Dice pool game design woes

[Morrus]

I'm tinkering with a dice pool system and have a stumbling block.

The system involves rolling a pool of up to 6 d6s with a 50% chance of 'success' on any given die (3 of the sides have a symbol on then, 3 do not).

The target number is a number from 1-6. The player is attempting to get a number of successes equal to the target number, which is usually a Defense score or something.

So, if an attacker has 3 dice in their attack pool, and the target defence score is 2, they'd roll the 3 dice and hope for 2 successes.

These are the basic odds:

TARGET NUMBER ->	1	2	3	4	5	6
1 die	50%	0%	0%	0%	0%	0%
2 dice	75%	25%	0%	0%	0%	0%
3 dice	87.5%	50%	12.5%	0%	0%	0%
4 dice	93.8%	68.8%	31.3%	6.25%	0%	0%
5 dice	96.9%	81.3%	50%	18.75%	3.2%	0%
6 dice	98.4%	89%	65.6%	34.4%	10.9%	1.6%

Sooo.... the basic problem is that any target number higher than your dice pool is an automatic failure. You can't roll 4 successes on 3 dice.

I'm trying to think of solutions to this before I jettison the whole thing and try something else. One is that maybe one of the sides on the attack dice is a critical success and counts as 2 successes? Or explodes? I've no idea how to calculate the odds for that though.

Crit x2 -- If a crit counts as 2 successes it just pushes the problem downhill. It makes it less of an issue, but now the impossible targets are those more than twice your attack pool.

Crit explodes -- If a crit explodes, the total is potentially 'infinite' so there are no impossible targets (which is good--there should always be a chance, however slim). But does anybody know how I calculate those odds into a table like above?

Alternatives -- make everything an opposed roll, so even on a pool of 1 vs a target of 6, there's a chance the defender will roll 0 successes. This slows things down a bit though, which is one reason I've never been super keen on opposed rolls, and the game does have a number of static target numbers for tasks which it would be thematically weird to make an opposed roll (the tree is opposing you climbing it?)

 

[Sacrosanct]

I think explodes is more fun than a crit success, but that's just me. It's because of the unknown I think, kinda like gambling. I remember when I was playing WFRP 1e and I decided to fight a minotaur in an arena when we just started. Statistically I was going to be meat. But I rolled 4 sixes in a row. I'll always remember the excitement around that. My math skills don't know the exact probability though. I only know the basics (rolling X on 3 dice = 6*6*6, or 1 in 216)

Alternatively, I prefer an opposed roll, kinda like RISK. That's what I'm doing in my current project. I use more than d6s, but essentially you roll your pool, and if you beat the highest result from the opponent/challenge, you win. I'm finding this to have a lot of flexibility, because situational modifiers are more than just "one bonus die". A minor boon might be a bonus d6, while a major boon might be adding a d12 to your pool.

This is basically what I think I've landed on:

And to answer your question how do I handle something impossible:

Boxcars!
If it is mathematically impossible for you to beat a TCN before anyone rolls their dice pools, you can invoke this rule. Roll 2d6, and if both dice come up as 6s, you succeed! Note that this rule only applies if the GM is using the Take Half rule above, because if the GM is rolling, there is always an opportunity (even very slim) that you might succeed.

 

[Thomas Shey]

You can't actually list the specific odds of completely open-ended dice rolls because the numeric possibles are infinite. The closest you can manage is to get a practical expected limit and ignore the ones above that. With D6, the chance of any given die getting a result above 24 (i.e. four 6's) is less than one in twelve hundred. You probably really don't care about even that result, let alone the one above it.

 

[pemerton]

Prince Valiant has a rule that if all the dice are successes, an additional success.

The Burning Wheel family of games have various rules which make 6s "open ended" ie each 6 adds another die to the pool, which is also open-ended.

Calculating the odds for open-ended dice is a bit tricky for the reasons @Thomas Shey gives, but some rough noodling around is possible.

