micro-mechanic opinion

[contracycle]

Hi, I came across a wargame emchanic I want to steal but am curious to know what the statisticians think of it.

It is a penalty die added to a dice pool when appropriate.  It rolls normally with the rest of the pool, and the highest rolled value is discarded.

This is a refinement of roll pool and drop highest; it is roll extra dice and drop highest a number of times equal to added dice.  

What effect will that have?

[Bailywolf]

Over the Edge makes good use of this mechanic- both in the positive and the negative.  A bouns die is rolled along with the normal pool, then the low die (or dice) are ditched.  A Penalty die is the same thing, only as you say, the best roll is ditched.

[Christoffer Lernö]

I use this system for Ygg's combat too to avoid modifiers. I think there is some thread where the probabilities are written down.

If "the highest" is compared to a target number, the effect is that the better you are, the less you are affected by penalities. On the other hand, the lower the skill, the bigger the increase in chance of success from advantage dice.

[Bob McNamee]

It dropping multiple dice?

Fer instance...
I roll 8 dice plus a penalty die
I get a 5 on the Penalty die...drop the highest 5 dice? in my pool of rolled dice?

Is the value of the Penalty die also included in the pool? Does it get dropped as a die value too?

Pretty funky stats probably...success values for each size of die pool, and an extra dimension based on the value of the penalty die for each size pool.  I'm no stat wiz though... my Probability and Sadistics was long ago

Bob McNamee

[mahoux]

Another variation on this is to use the number on the penalty die and subtract that from the highest die rolled - ie.  subtract 2 from a 5, get three, subtract 5 from a 3, get -2.  That could be a fun mechanic.

I may use that idea somewhere myself.  Personally, I think the idea could lend itself to some fun situations.  Sounds cool.

Aaron Houx

[contracycle]

I want to do use it in a WOD style pool; number-on-die-over-threshold.  In this scenario, you drop dice from the top down.  So if you had 3 penalty dice, you would roll Pool+3 dice and drop the top 3 dice.

The obvious implication is that you still have the same number of possible successes as before.  If you were rolling 5 dice and 2 penalty dice added, you could still get 5 successes if all 7 dice succeeded (beat the threshold).

So my stats question was aimed at that.

[Mike Holmes]

This is a very complicated stats question. I think what you are asking is something like, "Given a pool of X dice, and a penalty of Y, how many less successes can one expect." Even a practical would be difficult to look at more than a few examples.  

Here's the trend I detect just looking at some examples.

Obviously, as the penalty dice increase, the expected value drops, and the higher the chance of failure (higher target number) the more the penalty dice hurt you, but
--a. almost as obvious, the number of dice in the base pool increase, the reduction caused by each penalty die is decreased. However,
--b. in the case of a proportional number of penalty dice to pool dice, the higher pool will be penalized more in the sense of fractional and actual reduction. But,
--c. actual expected value is still higher for he case with more dice and proportional numbers of penalty dice.

Example: given rolling d10s, and a target number of .5 (50% chance of success on each die, base; the simplest example I could think of).

A 1 die pool has an expected value of .5;
with a one die penalty it has a value of .25.

A four die pool has an expected value of 2;
with a four die penalty, it's reduced to just over .5 (.53?)

So, the larger pool has been reduced to one quarter or so it's original value, and suffered an actual loss that is larger, as well, but that value is still larger than the smaller pool even started.

Other than that, do you have any specific questions that wouldn't take days to answer? Like what are the odds for all combinations, and all outcomes (for a stat range of just 1-5 and similar penalty range that would be 25 very complicated charts).

Mike

[Walt Freitag]

Um, what Mike said. The problem is that there are four variables here: the number of dice in the pool, the number of penalty dice added, the probability of success per die (indicated by the TN and the die type), and the number of successes needed for achieving some goal. Pick any three variables and you can get a probability distribution across the fourth.

Let me add one simple point to Mike's generalizations: apart from all other factors, a penatly die can only reduce the number of successes if it does not itself roll a success. Therefore, the higher the succes chance per die, the less noticeable an effect each penalty die will have.

- Walt

[contracycle]

So, the larger pool has been reduced to one quarter or so it's original value, and suffered an actual loss that is larger, as well, but that value is still larger than the smaller pool even started.

Thanks guys, thats pretty much what I was after.  Just wanted to rule out a quirky effect.

[contracycle]

Let me add one simple point to Mike's generalizations: apart from all other factors, a penatly die can only reduce the number of successes if it does not itself roll a success. Therefore, the higher the succes chance per die, the less noticeable an effect each penalty die will have.

Yes, thats one of the virtues I think.  I want these to be used as side pools to the mechanic I posted the other day, that players can add to opponents pools.  This will introduce an interesting choice in which of the opponents rolls to apply the penalty dice to.  The best use would be in small doses when the TN is already high; but if it aint and your desperate, you'll be motivated to throw the lot in.

[Walt Freitag]

That sounds like it should work fine.

Actually it simplifies down even more than I realized before.

