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Ashtagon
2018-01-12, 02:51 AM
For any given task, add the relevant attribute and skill together. For example, climbing a wall is typically Strength + Climb. This is the number of d6s that you roll. Any time a six is rolled, roll that die again, and add five to the total. The single best result is then compared against a Target Number (TN) for that task.

Example: Jack Carter, secret agent, is climbing a wall. He has Strength 2 and Climb 2, so he rolls 4d6. He rolls a 3, 4, 6, and 6. He rolls the two 6s again, and this time scores a 3 and a 6. He rolls that six one more time, and this time gets a 1. His final results with the four dice are 3, 4, 7, and 11. He reports a result of 11 to the GM.

Under this system, "ordinary humans" would typically have a score of 2-3 in a given attribute. Attributes would only improve under truly exceptional circumstances, although skills would have a freer scope for improvement. With a typical hand of four dice, you have the following odds:

6+: 52%
8+: 38%
10+: 20%
12+: 9%
14+: 5%
16+: 2%
18+: 1%

Any thoughts on how this might work in actual play? Is the maths involved too complex? Does it feel it descends into a dice-rolling festival? Does it lack potential for fine-detail? Anything else?

Composer99
2018-01-12, 02:57 PM
Example: Jack Carter, secret agent, is climbing a wall. He has Strength 2 and Climb 2, so he rolls 4d6. He rolls a 3, 4, 6, and 6. He rolls the two 6s again, and this time scores a 3 and a 6. He rolls that six one more time, and this time gets a 1. His final results with the four dice are 3, 4, 7, and 11. He reports a result of 11 to the GM.

I'm confused as to how Jack gets to 7 and 11 with the exploding dice. The rule you cite for exploding dice is:



Any time a six is rolled, roll that die again, and add five to the total.

Does that mean you ignore the die roll result and add five, only "proccing" it again if the die comes up '6' and explodes even more?

The 11 result I think I can make sense of with this rule: Jack rolled a 6, and then another 6, so adds 5 to the first roll. The third die roll is 1, so nothing is added. Final total is 11. Is that about right?

But I got nothing for the 7 result. Ought it to be a 6 only?



Generally speaking, it does seem a bit fiddly, although "add a flat number each time you roll another 6 on an exploding die" isn't that hard to remember. Is there some particular reason you wouldn't want to just add the die roll result of each exploding die to its original total? Doesn't make the maths work out the way you want?

One other general question: what is the objective of this resolution mechanic? By that, I mean, what real-life or plausible fantastic (*) scenario is it trying to model? What would you consider to be the typical range of easy, medium, and difficult target numbers?

(*) By fantastic I don't necessarily mean 'fantasy', the genre. Jack Carter, secret agent, could very well get up to feats of automobile driving, martial arts, parkour, or firearms operation that could qualify as fantastic if the game means to allow them.

lesser_minion
2018-01-13, 08:58 AM
Generally speaking, it does seem a bit fiddly, although "add a flat number each time you roll another 6 on an exploding die" isn't that hard to remember. Is there some particular reason you wouldn't want to just add the die roll result of each exploding die to its original total? Doesn't make the maths work out the way you want?

I'm fairly sure that would make it impossible to get a multiple of '6' as a final result.

In general, this system inherently has the property that you literally cannot be asked to make a roll that you cannot succeed at. If you're happy with binary success/failure or some sort of abstracted contest with "winner takes all" rules, it's probably fine, but it would be less effective for questions like "how long does it take me to open this door?" or "how much money do I make performing in the bar?"

Amechra
2018-01-13, 06:30 PM
In the example (if I'm reading the mechanic correctly), the final results would be 3, 4, 8, and 11.

1: He rolls a 3, 4, 6, and 6.
2: That turns into 3, 4, 5+1d6, 5+1d6
3: Rolling again, he gets 3, 4, 5+3, 5+6.
4: That turns into 3, 4, 5+3, 5+5+1d6
5: Rolling again, he gets 3, 4, 5+3, 5+5+1, for a final result of 3, 4, 8, and 11.

You can get multiples of 6 - if I roll a 6 and then follow it up by rolling a 1, my final result is 6. This kind of die system is essentially the only way to do exploding additive dice where you don't end up with discontinuities.