Eg with 3D, the probability of no sixes is 5/6 cubed, so the probability of at least 1 six, ie actually counting as a pool of 4D+, is 91/216, or not much short of half. So it is a meaningful change to the possible range of outcomes.

 

[Bagpuss]

Sooo.... the basic problem is that any target number higher than your dice pool is an automatic failure. You can't roll 4 successes on 3 dice.

It's a feature not a problem. There solved it for you.

If they want to succeed they need to lower the TN some how, like taking extra time, or getting help.

To be honest I think that issue is the least of the problems looking at that probability chart, it isn't at all intuitive.

Having a skill of 5 out of six seems really skillful, but if the TN is 3 which sounds low, you only have a 50% chance of success, it moves up to 4, and you are very likely to fail. People with Skill 3, barely have a chance to succeed as TN, even though both sound average.

Adding things like crits explode and stuff like that makes it even less intuitive to understand.

 

[Morrus]

To be honest I think that issue is the least of the problems looking at that probability chart, it isn't at all intuitive.

Having a skill of 5 out of six seems really skillful, but if the TN is 3 which sounds low, you only have a 50% chance of success, it moves up to 4, and you are very likely to fail. People with Skill 3, barely have a chance to succeed as TN, even though both sound average.

Yeah, dice pools are notoriously hard to intuitively graps the odds. It's always been one of their biggest weaknesses.

 

[billd91]

Sooo.... the basic problem is that any target number higher than your dice pool is an automatic failure. You can't roll 4 successes on 3 dice.

I'm trying to think of solutions to this before I jettison the whole thing and try something else. One is that maybe one of the sides on the attack dice is a critical success and counts as 2 successes? Or explodes? I've no idea how to calculate the odds for that though.

Crit x2 -- If a crit counts as 2 successes it just pushes the problem downhill. It makes it less of an issue, but now the impossible targets are those more than twice your attack pool.

I don't think you've got a problem with that structure, per se. There's nothing wrong with the potential for there to be impossible tasks - as long as the rules you use to derive those success thresholds (the defense value) appropriately set the difficulty for the applicable skill being applied (attack pool). It's only really a problem if it's too easy to set a higher defense value than number of dice in the attack pool and that doesn't work for your goals in designing the system.

 

[Fenris-77]

Yeah, dice pools are notoriously hard to intuitively graps the odds. It's always been one of their biggest weaknesses.

30 odd years of playing Warhammer helps. I'm a big fan of exploding die pools. In your case I think I'd add one result per die that explodes and see how if feels.

 

[Morrus]

I don't think you've got a problem with that structure, per se. There's nothing wrong with the potential for there to be impossible tasks - as long as the rules you use to derive those success thresholds (the defense value) appropriately set the difficulty for the applicable skill being applied (attack pool). It's only really a problem if it's too easy to set a higher defense value than number of dice in the attack pool and that doesn't work for your goals in designing the system.

Part of the problem is that the attack and defense values are pretty much fixed (they come from somewhere else, and compatibilty is a design goal) so as-written, 'impossible' attacks (stuff like 2 dice vs a defense of 4 etc) would be common. As I can't alter those starting numbers, it's the actual dice mechanic itself which I need to play with.

 

[Temperantia]

So the idea is that there should be no impossible rolls even if the characters Dice pool is smaller than the Difficulty?
Maybe give the characters then a separate dice pool for the ones that they miss, but on those, only the 6s are counted as successes, not 4-6.
So if Player A has a pool of 2D and needs 4 successes in your example above they roll 2 dice where they need 4-6, and another 2 where they need to roll 6.
I'm not good enough to do the math on the probability, but it would not remain impossible

 

[Haiku Elvis]

I think the only way is to have successes be more than 1 per dice but that may defeat the purpose of a success or fail dice pool mechanic.
For example each six sided dice has 3 blank 0s and 1, 2 and 3 on the remaining faces.
That only leaves impossible rolls with a pool of 1 as two dice have a 1 in 36 chance of rolling two 3s to hit the 6 target.
Actually any one outcome on two dice is 1 in 36 so the example of a pool of 2 dice hitting a target of 4 would be 5 in 36 I think.
Wolfram Alpha can do the maths if you don't mind typing in the results one at a time.