Any penalty die that rolls a success, has no effect on the number of successes.

Any penalty die that rolls a failure will always reduce the number of successes in the roll by 1, unless the number of successes is already down to zero.

So given a certain success probability per die, the effects of the penalty dice (at least, on mean outcomes) in many cases are pretty straightforward to determine. Example: rolling a pool of 7d10, target =7+:

Expected number of successes without penalty dice: 7 * 0.4 = 2.8

Expected number of successes with three penalty dice added: (7 * 0.4) - (3 * 0.6) = 2.8 - 1.8 = 1.0. (This is only approximate; it's actually a bit higher because the mean effect of the penalty dice is reduced by those cases where the penalty dice roll more failures than the other dice roll successes).

I don't know why this seemed so much more complicated 2 days ago. :-)

- Walt

[Mike Holmes]

I don't know why this seemed so much more complicated 2 days ago. :-)

True, but then that effect that you mention where the penalties cannot lower below zero is somewhat significant. Given my example, 4 regular d10, and 4d10 penalty dice, and TN 6 the average result is over .5 (determined by over 20,000 practical attempts now). Your method would predict zero. This remains aproximately proportional, BTW, 1/1 thows an average .25 (which we predicted), 2/2 throws .37, 8/8 throws .78. Sounds like a natural log curve.

To look at another circumstance, 2d10 and one penalty die at TN 6 would predict to .5, and the actual result is more like .62. Testing 8/2 the result is very close to 3. So we can see that as the penalty gets relatively smaller to the ability, Walt's prediction becomes almost perfectly accurate.

So, the worst case scenario for using Walt's predictive measure is when the penalties are about as large as the skill.

BTW, just to look at some cases where penalties exceed skil, 4/6 returns .2 average, and 2/8 may as well be zero.

This is interesting. If we are assuming a system where the successes generated are significant (one success means that the character did something good), then the traditional "average" task that gives you a fifty percent chance of "succeeding", is very much one where penalty dice are equal to, or near equal to the total ability. For example, the 4/3 situation produces a success about 50% of the time. This, of course would change if the TN changed from 6 (on a d10, or 50% success). Dramatically. The 4/3 example drops to only 29% if the TN is 7 instead of 6.

Has anyone noticed as well, how tight the results are on such a curve? For example, on 4d10, TN 6, the most one can hope for is no penalties, giving an average of 2 successes. And, of course it can never drop lower than 2 to near zero. This means the large range of potential penalty has little effect in terms of number of successes generated. I think this may be just what some designers are looking for, a dice pool system that's more binary than based on a large range of successes. So, for example, if you wanted to do a game where there were only three levels of success, this might be a good system as long as you keep the TN relatively high (6+). Reduce the TN, however, and you get a system that has a much wider range of success production, and one in which you can pile on the penalty dice (as each will have little effect).

Interesting.

Gareth, did you plan on this being an "all opposed" system then? Or an "only player rolls" system? Or what?

Mike

[contracycle]

At the moment is "active party rolls + narrates", all rolled against a static TN.  This produced a bit of an issue with order of action though; to mix it up a bit and to incorporate the bells and whistles I wanted a way fthat players could intervene in someone elses narration before the dice are rolled.  This in the hopes of avoiding assumption clash.  So the sequence of play I have in my head is: player gives statement of intent and calls for interventions.  Other players add dice, either bonus or penalties.  The active player takes one Detail for each added die by the adding player which is incorporated into the active players narrative.

Kinda like:

Player 1: "Right, I'm having that goblin with my Sword ability.  Any offers?"
Player 2: "I send fire elements to add you; have a die.  They look like whisps of smoke."
GM: "The footing is bad and the ground muddy.  Have two penalty dice".

The player is now rolling three dice more than their own pool, two of which are penalty dice.  They have to incorporate the slippery ground and get to exploit the smoke whisp in their narration.

Partly this idea is being exploited so that you are always adding dice to a pool, nice and concistent.  Partly its intended to give magic an interesting function, as this will be the major source of dice in side pools which can be so applied.  Or whatever Special Effects McGuffin is employed.  Not to put too fine a point on it, this is inspired by SA's in TROS.  There are some other implications in the Actio-Crisis model to do with how big die pools get and what you're rolling against yada yada.  It's coming along nicely; my Actual Play model seems to resolve a 5-participant fight in about 10-12 rolls, but I have not tested it comprehensively yet.  The one major implication in the penalty die system is that I think that side pool dice will often be given in big numbers to opponents who go first; the intervention structure is actually allowing such players to "act" in another players action (inpired by the wriggle effect seen in a recent FITM proposal).

And becuase I'm a rather old skool illusionist, I'm rather wary of unqualified authorial power; the penalty die system allows the GM-player to "scene set" to an extent.

[Mike Holmes]

Sounds like it'll work well to me. Gonna give us more details at some point? :-)

Mike

[contracycle]

Yeah I'll post it when I think its done.  Soon.  I just didn't want to clutter the boards with too many bits of work-in-progress.