Dice pool game design woes

[Morrus]

Here we go. We have a potential dice mechanic!

 

[Morrus]

I'm looking at those two tables, and it stirkes me as odd that simply adding exploding dice means the 50% chance goes from 'about' twice as many dice as the TN to exactly the same number of dice as the TN. That's making me think one of those two tables has to be wrong.

 

[clearstream]

Here we go. We have a potential dice mechanic!

View attachment 283596

As a space fight, it puts me in mind of lights on a display panel or HUD. The colouring could be reconsidered in that light.

You've probably already considered this, but are there likely to be any sight-related readability issues on the red-yellow scheme? There's a type of colour-blindness for which red looks more green and less bright... which seems quite close to saying it looks yellow.

 

[Morrus]

As a space fight, it puts me in mind of lights on a display panel or HUD. The colouring could be reconsidered in that light.

You've probably already considered this, but are there likely to be any sight-related readability issues on the red-yellow scheme? There's a type of colour-blindness for which red looks more green and less bright... which seems quite close to saying it looks yellow.

The colours don't communicate any information, they're just what I had handy for the playtest. One die type has dots, the other has numbers, which is the important difference. But no, the colours can be anything, so they won't necessarily be those colours in the final thing.

 

[Morrus]

I have made the dice ready for play testing!

 

[mamba]

I'm not sure I'm reading it right. If I'm reading it right, the table then looks like this:

those % are too high, there is no way one die has a 2% chance of exploding 5 times

 

[clearstream]

those % are too high, there is no way one die has a 2% chance of exploding 5 times

The % in anydice is 0.78. Less than 1%. I calculate it as lower still.

 

[clearstream]

@Morrus maybe this calculator does it [it does not, see edited edit]

Shadowrun dice calc

EDIT You enter 4 as your success number, and explode is fixed at 6. Choose "cumulative". However, there is no way to set a TN.

 

[mamba]

The % in anydice is 0.78. Less than 1%. I calculate it as lower still.

it certainly is lower than that: (1/6)^5 / 2, so 0.0000643 (to meet TN 6, exploding 5 times is twice that)

 

[pemerton]

This makes a too-small-by-one pool twice as likely to succeed at a task than an just-enough-to-succeed pool.

TN 2. 1 die = 50% chance, 2 dice = 25%
TN 3. 2 dice = 25%, 3 dice = 12.5%
...

Basically, you are replacing a 50% success die with a guarenteed 100% success.

In other words, it would often make mechanical sense to have a less skilled character try something to improve the chance of success, if you know the TN going in.

Though with 1 die you can't succeed vs TN 3 (0%) but with 2 dice you can (25%).

The way that Prince Valiant handles this is by (i) using a lot of opposed rolls, and (ii) not being a party-based game in which one character from a group of them "tries something".

 

[Blue]

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

I am having the darnedest time finding the free basic rules. Do you have a link?

 

[Morrus]

those % are too high, there is no way one die has a 2% chance of exploding 5 times

I rounded up from 1.56%. This is what AnyDice shows me. I think I must be reading it wrong.

 

[Blue]

It looks like you are pretty far into this, but just for completeness another thought hit me I wanted to post. Specifically about the "lower number of dice have no chance".

What about two types of dice, a "standard" and a "risky". Standard is what you've suggested. (Or maybe four success sides, but that's a different discussion.)

Risky has two success sides, but all of the successes are criticals that count as two. And it a "AND..." side, which if rolled will amplify the results. What I mean by that is that if you fail the whole roll, it's "No, AND..." and you suffer some additional consequence. But if you succeed, it's "Yes, AND..." and you gain extra effect.

When rolling, players make up the die pool from their choice of the dice. So something they are going to have a good chance on will likely all be standard. Or maybe they will throw in one Risky looking for the AND. Ones they can't succeed at without additional successes but are doing anyhow will likely be all Risky. Ones where it's an okay but not great chance (the majority of rolls) will really depend on the player and the situation - which is good, that puts a meaningful choice in there.

With 3/6 successful sides, Standard would add 1/2 a success on average, and Risky would add 2/3 of a success on average, with a higher maximum successes but more chance of nothing.

With 4/6 successful sides, Standard would also add 2/3 chance of success, so the benefit of Risky is increasing the maximum (which isn't important in a boolean succeed/fail where you already can make it), but with increased consequences either way.

 

[SpringRoll]

I think the problem needs to be tackled with a little lateral thinking, because changing the roll+bonus system into a dice pool really means changing the paradigm. It's not just a matter of arithmetic.

The advantage of using a pool is the immediate granularity of the results. Therefore, instead of establishing the number of successes required to satisfy a binary success/failure mechanism, I would use a fixed table that determines the quality of the action.
Number of HITS => Quality.
All '1' > Fumble
0 > Failure
1 > Failure or success with consequence
2 > Sufficient success
3 > Special success
On a single die you can aim for average to succeed poorly, which conforms to your character being poor in that area.
From the table above, decide for an average (look 4 is a good average).

