Two Versions of a Dice Mechanic

[Manxome]

I've got two alternative ways for a die roll to work. I'd like opinions on which seems easier to understand or to use.

Background (both versions): When you are attacked, you roll a number of six-sided dice equal to your defense pool. Each individual die that meets or exceeds a target number (usually 5) counts as a "hit". You count up your hits and compare to a small table to determine the result of the attack (e.g. 0-1 hits means a mortal blow, 2-3 hits means a heavy blow, 4-5 means a light blow, 6+ means a glancing blow).


Option #1: For each wound you've taken, you reroll one of your dice that comes up as a hit. Keep rerolling the dice until you've made one reroll per wound or you have no hits left to reroll.

Option #2: For each wound you've taken, you add one extra die to your defense roll, but subtract one hit from the result (to a minimum of zero). For example, if your normal defense pool is 8 and you have 3 wounds, you roll 11 dice, but then subtract 3 from the number of hits you roll.


Both options are statistically equivalent; I just want to know which one seems easier to learn/play with.

[TarkisFlux]

Option two looks significantly faster to resolve and doesn't involve tracking (potentially) multiple re-rolling steps.

[PhoneLobster]

Where is the "neither" option?

[Josh_Kablack]

Background (both versions): When you are attacked, you roll a number of six-sided dice equal to your defense pool. Each individual die that meets or exceeds a target number (usually 5) counts as a "hit". You count up your hits and compare to a small table to determine the result of the attack (e.g. 0-1 hits means a mortal blow, 2-3 hits means a heavy blow, 4-5 means a light blow, 6+ means a glancing blow).

So you're expecting people to roll pools of up to 18d6...

IMX, more than about 10-12 becomes problematic in tabletop for resolution time, as well as table space, and even available dice if any players are picky about "MY dice" issues,

[Username17]

It looks like people are expected to soak with way more than 18 dice. Since you're going to be increasing Glance threasholds for injuries, I can only conclude that monsters that are "tough" are supposed to be rolling 30 dice or more. Seems like a lot.

-Username17

[Manxome]

The wound table numbers are crap because I haven't done all the math yet, but I'm expecting defense pools on the order of 8 dice, and wound totals to get in the vicinity of 4-5 before people die, so I will tweak the table until I get close to that. There may also be something like clue tokens from Arkham Horror, but I still expect rolls to cap out around 15 dice, and typically to be more like 10 (or less).

As a rule of thumb, "glancing blow" means no effect, "light" is 1 wound, "heavy" is 2 wounds, "mortal" means you die. It's loosely based on the CAN discussions from TNE.

Monsters don't roll dice at all, but the kind of monster attacking you determines the table you roll against; stronger monsters require more hits on your defense roll for the same result. And it's for a board game, so numbers don't need to scale much.

[JonSetanta]

I don't like absurdly large dice pools, but my reason for voting #1 is that it seems quicker.

I've done similar with WH40k and it is indeed easy and fast to grab a die and drop it again. Helps to have lots of d6s though.

Polls are a great way to gather info here. I'm glad we have them.

[Sashi]

#1 is less deadly.

For Option 1, as wounds -> pool size, average successes/die converges to 1/9

For Option 2 it converges to 0

It doesn't start to diverge until around wounds = pool/3, though.

[Manxome]

#1 is less deadly.

For Option 1, as wounds -> pool size, average successes/die converges to 1/9

For Option 2 it converges to 0

It doesn't start to diverge until around wounds = pool/3, though.

Um...no. You're way off in the weeds here.

First, checking limits as wounds approach pool size doesn't make sense conceptually. Under option #2, pool size is a function of wounds; they do get closer as wounds increase, but you're effectively taking the limit as wounds go to infinity, while you're taking some other limit for option #1.

Secondly, you seem to be neglecting the fact that a single die can be rerolled more than once under option #1. For example, if your initial roll only gets 1 hit, and you have 5 wounds, you have to reroll that single hit five times (or until it's no longer a hit). The average hits per die drops below 1/9 even before wounds = dice pool.