Probability-wise, each result shows up 1/6n+1 of the time, where n is that value divided by 5, rounded up. So yes, a feeble old granny with 1 die for Strength things could potentially beat a TN 18... but it would happen about once in every 324 rolls.

That granny chances of hitting a TN 5 would be one in three. TN 6 would be one in six, and TN 7 would be about five in thirty-six. Increasing the TN has some odd diminishing returns - Mr. 4 Dice would have a 93% chance of hitting TN 4, an 80% of hitting a TN 5, a 51% chance of hitting TN 6, and a 45% chance of hitting TN 7.

lightningcat
2018-01-13, 11:00 PM
While this is not a hard mechanic to understand, it is just different enough from most other core mechanics that you will want to use plenty of examples in the book. And you should have at least one section where you fully explain the mechanics, maybe with pictures.

Also, you will want a table of the TNs for easy, hard, stupid hard, etc. As well as a few tasks of that level. This will make it easier for GMs to figure out the TNs in such a way that they don't make things too hard or to easy.

It may be the first example of exploding dice where there is not that hiccup in the possible results, at least that I have seen.

lesser_minion
2018-01-14, 05:39 AM
It may be the first example of exploding dice where there is not that hiccup in the possible results, at least that I have seen.

Well, it was almost certainly designed to avoid the discontinuity.

This table gives the total dice pool needed to have an even chance of succeeding (as long as it's not too early in the morning). Adding the same number of dice again will halve the probability of failure (so if you have as many dice as indicated, your probability of failing is 50%, if you have twice as many then your probability is 25%, and so on).



TN
Dice pool requirement


2
0.39


3
0.63


4
1.00


5
1.71


6
3.80


7
4.64


8
5.88


9
7.97


10
12.13



The requirement is equal to log(0.5)/log(P(failure), if I'm remembering my logarithms correctly (you're trying to get the logarithm of 0.5 to the base of the probability of failing, so the base of the two logarithms doesn't matter as long as they're the same).

With an attribute rating of 3, you'd need 10 dice from skills and other bonuses in order to have a better-than-even chance of hitting TN10. The number of dice needed shoots up by a lot each time the number of sixes you need increases.

Calculating actual expected results for a given number of dice is waaaaaaayyyyy beyond my maths capabilities at this time in the morning on a Sunday (and they're more than a little rusty anyway). You might be able to express it in a form that can be summed as an infinite series, maybe?

Ashtagon
2018-01-14, 11:42 AM
I'm expecting typical TNs to be in the range of 4-8 for standard-hard tasks. As a rough guide, a TN 4 task in this system is a DC 10 task in D&D, then add +2 TN for each +5 DC.

I'm also envisioning that beating the TN by doubling it is a critical, and tripling it is a super-critical (and quadrupling the TN ia super-super-critical, etc.).


3.5e D&D - EDP (exploding dice pool)
10 - 4
15 - 6
20 - 8
25 - 10
30 - 12


Have a table...

https://orig00.deviantart.net/b69d/f/2018/014/0/a/exploding_pool_probability_by_ashtagon-dbzz0uy.png

jqavins
2018-01-15, 03:51 PM
Oooh, big numbery table. I think I'm in love! :smallredface: How about making a graph, chance of success vs. target number, with a curve for each number of dice. Or the other way: success chance vs. number of dice, with curves for each target number. (My excitement is becoming unseemly. :smalltongue:)

But, Composer99's is still an important question that you have not answered.
[W]hat is the objective of this resolution mechanic? By that, I mean, what real-life or plausible fantastic (*) scenario is it trying to model?
In other words: it's OK, but why?

Ashtagon
2018-01-15, 04:59 PM
Here are the odds of rolling each number exactly. I'm not happy with how janky the bell curve (or rather, lack of bell curve) is. I think I'm going to drop this concept.

https://orig00.deviantart.net/61da/f/2018/015/4/5/exploding_pool_probability_2_by_ashtagon-dc03ovl.png

lightningcat
2018-01-15, 08:59 PM
While there is definately not a bell curve to it. I think this could be a useful mechanic for lower power "realistic" style games. Maybe something of a investigative style game.
Maybe a CoC or a X-Files like game.