The exploding die is "syntactic sugar", my players don't like it because it makes everything too unpredictable and simple. You can always hope for an extra HIT, which means having a lot of dice rewards even less. In fact, you have to consider that beyond a certain amount, adding more dice is less and less significant. With 6 exploding the gap between "poor" and "very good" is reduced even more. In my opinion, having limits helps to try more creative solutions.

The added advantage of the pool system is that you can easily adjust a lot of parameters, including the very way in which the player approaches the test, simulating "narrative" stuff. As an example, + 1 die if a personality trait conform to the action, convert a pool in a single "all in" die (simulating rush) or converting couple of dice into auto-hit (simulating carefull maneuvers). There's a lot one can figure out with a pool of dice, so reducing everything to % of success is very limiting.

As for the opposing actions, here too I suppose a paradigm shift is needed. Passive value roll is perfect for systems where you battle frequently and where you have a primary currency (HP) that gets eroded by context. You want thousand combat rolls and Saving Throws to be lightning fast, so you get back to what matters (choices and using wildcards).
I think a dice pool system should instead use opposing rolls, obviously trying to rationalize them. Subtract the higher HITs amount from the minor ones and determine the quality of the result. Increasing penalties for many defences in the round. A round-based death spiral. This slows down the combat phases, but it's not automatically a bad thing: the setting determines whether this part of the game should repeat itself often or not and being abstract or detailed.
So, in the end - to me is not just a matter of core mechanics, but of yours aggregated methods.

 

[Sacrosanct]

I rounded up from 1.56%. This is what AnyDice shows me. I think I must be reading it wrong.

View attachment 283646

Forgive me if I've totally gotten this wrong, but if I understand, when using a d6, the definition of exploding means you roll a 6, right?

So in order to get 5 exploding dice, you need to roll 5 sixes in a row, is that correct? And that would be defined as 6*6*6*6*6, or 1 in 7,776 chance.

 

[mamba]

Forgive me if I've totally gotten this wrong, but if I understand, when using a d6, the definition of exploding means you roll a 6, right?

So in order to get 5 exploding dice, you need to roll 5 sixes in a row, is that correct? And that would be defined as 6*6*6*6*6, or 1 in 7,776 chance.

yes, hence the chance for one die to meet a target of 6 is (1/6)^5 / 2 (the /2 because there is a 50% chance the last roll scores one point), or 0.00643% chance of this.

I have no idea what the percentages shown represent, but certainly not this.

 

[ruemere]

I am having the darnedest time finding the free basic rules. Do you have a link?

Apologies, I wasn't precise - the data is spread over a few freely available downloads.

Start with Creator's Kit:

Slayers Creator Kit by Gila RPGs

A toolkit for making your own content for the Slayers RPG.

gilarpgs.itch.io

Then head to Slayers by Gila RPGs, scroll down to Rules reference and character sheets. Between the two you get everything besides character creation and hunt design.

Go to
Slayers Third Party Content - Collection by Gila RPGs for third party content, some of which is pay what you want.

Good luck.

 

[Morrus]

So I found somebody asking a similar question which led me to another AnyDice script.

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com

Now, assuming I'm reading this one correctly we have:

TARGET NUMBER ->	1	2	3	4	5	6
1 die	50%	8.33%	1.39%	0.23%	0.04%	0.01%
2 dice	75%	33.33%	9.03%	2.08%	0.44%	0.09%
3 dice	87.5%	56.25%	25%	8.22%	2.29%	0.57%
4 dice	93.75%	72.92%	43.4%	19.68%	7.16%	2.24%
5 dice	96.88%	83.85%	59.98%	34.30%	15.86%	6.15%
6 dice	98.44%	90.63%	73.05%	49.32%	27.58%	12.96%

The numbers of the single die still don't look right to me though. Quick calculations using a spreadsheet for the odds of numbers of explosions:

# of explosions needed	is 1 in....	as a %
1 (TN 2)	6	16.66666667
2 (TN 3)	36	2.777777778
3 (TN 4)	216	0.462962963
4 (TN 5)	1296	0.07716049383
5 (TN 6)	7776	0.0128600823

So it's still not right. And if the single die row is wrong, they probably all are.

Hang on, I'm not counting the final die as not needing to explode and so it's 1/2 for a success not 1/6 for an explosion on that one. Dammit my head hurts!

 

[Morrus]

For one die the following results are a hit on TN 6 (focusing on that number as it's the extreme one):

666666
666665
666664

All of those are a hit. 5 explosions then 50% on the final die. Whip out a spreadsheet and work it through...

	1 in		1 in	1 in	%
TN	base chance	# explosions needed	chance of those explosions	and then 50% final roll	as a %
1	6	0	1	2	50.000
2	0	1	6	12	8.333
3	0	2	36	72	1.389
4	0	3	216	432	0.231
5	0	4	1296	2592	0.039
6	0	5	7776	15552	0.006

Aha! These are the same numbers as in the AnyDice chart in my last post. Which means I think that chart is actually correct!

 

[Miyagiyoda]

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.

This calculates 6s adding an additional die.

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com