 

[Sacrosanct]

Yeah, dice pools are notoriously hard to intuitively graps the odds. It's always been one of their biggest weaknesses.

For a designer, yeah. I might not be the best writer. And I'm a mediocre artist. But I do seem to have a good intuitiveness when it comes to figuring out dice pools and what odds feel right. In that case, I find it a boon, not a weakness, because when something isn't easy to figure out, it discourages optimization (looking to squeeze out every single + you can find).

Part of the problem is that the attack and defense values are pretty much fixed (they come from somewhere else, and compatibilty is a design goal) so as-written, 'impossible' attacks (stuff like 2 dice vs a defense of 4 etc) would be common. As I can't alter those starting numbers, it's the actual dice mechanic itself which I need to play with.

If you can't change the mechanic (I used opposed rolls above rather than static like it looks like you use), then I'd suggest exploding vs. crits.

When I was checking my math, I found this site was helpful.

Dice Probability Calculator

With this dice probability calculator, you can easily find the various probabilities related to rolling a set of dice.

www.omnicalculator.com

 

[ruemere]

@Morrus

I have toyed with a few dicepool mechanics in my Storyteller and Year Zero eras. Probably best implementation is to be found in Slayers (Slayers by Gila RPGs) - I cannot recommend enough the game. A must read for any modern dicepool designer.

Here are a few observations:

1. For heroic games use exploding dice (max die grants a reroll and potentially adds a success). There is nothing like the happiness on the face of a player who makes a narrow escape like this.

1.1 The exploding dice must be limited. The pools must be smaller than exploding dice size. Otherwise explosions make the game too unpredictable. Recommended limitations: explosions allowed only once per a maxed die. Explosions for d6 dice allowed only for pools of up to 5.

2. Keep the pools low, keep the thresholds low. This keeps results predictable (easy to score a basic success at a cost in), the players feel competent and confident (hated that constant failing in Blades games - people hated confrontations) and when needed, you can always up the difficulty for that final roll to suddenly skyrocket tension level.

2.1 Recommended pools are 3-5 for thresholds of 2 (routine, drive early to work task), 3 (challenges faced everyday, struggle to complete a project against a deadline without making too many mistakes) and 4 (making hard choices under pressure, facing bad consequences on fail - killing stuff on front lines while trying avoid getting hit). Threshold of 5 - keep it as a last resort for that badly wounded making a last ditch effort against all odds.

2.2 Why the low pools? Because it keeps the resolution fast. Why 3+ die for d6? Because fewer dice is too simple. Also, keep 3 or more dice so that you can easily grade success levels, produce successes for gauging contribution levels for multicharacter activities.

2.3 Why not use 6 as difficulty threshold? Because constant failing is unfun (hello Vaesen and other Year Zero games), because 6 should be epic, because it leads to ambiguities.

Again, please have a look at Slayers. The basic rules are free.

 

[Kannik]

If you’re tinkering with an existing dice pool system then this may be much more than you’re looking for, but I worked out a d6 dice pool system that I think works well to give a good handle on success probabilities for both players and GMs. (Along with a host of other things, including a simple method to include a margin of success system, you can see it in full here: The Aurora RPG Engine)

Roughly, these are the chances for success:

3d = 10%

3½d = 25%

4d = 50%

4½d = 66%

5d = 75%

5½d = 90%

(Note that a ½d is a d3)

At the table, most players will really only need to remember the values between 3½d and 5d; anything less than that is unlikely or impossible, anything above that is very likely to succeed. The system is also nicely visceral – with a fixed target number, the greater number of dice in hand always equates to a greater chance of success.

