need to finish it in 4 or Less rounds if you want an enhancement or under a time constraint. But if you fumble you stuck with an inferior object.
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Re: Task Rounds

Postby Matt_E » Wed Oct 19, 2016 8:21 pm

Your math is right, if you lump in crits with regular successes and fumbles with failures--but you should (must) not. Because of that, the calculation is significantly more complicated.

You need to compute the chance to get 100 Task Points in 4 rolls, which includes combinations of all 4 types of results: crits, successes, failures, and fumbles. That means there are 4^4 = 256 possible results (e.g. crit-crit-crit-crit, crit-crit-crit-success, ...), each with a probability that is a *product* of the individual probabilities for the result types involved, and the *sum* of those 256 product probabilities being 100%. Each of those 256 possible outcomes (points in sample space) yields a Task Score, which could be >= 100 Task Points. You need to count up how many of those there are, out of the 256 possible results. That will give you your answer.

There is also a more sophisticated way for the probability experts to do it, involving weighting factors that are the numbers of combinations for particular *types* of results, but I am much more comfortable doing it the straightforward way outlined above. I make too many mistakes the other way.
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Re: Task Rounds

Postby Matt_E » Wed Oct 19, 2016 9:40 pm

EDIT ABOVE: Wait, duh, I wrote the wrong thing. You have to sum the probabilities for the outcomes that yield a successful Task Score, not count the number of such outcomes out of 256. That number is always 66 out of 256, for our example, no matter the craftsman's skill score.

I tabulated all 256 points in sample space using a spreadsheet, and did the calculations.

DigitalPagan, for your suggested skill score of 75%, we have
P_crit 0.08
P_suc 0.67 (= 75% skill score - crit chance)
P_fail 0.23
P_fum 0.02 (fumble on a 99 or 00)
and
S_crit 50
S_suc 25
S_fail 0
S_fum -25 (how you score Task Points with a given result)

The big table shows that there are 66 out of 256 outcome that yield a Task Score of 100 or more. The sum of those probabilities is 0.43093073, or 43.1%.

I agree, that seems pretty low, for a character who's a rather skillful 75%.

Repeating the calculation for a master with 90% skill, we find the sum of probabilities for those 66 winning cases to be 0.72126288, or 72.1%.

Repeating the calculation for a paragon with 120% skill, and
P_crit 0.12
P_suc 0.83
P_fail 0.04 (still fails on 96--99)
P_fum 0.01 (fumbles only on a 00)
we find the sum of probabilities for those 66 winning cases to be 0.86184193, or 86.2%.

That's pretty depressing, actually.

I think, then, that this rule may need to be adjusted... Either raise the number of rolls, or change the Task Point scores for the four kinds of skill check results. Maybe make a crit worth 60, a success worth 30 and a Fumble worth -20, so that a result of type (1 crit & 2 successes & 1 fumble) totals 100, instead of 75. That would make the number of successful combinations 90 out of 256, better...but our paragon at 120% skill still only has an 87.2% chance of task success--hardly any better.

Loz or Pete, did you realize how difficult it would be to actually succeed at a task according to these rules?

Can someone check my math? skoll, you're good at this sort of stuff.
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Re: Task Rounds

Postby Matt_E » Wed Oct 19, 2016 9:57 pm

Or you could lower the target Task Score from 100 to 75, or whatever.

The point is, if you're meant to have a better chance of Task success than I have outlined above, then you need to choose the problem's parameters so that more than 66 out of 256 points in sample space are winners. The parameters here are the number of rolls (but I suggest that stay at 4), the scores for the four types of skill-check results, and the target score.

I can see the aesthetic appeal of having the target number be 100, and having a failure be worth 0, but the results are a bit harsh.
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Re: Task Rounds

Postby skoll » Thu Oct 20, 2016 2:23 am

I got the same results, so you math seems to hold up. I have to admit, I'm especially surprised about how high chance of failure (14%) the paragon has.

Here are some more results:
Skill - chance of 4 or more successes
25% - 2.14%
50% - 13.13%
60% - 22.22%
75% - 43.09%
90% - 72.13%
100% - 85.46%
110% - 85.82%
120% - 86.18%
150% - 87.23%
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Re: Task Rounds

Postby Belgath » Thu Oct 20, 2016 4:42 am

Remember this is jest for being under a time constraint or your chance and adding an enhancement. So at 90% you have a 72% of trying for an enhancement. That not to bad. "If a project reaches 100% in four or fewer Task Rounds, the maker has the option to continue refining it. To do this he continues to work on it for a further Task Round and, depending on the result of the skill roll for the Task Round, may enhance it."
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Re: Task Rounds

Postby Matt_E » Thu Oct 20, 2016 9:11 am

Yes, I agree, under everyday circumstances for everyday tasks the typical crafter doesn't even have to roll. However, this whole Task mechanic was meant to handle the more interesting cases.

