I have an embryonic idea for a non-combat resolution mechanic, it's not particularly developed as yet (been spending most of my spare time on a combat mechanic (http://www.indie-rpgs.com/forum/index.php?topic=27476.0)

I'm not sure how to work out the spread and deviation on these figures.

The basic idea is that a more experienced/skilled character should have a higher base (median) probability of succeeding at a given task, but also be more reliable/less random in their attempts.

My idea is that a task has a target number and a pool of dice that is rolled with the hope of succeeding, let's say 6d10. Skilled characters have a number of Aces, that is dice that are set aside and assumed to have already rolled 10s (on the assumption that a skilled - say, surgeon, is not going to every fuck up on the early easy parts of a procedure and it's only the critical moment that could go either way).

So the number ranges could work from:

Unskilled (no Aces) - Roll 6d10
Talented (one Ace) - Roll 5d10 + 10
Competent (two Aces) - Roll 4d10 + 20
Experienced (three Aces) - Roll 3d10 + 30
Adept (four Aces) - Roll 2d10 + 40
Expert (five Aces) - Roll 1d10 + 50

But I don't know the formulae for figuring out the average and standard deviations from these rolls, which I'd need to know before I can start on a framework of target numbers for tasks/skills.

Can anyone help?

You don't say so, but I assume you are adding the result of each die in the roll together? That is, if you rolled 1,2,3,4,5,6, the result is 21?

If so, the thing to know is that the average result of a single d10 is 5.5. (You can figure this out by assuming a "perfect" world where, if you rolled the d10 ten times, you'd get each possible result exactly once. Sum those and divide by the number of rolls: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55. 55 / 10 = 5.5.) So the average results are:

Unskilled (no Aces) - Roll 6d10:
average = 6*5.5 = 33
min = 6
max = 60

Talented (one Ace) - Roll 5d10 + 10
average = 5*5.5 + 10 = 37.5
min = 15
max = 60

Competent (two Aces) - Roll 4d10 + 20
average = 4*5.5 + 20 = 37.5
min = 24
max = 60

Experienced (three Aces) - Roll 3d10 + 30
average = 3*5.5 + 30 = 42
min = 33
max = 60

Adept (four Aces) - Roll 2d10 + 40
average = 2*5.5 + 40 = 51
min = 42
max = 60

Expert (five Aces) - Roll 1d10 + 50
average = 5.5 + 50 = 55.5
min = 51
max = 60

I'd have to crunch the numbers to get standard deviation. You can pretty much tell right away, though, that all but the Expert rolls will be some normal distribution (i.e. a standard bell curve), shifted by a constant value. As skill increases, three things happen to this curve: a) it shifts further to the left, b) it gets narrower (that is, contains fewer possible values) and c) flattens out (to the point that it is completely linear by the time it gets to Expert).

Change a) means that, indeed, the character does have a higher median probability of succeeding as skill goes up.

Change b) means that, indeed, the character is less random in their attempts, because the range of values they can actually generate decreases as skill increases. (That is, at Unskilled, there are 54 possible results, from 6 to 60, but at Adept, there are only 18 possible results, from 42 to 60.)

Change c) works slightly counter to your purpose but not significantly so. It means that within the shifted, narrower range of possible results the character is less likely to get the median within that range. At the expert level, for example, the character is guaranteed to get between 51 and 60, but each result within that set is equally likely.

Oh, yep. Totalling the dice. Forgot to mention that, but you're quite right.

Thanks for response there, what I was looking for was a hint on what formulae to use to work out the standard deviation, because I'd need that to start assigning TNs and doing some tests.

a) and b) that's exactly what I was looking for!

c) yeah I realised that an Expert roll would go back to flat distribution, I'm sure there's ways around it, like an Expert rolling 3d4 + 50 or something, but that wouldn't line up with the number range exactly and certainly wouldn't be keeping it simple. I'd guess it wouldn't come up so often, if a Target Number for a tast was like 30, then someone with four or more Aces would just succeed automatically.

Another thought I had since I posted this last night was that Aces could have a few other gameplay uses. Aces could be somehow "spent" for a riskier attempt at a more elaborate version of the intended outcome, or could off-set a situational penalty (like tying a rope on a boat in heaving seas could have a two-Ace penalty). And contested rolls could just be that each actor rolls a number of dice equal to the number of Aces they'd normally have in an unopposed situation.

Upon looking at this concept, he first thought that came to mind was...

What if the experienced characters didn't get their dice replaced with automatic 10s?

What if they were replaced with automatic 9s (or even 8s)?

This would mean that an unskilled individual would take more risks with what they were doing. They wouldn't realise that these risks were being taken, and more often than not these risks would lead to unpredicatble and worse results, but there would be occasions when the unskilled individual would pick up a bit of "beginners luck" and actually do better than the skilled character.