Thirdly, this is a discrete system, so talking about limits at any point other than infinity doesn't actually work in the first place; there always exists some epsilon such that no calculable value of the function is within epsilon of the "limit" before the input equals the value you're trying to take a limit at, so formally, no limit exists (or, alternately, every number is the limit). You should just talk about the actual precise answer for any other point.

Both systems converge to an average of zero hits as wounds go to infinity. Neither of them averages zero for any finite number of wounds, because there is always nonzero probability of rolling more than zero net hits, and zero probability of rolling less than zero hits, so the average has to be more than zero.


So look, if it'll help you focus on the actual question (ah, who am I kidding?), here's the proof of equivalence:

Consider option #1, and suppose that you have at least 1 hit left at the very end. We know that every wound triggered the reroll of a die, because otherwise you wouldn't be done (you'd still need to reroll one of your remaining hits, and you have at least one). Therefore, every wound resulted in replacing one hit with the result of a new die roll: you've rolled a total number of dice equal to your initial dice pool plus your number of wounds, and each wound has negated one hit. So that's exactly equivalent to option #2 (you rolled the same total number of dice, and discarded the same total number of hits).

Now suppose you're using option #1 but you end up with zero hits. It's possible that some wounds were never "used": for each reroll you didn't use, option #2 would have resulted in rolling 1 additional die and subtracting 1 wound, compared to what you actually did. But that means that the highest possible result under option #2 is zero hits (because even if every extra die resulted in a hit, you're subtracting a number of hits equal to the number of extra dice). Since zero is also the explicit minimum result of the system, the roll under option #2 must have been exactly zero, which means it's the same as the result you got using option #1.

[Akula]

I would need nailed down values for the results of hits, and what each wound level does, before I could comment about which of the dice systems I like more. Expected dice pool size should also be given.

Because right now people seem to just explode in a hit or two with either system. The system doesn't matter because, barring exceptional luck, that 8 pool guy is going to get 2-3 hits then get 3 wounds and then go down to about 1 or 2 hits under either system. The 3rd attack is almost certain to kill someone with a dicepool of 8. Which is what you stated you wanted an average dice pool to be.

[Sashi]

Secondly, you seem to be neglecting the fact that a single die can be rerolled more than once under option #1. For example, if your initial roll only gets 1 hit, and you have 5 wounds, you have to reroll that single hit five times (or until it's no longer a hit). The average hits per die drops below 1/9 even before wounds = dice pool.

You are correct, I did miss this part. And I was also loose with my math terminology.

You're wrong about the average not hitting zero, though.

Each die in the pool is worth 1/3 of a hit, and each wound adds a die and subtracts a hit, so when wounds equal half your starting pool you average zero hits. If you round all the negative results to 0, then the "practical average" will be nonzero, but your statistical chances of getting even one hit hit "basically nil" (what I meant by "converge") once wounds = initial pool.

[Manxome]

I would need nailed down values for the results of hits, and what each wound level does, before I could comment about which of the dice systems I like more. Expected dice pool size should also be given.

Because right now people seem to just explode in a hit or two with either system. The system doesn't matter because, barring exceptional luck, that 8 pool guy is going to get 2-3 hits then get 3 wounds and then go down to about 1 or 2 hits under either system. The 3rd attack is almost certain to kill someone with a dicepool of 8. Which is what you stated you wanted an average dice pool to be.

It certainly says something about this board that when I ask a simple question about which procedural instructions are easier to understand and follow, I mostly get posts attempting to analyze the game balance of the system. Despite specifically and intentionally not providing enough information to do so.

If you're all very good and don't drive me into the loony bin first, I'll post the real numbers for you to shit all over at some point after they actually exist. But for the time being, you're completely missing the point.

You're wrong about the average not hitting zero, though.

Each die in the pool is worth 1/3 of a hit, and each wound adds a die and subtracts a hit, so when wounds equal half your starting pool you average zero hits. If you round all the negative results to 0, then the "practical average" will be nonzero, but your statistical chances of getting even one hit hit "basically nil" (what I meant by "converge") once wounds = initial pool.

