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