Smaller Dice Advance

[Ancient History]

The argument about d4 vs d6 in the other thread kicked my brain in the ass. The problem in Savage Worlds and similar dice-step systems is that a character rolling an exploding d4 is more likely to succeed at certain rolls than a character with a d6. Math:

Target Number 6:
d4: a (1:4) chance of rolling a 4, explodes, (3:4) chance of rolling a 2, 3, or 4 - total probability is 25% * 75% = 18.75%

d6: a (1:6) chance of rolling a 6, total probability is 16.67%

So, an idea - instead of having dice steps and target numbers /increase/ with difficulty, why not have them decrease? A character starts out with a d12, and as they advance progress through a d10, d8, d6, d4. Simple target numbers might be pretty high - 10 or less, 8 or less, that sort of thing - and characters with very low dice would succeed automatically. Very difficult target numbers would be very low - 3 or less, 2 or less, etc.

[fectin]

Interesting, but it removes the excitement of exploding dice and gives nothing on return.

The probabilities are a bit wonky, but much less so than you think. I have it graphed out somewhere; I'll try to dig that out.

[fectin]

Okay. That's d4 vs. d6, exploding on the top two numbers. Top one had the same shape, but was much less emphasized.

[wotmaniac]

I did the probabilities for SW a while back ... HERE you go.

The way I have it figured, you could very well do a reverse step (i.e., "step-down") and "roll low", to remove the wonkiness.
To keep the same kind of dynamic, set the default TN to 3 (that is to say, a 3 or less would be success); and instead of modifying the TN, you'd modify the die result (i.e., add to it to increase difficulty). You might have to play around with the size of the modifiers, as a standard +2 might be a little weird.
I haven't tested explosions too much, but just off the top of my head ... you could have 1's let you re-roll, lowering any modifiers.

[spaceLem]

You can completely fix the problem by saying subtracting 1 before a dice explodes (so a 6 on a d6 is actually 5+reroll, and 6,6,1 would give you 5+5+1 = 11).

Probability of rolling 5
With 1d4: roll 4 then 2,3,4 = 1/4 * 3/4 = 0.188
With 1d6: roll 5,6 = 0.333

Probability of rolling 6
With 1d4: roll 4 then 3,4 = 1/4 * 2/4 = 0.125
With 1d6: roll 6 (=5, but upgrade to 6 with a 1) = 1/6 = 0.167

Probability of rolling 8
With 1d4: roll 4 then 4 then 2,3,4 = 1/4 * 1/4 * 3/4 = 0.047
With 1d6: roll 6 then 3--6 = 1/6 * 4/6 = 0.111

On the other hand, the wonkiness isn't really all that bad, and you still get a higher expected result (or number of raises) with a larger die.

[Username17]

You can completely fix the problem by saying subtracting 1 before a dice explodes (so a 6 on a d6 is actually 5+reroll, and 6,6,1 would give you 5+5+1 = 11).

No you can't. The problem is that the probabilities are completely wonky. The thing where probabilities actually make things better for smaller dice is just a relatively symptom. Variable TNs on d6s with exploding dice cause the increase in TN from needing a 5 to needing a 6 to reduce your hits per die by 50% and the increase from needing a 6 and then a 2 to needing a 6 and then a 3 to only reduce your hits per die by 20%. It's completely fucked.

The thing where d4s are actually better than d6s from rolling 6s is a really small part of how completely fucked the entire RNG is.

-Username17

[Murtak]

Even with substracting 1 it still scales weirdly

Code: Select all

TN	probability	reduction in success probability
1	100%	-
2	83%		-17%
3	66%		-20%
4	50%		-24%
5	33%		-34%
6	17%		-48%
7	14%		-17%
...repeat ad infinitum

Unless the change column looks smooth your system is wonky. The accelerated increase in difficulty in inherent to this type of system and resetting it gives you a sawtooth shape instead of a curve. And that won't work at all. You could conceivably use only part of the curve and reroll much sooner - say reroll 4, 5 and 6, then substract from the reroll based on what you the first result was - but that is much too confusing to use at a gaming table. But it would give you a smoother curve.

Code: Select all

1,2,3: use as rolled
4: roll again, add result -3 (minimum 0)
5: roll again, add result -2 (minimum 0)
6: roll again, add result -1

TN	probability	reduction in success probability
1	100%	-
2	83%		-17%
3	66%		-20%
4	50%		-24%
5	42%		-16%
6	33%		-21%
7	25%		-24%

This is probably smooth enough to use as a core mechanic. Too bad it's unuseable.