This could even tie in with an experience system. Every time a 10 is rolled on a skill attempt, the character may choose to improve their skill level, or stay at their current level of expertise. The 10 represents that the character has found a cool new way to perform the task at hand. If they choose to rely on this new trick, then their margin for error decreases, but their degree of experimentation with the skill decreases as well.

With second thoughts about the system, perhaps all players roll the standard number of dice whether they are skilled or not. Before the dice are rolled, a player may choose to have their character substitute one or more dice with automatic 8s from their skill. Once the dice are rolled, a player may use any remaining unspent skill levels to increase any poorly rolling dice into automatic 6s.

My reasoning behind this concept is pretty simple.

A player can choose how much they want to experiment with a task. They can use all of their accumulated tricks to reduce the margin of error and get a fair;y consistent result, or they can take some risks for the chance of getting better results (but on the down side, they also risk getting worse results).

Doctor Ziggy has three patients with shrapnel embedded in their flesh from the explosion of a cannon. He's a pretty good field medic with "4 aces".

For the first patient, he tries some radical new techniques that he hasn't experimented with yet. He doesn't use any of his aces on this attempt and rolls six dice [1,3,5,7,9,10] for a result of 35. Because he didn't use any of his aces before the test, he may now use them afterward. Three of the dice he converts to a minimum result of 6 [6,6,6,7,9,10] for a result of 44. With his 10, he could improve the skill by a degree indicating that he has perfected one of the new techniques, but for this example, we'll say that he doesn't.

For the second patient, he tries a few of his established techniques, and a some of the new techniques that he's still trying to perfect. He uses half of his aces before the roll, then throws the remaining four dice [2,4,6,8] for a final result of [{2x8} + 2 + 4 + 6 + 8 =] 36. He uses his remaining two aces after the test to improve two of the dice giving a final result of 42 [6,6,6,8,8,8].

For the final patient, he just relies on his tried and true methods, using all four aces and rolling the remaining two dice [5,7]. The total is [{4x8} + 5 + 7 =] 44.

Doctor Ziggy is better off using his skills, but he's less inclined to roll 10's and therefore less inclined to improve his knowledge in the skill field.

This system also allows more chance of a bell curve for the distribution of results among skilled characters because any time a character choose to take a bit more risk with their skill, they are rolling more than one die.

On the down side, standard deviation calculations become a bit more complicated once this sort of mechanism is in place.

Just an idea, I know it complicates things but I thought I'd throw it out there.

V

Only mildly helpful, I'll try to keep it short.

I've been working on a system using the Roll and Keep mechanism from 7Th Sea.
Add Stat (1-6) to Skill (1-6) roll that many D10, keep and total the best Skill level of them.

Part that applies to you, and comes from similar thinking i've been mulling over for very high level skills competitions (Olympic level stuff, like ski races where its 100s of a second differences) is this:

I allowed that you could set skill-1 d10s of the whole pool to 5, then roll the rest, select the best Skill level dice and total. Much like take 10 from D&D. Skill-1 to represent that there is always some variability, skill-2 dice in very uncertain situations like combat, minus more if the person is shaken or surprised.

Likewise your Aces idea could set some dice to 8 or whatever, and you work from there.

Another game out there used a 1-20 scale, 1 being best, 20 worst. Satrting skill was d20, and it worked down through the dice so that an expert was rolling a d4. The beginners 2 still beat the experts 4.

I see what you mean about setting Aces to 8 or 9, but it's not really what I'm going for. The element of risk in sacrificing aces shouldn't be for a higher numerical result, because who would sacrifice an automatic 9 for a 10% chance of rolling 1 better?
I was thinking more along the lines of risk in exchange for a higher tangible result than a less-trained individual would be able to manage. Using climbing as an example, say a character had to take a climbing check to avoid falling every round, in which they'd climb one metre. If two characters were both trying to reach the top ahead of one another, the better climber could sacrifice 2 aces to climb at twice the rate, but their probability of failing would be back near the amateur's odds.

Vulpinoid, I hadn't considered how an expert taking risks by sacrificing aces could contribute to learning. I might have to figure a way to incorporate that, like a set probability of advancing a skill per ace spent?

Let's say an Ace give you an automatic 10 in the previous level of expertise as originally stated, and spending it could give the character the chance to try something on the next level of expertise. This could do it only if less skilled characters would roll a number of dice under 6d10. I'm not so sure that an unskilled character could do a succesfull brain surgery by getting 10 in all six dice without ever having heard of such procedure. Maybe having reference books and all proper equipment could give the character access to the 6 dice, but doing it completely unskilled would be into the range of impossible, unless your system rules otherwise.