I like the Task mechanic very much and find it an excellent part of Mythras's design, especially as it can be applied in so many circumstances, to avoid the problem of "failure due to a single bad roll", which we have discussed numerous times.

Kudos to DigitalPagan for pointing out the actual arithmetic problem. I had always shrugged it off with, "Well, that's why your character should be better at her key skills," but as it turns out, because of the parametrization in RAW, there is basically no character who is good enough to expect to succeed almost all the time at a Task.

In fact, your expert or paragon (or anyone else, I think--haven't checked actual expectation values for Task Score, though simple to do now that table has been assembled) is better off with a single skill check than a Task situation! This is sadly ironic.

Again, I believe this could be fixed by judicious reparametrization, but at this stage I think Loz and Pete should weigh in.
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Re: Task Rounds

Postby Matt_E » Thu Oct 20, 2016 9:23 am

skoll wrote:I got the same results, so you math seems to hold up. I have to admit, I'm especially surprised about how high chance of failure (14%) the paragon has.

Here are some more results:
Skill - chance of 4 or more successes
25% - 2.14%
50% - 13.13%
60% - 22.22%
75% - 43.09%
90% - 72.13%
100% - 85.46%
110% - 85.82%
120% - 86.18%
150% - 87.23%


Yes, notice the strong leveling effect (saturation) at high scores. This is because there is always that 4% chance of failure, and 1% chance of fumbling. The only thing that changes for those higher scores is the swapping of success percentages for critical percentages, slowly, slowly. There is also a (less interesting) leveling effect at very low scores, because there's always a 4% chance of success and a 1% chance of crit.

Part of the problem is the thresholding effect. In other words, you just have to accumulate 100 Task Points; beyond that, it doesn't matter whether you get exactly 100 or the maximum 200. This is relaxed by setting up a table of Task Results in the six-category "no, and"/"no"/"no, but"/"yes, but"/"yes"/"yes, and" style that I have mentioned in other threads--to decide how well detective work turns out, for example--, where those extra levels of success (and degrees of failure below 100 Task Points) would matter. In that case a skilled character could expect some much better outcomes than a noob (though probably nowhere near as often as the player would like).
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Re: Task Rounds

Postby loz » Thu Oct 20, 2016 9:52 am

The task mechanic is very much designed to act as a montage scene from [insert favourite title here]. It's there to help decide an overall outcome over a period of time in a dramatic context. As Matt and Belgath point out, it's not there for routine, everyday occurrences, but those occurrences where there's some overwhelming importance, urgency, risk or whatever. You can handle such situations in a single roll, and indeed, statistically you might be better doing so, but the task system does introduce pressure, some higher odds of failure, and therefore dramatic tension - and that's deliberate. It's also designed to be collaborative too: a task might require a team of people pooling different skills, each on contributing one roll to the pot (indeed, this is how I often use the task system in my own games). So it can also be a collection of individual rolls from different contributors, each, perhaps, at a varying chance of success, to achieve an overall goal.

Like any skill rolls, you can also augment the skills needed for the task - with passions or other skills, thereby enhancing your base chance. The GM might decide that with the right resources, your skill grade is one or even two steps easier. Raw materials might even give you a starting point of 25 rather than 0.

The Task system is an abstraction. Like all abstractions, it has its quirks. However, context is everything and the dramatic context is key. The quirk of having a compromised overall chance of success, because you need to make 4 rolls successfully in sequence, can be a great way of building tension that leads to some great story telling developments that you simply wouldn't get by relying on a single roll from a highly skilled individual. Here's an example from my Mythic Britain campaign. Three armies commanded by the player characters had to amass on Lugh's Gorge to defeat the villainess. She'd set ambushes and called on curse spirits to hamper their progress. Each commander had to make either a Lore (Strat & Tac), Stealth or Locale roll that contributed to the overall outcome of their combined forces' success to reach the battle ground. I think they succeeded in either two or three of the four rolls. Their armies got there, but they were weary, sick and had sustained some light casualties from skirmishes and ambush attacks along the way. Now, a single roll could've been used as the abstraction and it would most likely have succeeded too. As GM, I could always rule that the armies were still weary and ill, but it's harder to justify, and the task process actually allowed each player to participate, to understand the stakes, and for me to narrate the effects based on each roll, as the task progressed.

In short, the math outlined in earlier posts is correct - and yes, there are quirks (and we knew about them; it was raised in playtest, if memory serves) - but we don't consider the system to be broken, because it's there to represent those occasions where the heroes are placed under prolonged stress with heightened stakes. Indeed, that quirkiness is something I consider a feature, not a bug.

A somewhat convoluted answer, but hopefully it illustrates our way of thinking. One thing that's already been suggested - by all means adjust the points required, the number of rolls needed, or the skill grade the task operates at, if that seems like the right and appropriate thing to do within the context of both the task and story. And as ever, don't forget Luck Points - if this is a team endeavour, then you may also have Group Luck points too...
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