No, I'm precisely and provably correct. You're talking out of your ass because you apparently don't know what words like "average" mean.

The median result reaches zero somewhere around the time wounds reach half of your defense pool. Which means that your odds of dying to the next attack reach 50% around that point if you only die on a zero.

Which sounds like pretty much exactly what I want, since I said I expected defense pools around 8 and wanted people to die around the time they have 4-5 wounds, which is, shockingly, around half their defense pool.

Of course, the real story is more complicated because there are a bunch of game mechanics that I haven't told you about because that's not the point of the thread.

And, incidentally, the average tells us basically nothing about how the system will perform, because the number of hits is put through a threshold filter before it's used for anything. The only reason your previous calculations of average were even tangentially relevant was because you were using them to argue that the two options produced different distributions (which, incidentally, they do if you ignore the "minimum of zero" part).

[Akula]

It certainly says something about this board that when I ask a simple question about which procedural instructions are easier to understand and follow, I mostly get posts attempting to analyze the game balance of the system. Despite specifically and intentionally not providing enough information to do so.

If you're all very good and don't drive me into the loony bin first, I'll post the real numbers for you to shit all over at some point after they actually exist. But for the time being, you're completely missing the point.

Okay, I'm with Phonelobster, both systems are too complicated and will slow down combat. I would favor the second though, because the first is always going to add extra time because you cannot avoid rerolling after your initial roll. Where as the second is merely almost always going to slow things down because people will have to change their dice poll size and then perform an extra calculation; which they might be able to do quickly, if they are on the ball all the time. I would favor a system that added one extra step.

[Zinegata]

When you are attacked, you roll a number of six-sided dice equal to your defense pool. Each individual die that meets or exceeds a target number (usually 5) counts as a "hit". You count up your hits and compare to a small table to determine the result of the attack (e.g. 0-1 hits means a mortal blow, 2-3 hits means a heavy blow, 4-5 means a light blow, 6+ means a glancing blow).

Clarification:

How does the attack work though? Is your defense ability constant regardless of the attack, or is there a way for attacks to reduce your defense pool?

[Sashi]

Manxome, I apologize, I'm not making sense because I'm using rules of thumb as if they're statistical rules, and that's wrong. Also, I didn't mean to "shit all over" your thread. My first comment should have been on why I voted how I did, not statistics.

Question: I don't get how you're using 'average' and 'median' in this sense. Could you explain?

[Username17]

It certainly says something about this board that when I ask a simple question about which procedural instructions are easier to understand and follow, I mostly get posts attempting to analyze the game balance of the system. Despite specifically and intentionally not providing enough information to do so.

Well as presented, both mechanics appear to be basically unplayable. You're talking about rolling 4 dice with a TN of 5 and having your hits rerolled if you get hit with a large attack. Since you only expect a hit or two, having a hit or two rerolled will leave you with no hits most of the time. Sounds very similar to the "one hit point" system common to mass combat games, but with more die rolling.

Without seeing more of the system, I would provisionally want to vote "neither" just like Phone Lobster. The amount of dice in the pool before that mechanic would start being interesting and stop being "you explode all the time" is large. Much larger than the amount of dice I am comfortable rolling.

-Username17

[Manxome]

Is that supposed to be hyperbole, or are you just ignoring everything I say in favor of pulling weird numbers of dice out of thin air?


Though having done a bit more of the math, now, it does look like I'm probably better off setting the TN to 4 instead of 5; at a TN of 5, I don't seem to have much flexibility to adjust the target numbers to represent different powers of attacks without going outside of my desired parameters.

But at TN 4, with a defense of 8 dice, against threshold numbers of, say, 2/3/6, it takes an average of 4.6 attacks to kill a PC. That looks like a pretty reasonable baseline; it's roughly what a medium-armor hero gets in Descent. Kill chance (for a single attack) starts at 4% and reaches 50% when you've got 5 wounds.