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?

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.

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.

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

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

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.

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

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

Mike Holmes wrote:
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.

wfreitag wrote:
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.

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

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

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.

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

Mike

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.

Contracycle wrote:
...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...

I'm just jumping in here, but to avoid this I adapted/borrowed an idea from Godlike.

I use two d10's... one for degree of success (Control) and another for the initiative roll (Speed.)

The dice are rolled against a TN and then the dice are assigned. The highest Speed has the first option to act/narrate. They can choose to act at a later Speed by interrupt before any other participant begins their turn to act/narrate.

Is some variation on this something you can use?

Sparky