This system doesn’t solve your issue of what to do with ‘impossible’ rolls (ie, if you’re reduced to 3d or less), though there I find it can be a signal for the players to get creative, whether by getting help, researching more information, setting up other advantages or equipment, or by tapping a meta-currency for extra dice. But if there’s a desire for some chance of critical or lucky success, one way to do it would be to say that if three or more of the dice (round up) come up as 6s, then that counts at least as a bare success.

Again, this may be of little use for your current predicament if you’re tied to an existing dice pool system. Though perhaps the same kind of thing for ‘impossible’ rolls could be used: determine what the typical “lowest” pool that most characters would roll, and use that as the baseline to say that if that number of dice comes up as 6s, then it counts as a bare success. Could also include something like if the roll succeeds normally and that same number of dice are 6s, then it could count as an enhanced or critical success.

 

[darjr]

I like the idea above, always roll six dice. Sixes are always a success.

Your skill, a number between 1 and 6, determines how many dice are a success on a roll of 4-6.

So with a skill of 2 I roll
5 3 2 1 6 5
I can take the fives as success and the 6 automatically is. Three successes

 

[Bedrockgames]

I'm tinkering with a dice pool system and have a stumbling block.

The system involves rolling a pool of up to 6 d6s with a 50% chance of 'success' on any given die (3 of the sides have a symbol on then, 3 do not).

The target number is a number from 1-6. The player is attempting to get a number of successes equal to the target number, which is usually a Defense score or something.

So, if an attacker has 3 dice in their attack pool, and the target defence score is 2, they'd roll the 3 dice and hope for 2 successes.

These are the basic odds:

TARGET NUMBER ->	1	2	3	4	5	6
1 die	50%	0%	0%	0%	0%	0%
2 dice	75%	25%	0%	0%	0%	0%
3 dice	87.5%	50%	12.5%	0%	0%	0%
4 dice	93.8%	68.8%	31.3%	6.25%	0%	0%
5 dice	96.9%	81.3%	50%	18.75%	3.2%	0%
6 dice	98.4%	89%	65.6%	34.4%	10.9%	1.6%

Sooo.... the basic problem is that any target number higher than your dice pool is an automatic failure. You can't roll 4 successes on 3 dice.

I'm trying to think of solutions to this before I jettison the whole thing and try something else. One is that maybe one of the sides on the attack dice is a critical success and counts as 2 successes? Or explodes? I've no idea how to calculate the odds for that though.

Crit x2 -- If a crit counts as 2 successes it just pushes the problem downhill. It makes it less of an issue, but now the impossible targets are those more than twice your attack pool.

Crit explodes -- If a crit explodes, the total is potentially 'infinite' so there are no impossible targets (which is good--there should always be a chance, however slim). But does anybody know how I calculate those odds into a table like above?

Alternatives -- make everything an opposed roll, so even on a pool of 1 vs a target of 6, there's a chance the defender will roll 0 successes. This slows things down a bit though, which is one reason I've never been super keen on opposed rolls, and the game does have a number of static target numbers for tasks which it would be thematically weird to make an opposed roll (the tree is opposing you climbing it?)

I work with dice pools and they are challenge. Also be prepared for somewhat tougher marketing as dice pools do have their fans, but have a lot of enemies as well (some people simply don't like them). I think leaning into the side with 2 successes or more could work. You could even have a side with 3 or even four successes if you need. You would definitely want to run the probabilities though. I think you are also wise to focus on avoiding anything that causes it to lag or feel slow (that is definitely something that can happen if the dice pool system is too involved).

I think your best bet for calculating odds for the extra crits is finding the math genius in your group (or a resident math genius at En World?) and asking them or paying them to put together a spread sheet.

The exploding die is smooth. I kind of like that better because I feel it won't be as likely to get tripped up as the first option. Again, I would get a math genius to help you calculate (I've done this stuff myself and have found it is usually beneficial to get insight from a person who really understands math----I can do basic probabilities but I am definitely more of a language and music person). With dice pools though, especially if you are using d6s, the chances of hitting the exploding number really get big as the dice pool increases.