Edit: What Frank said, except look, shiny tables.

[spaceLem]

The problem is that the probabilities are completely wonky. The thing where probabilities actually make things better for smaller dice is just a relatively symptom. Variable TNs on d6s with exploding dice cause the increase in TN from needing a 5 to needing a 6 to reduce your hits per die by 50% and the increase from needing a 6 and then a 2 to needing a 6 and then a 3 to only reduce your hits per die by 20%. It's completely fucked.

Oh that. Well, the probability of success is monotonically decreasing, even if the derivative is not, so it's not a complete disaster. At the very least, it doesn't fail at having increased chances of winning (for any given TN) if you have a better die, and that's good enough for most people.

I once played a Unisystem game where the GM* replaced the d10 with a lookup table designed to give negative exponential failure rate. For every 10 you added, your chance of failure reduced by a factor of 10. It was very clever, but kind of fiddly (the fact he made it roll under too would have given you heartburn ).

* what does MC stand for again?

[echoVanguard]

Mister Cavern. A mistranslation of "Dungeon Master" from a Czech RPG system.

echo

[spaceLem]

Mister Cavern. A mistranslation of "Dungeon Master" from a Czech RPG system.

echo

Thanks -- I'd been wondering about that.

[wotmaniac]

Oh that. Well, the probability of success is monotonically decreasing, even if the derivative is not, so it's not a complete disaster. At the very least, it doesn't fail at having increased chances of winning (for any given TN) if you have a better die, and that's good enough for most people.

Another issue is variance.
Empirically (in RL, that is), all else being equal, the better you are at something, the less variance there will be; and the inverse is true as well.
This kind of disconnect between RL experience and the results of a step-die system (i.e., step-up) shatters the immersion for a lot of people.

[spaceLem]

Another issue is variance.
Empirically (in RL, that is), all else being equal, the better you are at something, the less variance there will be; and the inverse is true as well.
This kind of disconnect between RL experience and the results of a step-die system (i.e., step-up) shatters the immersion for a lot of people.

I had an idea for that (that I blatantly stole from a bunch of other people). The mechanic is roll 2d6; anything in your favour (e.g. skills, equipment, circumstance etc.) adds bonus dice, anything against you (e.g. opponent, bad conditions) adds penalty dice.

Bonus dice and penalty dice neutralise each other, and you take the best 2 (if you have bonus dice), or the worst 2 (if you have penalty dice), to get a result between 2 and 12. There is a table that describes the results, from worst possible outcome, to best possible outcome (and maybe has damage levels for combat).

This has 2 advantages.
1) the biggest variance occurs when a task is average difficulty, while the least occurs when you're really likely to succeed (or fail). This means that the random mook with 4 penalty dice is extremely unlikely to hurt you, while you have a pretty high chance of one-shotting them with a 12; they could get really lucky, but the chances are slim. However, when you're up against your rival, then the variance is highest, and you'll be looking for all the circumstances you can get to move the odds in your favour.

2) it's really quick, and the outcome is easy to interpret. Even when you're chucking 10 dice, finding the best/worst 2 only takes a second. You also get a (slight) bell curve, which is nice.

I'm sure there are problems with this (feel free to tell me), but I think it would be interesting to see where it would and wouldn't work.

[aseariel]

...anything in your favour (e.g. skills, equipment, circumstance etc.) adds bonus dice, anything against you (e.g. opponent, bad conditions) adds penalty dice.

It's not exactly the same as what you're describing, but this part in particular reminded me of the system Fantasy Flight uses for the Warhammer Fantasy rpg. There's an overview here, but the gist of it is that instead of numbers the dice have symbols that indicate things like success, failure, bonuses, penalties, and critical effects (both positive and negative). If you get net successes, you succeed. Net penalties, those apply, etc. Critical effects are a bit strange, and depending on what you're doing they may occur independently of your success or failure, and with some abilities you can get a positive and a critical negative effect if you happen to roll both.

I think they get a bit overcomplicated by adding in things like the potential for tasks to take more time, but that's also part of the whole risk/reward play they do with the reckless vs the conservative dice, a system which I do find interesting. I'm hoping to run a game sometime soon and see how the dice work in actual play, but I've found it interesting to look at regardless.


tldr; I've seen some custom dice that seem to work in part like what you're describing. I think the concept is neat, but have nothing else useful to contribute.