Also it isn't scientific but just try rolling the dice like 100 times and seeing what you get to get an idea for the feel of it. I find that helps in addition to having concrete numbers (something about seeing how often successes or critical actually come up, versus knowing the percentage chance gives me a better handle on things).

 

[clearstream]

I'm tinkering with a dice pool system and have a stumbling block.

The system involves rolling a pool of up to 6 d6s with a 50% chance of 'success' on any given die (3 of the sides have a symbol on then, 3 do not).

The target number is a number from 1-6. The player is attempting to get a number of successes equal to the target number, which is usually a Defense score or something.

So, if an attacker has 3 dice in their attack pool, and the target defence score is 2, they'd roll the 3 dice and hope for 2 successes.

These are the basic odds:

TARGET NUMBER ->	1	2	3	4	5	6
1 die	50%	0%	0%	0%	0%	0%
2 dice	75%	25%	0%	0%	0%	0%
3 dice	87.5%	50%	12.5%	0%	0%	0%
4 dice	93.8%	68.8%	31.3%	6.25%	0%	0%
5 dice	96.9%	81.3%	50%	18.75%	3.2%	0%
6 dice	98.4%	89%	65.6%	34.4%	10.9%	1.6%

Sooo.... the basic problem is that any target number higher than your dice pool is an automatic failure. You can't roll 4 successes on 3 dice.

I'm trying to think of solutions to this before I jettison the whole thing and try something else. One is that maybe one of the sides on the attack dice is a critical success and counts as 2 successes? Or explodes? I've no idea how to calculate the odds for that though.

Crit x2 -- If a crit counts as 2 successes it just pushes the problem downhill. It makes it less of an issue, but now the impossible targets are those more than twice your attack pool.

Crit explodes -- If a crit explodes, the total is potentially 'infinite' so there are no impossible targets (which is good--there should always be a chance, however slim). But does anybody know how I calculate those odds into a table like above?

Alternatives -- make everything an opposed roll, so even on a pool of 1 vs a target of 6, there's a chance the defender will roll 0 successes. This slows things down a bit though, which is one reason I've never been super keen on opposed rolls, and the game does have a number of static target numbers for tasks which it would be thematically weird to make an opposed roll (the tree is opposing you climbing it?)

The probabilities for exploding dice aren't so formidable, as the most successes you can benefit from are six. So long as you stop rolling when you succeed, and the TN is 1-6, the maths is straightforward. I'm not great at explaining it, but I'll make the table in Excel. The assumption is that a die explodes on a 6, so that a 4-5 is one success, while a 6 is one success + a third of one success (i.e. another 4-5) + etc...) As I'm in transit I'll likely do it over the weekend.

 

[bedir than]

Mayhap, use X number of autosuccesses for certain skill levels/attributes/etc

So the Character has a roll 3d with a +1 because they're god blessed and they need to hit the target of 4

 

[hawkeyefan]

Can you introduce an element that allows the player to add dice to the pool? Perhaps a Push mechanic? Or Assistance from other players? Or situational methods like high ground or flanking or what have you?

This leaves your math unchanged and possibly opens up other avenues of design. Which may be good or bad, depending on your goals.

 

[mr_monkius]

SuperSystem (and the various other games from the company) used the Goalsystem which used d6 dice pools.

You either were going against a fixed target number of successes or more usually as a contest against the defender who also rolled their defense pool.

When you rolled your pool:

• 4 or 5 counted as 1 success
• 6 counted as 2 successes

There were also various powers that let you get a certain number of rerolls. Those were shown as something like 5[2] which meant you got to roll 5 dice and could reroll up to 2 of them if you wanted.

Normally you would reroll failures. Although if you had something like 3[2] you might reroll a basic success if you needed more successes and had to try for the 6.

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