Idea for a dice system

[Doorhandle]

I've been thinking about this sytem for a while. It would allow players to choose how much spread they want in their dice rolls at any given time.

Basically, whenever they would make a roll, assuming they're not adding bonuses for whatever reason, they'd roll two dice: one negative , one positive. They'd then add the dice together to see what result they got.

However, they'd get to choose between 3 different dice sets:

Safe: 2 d4s, or perhaps 2 fudge die. Can't get very high or very low rolls, best used when you're almost guaranteed success and don't want to screw up.
Normal: 2 d6, or 2 d8 possibly. The acceptable amounts of risk and return.
Risky: 2d12 or 2d20. Will either go horribly wrong or horribly right. Best used when you have a slim chance of success anyway.

So I have a few questions;

>How could I figure out the proportions of each result (like the chance of getting 11 on Risky?)
> What target numbers would I need?
> Could I get the same levels of risk with less dice-rolling? It might slow the game a little.
>Should rerolls allow you to re-roll both dice in a pair, one of the dice in a pair, or both?
>I'm thinking that I'd only allow risky dice to have critical failures/success. What do you guys think about that idea?

[Kree West]

The risky dice basically have critical built in. As for the proportions of the rolls this (http://anydice.com/) works well. Type in next to 'output' "1d4 - 1d4", hit calculate, then repeat for the different sets. I think that some rerolls should effect the negative, some the positive, and some both. It would make game play more interesting. Finally, the two die wouldn't slow down gameplay if you had two colors, one for +, one for -.

[Doorhandle]

Thanks for the feedback!

Although looking at anydice, I seem to have created a normal distribution, making 0 very common which is the opposite of what I wanted for these dice. Hmm.

[Kree West]

If you want to have 0 not very common and the extremes common. This graph I found (not made by me) works for this, but it is complicated and might slow down gameplay.

[ace rooster]

What you are suggesting is functionally the same as subtracting the max value of the dice you choose to use +1, then adding 2 rolls. I think that might be simpler to implement.

ie modifier of 15 would mean one of 10+2d4 (15-4-1+2d4), 8+2d6 (15-6-1+2d6), or -6+2d20 (15-20-1+2d20).

To get the chances of each result we take the difference between the result and the modifer, subtract it from the size of the dice, and divide by the size of the dice squared. ie, on the d20 example a result of 17 would be 18/400 ((20-(17-15))/20^2). The chance of a result of more than a value we sum probabilities above that value, so for 17 again we get the sum of 1 to 18 over 400, which works out at 172/400, or 43%. This is a sawtooth distribution (straight line up to the middle, then straight line down again) rather than a normal. As you use more and more dice it will tend towards a normal though.

For a system like this to be meaningful then there must be at least 3 outcomes. If there are only 2 outcomes then the strategy is easy. If the result is above your modifier you use the largest dice you can. If it is below your modifier then you pick the smallest. If there is some sort of counterstrike mechanic then this might be relevent, and makes power attacks much more interesting.

That isn't very easy to follow, sorry. If someone wants to explain better then feel free.

[Doorhandle]

I have a vague Idea what you mean but that's WAY to hard to track outside of PBP.

I think I may simply the system a bit.

Safe: Roll 1d4/fudge. If you fail, you take the minimum possible failure. If you succeed, it's only a marginal success.
Normal: roll 1d6/1d8. Works as, well, Normal.
Risky: Roll 1d12/1d20. Possible to succeed with flying colors even beyond normal. However, If you DO fail with these die, you fail VERY hard indeed.

Ex. Jumping a cliff.
With safe, if you fail the jump you don't even leap; you lose nothing but time.
With risky, you can easily backflip over the cliff in the fraction of the time, but if you fail you launch yourself DOWN instead of across, with all the consequences that implies.

[CarpeGuitarrem]

Thanks for the feedback!

Although looking at anydice, I seem to have created a normal distribution, making 0 very common which is the opposite of what I wanted for these dice. Hmm.
The more dice you use, the more normal the distribution will be. :smallsmile:

The swingiest result would be simply to use a single die somehow.

[NichG]

The way you can get a swingy result is that you roll two dice (one negative, one positive), but the result is the more extreme value rather than the sum of the two. Ties can be zero. Adding more dice but always taking the most extreme value (e.g. 2 positive, 2 negative) will push the distribution even further towards the edges.

[jqavins]

What you are suggesting is functionally the same as subtracting the max value of the dice you choose to use +1, then adding 2 rolls. I think that might be simpler to implement.

ie modifier of 15 would mean one of 10+2d4 (15-4-1+2d4), 8+2d6 (15-6-1+2d6), or -6+2d20 (15-20-1+2d20)
Allow me to simplify this a bit. 1dN - 1dN is exactly equivalent to 2dN-(N+1). So 1d4-1d4 is the same thing as 2d4-5, 1d6-1d6 is 2d6-7, etc.

The average and most likely result from the dice is always 0; compare this to the average on a single d20 of 10.5, and you see that subtracting 10 from the DC for a d20 roll (if this is D&D3.x) would be a pretty good starting point. [No, I was wrong. See second edit below.]

I don't see any way of getting the same ability to choose a level of risk with less dice rolling, but if you use 2dN-(N+1) that really shouldn't slow things down at all.

For re-rolls to be of the same benefit as they are with a single die, I think you should re-roll both. If re-rolling only one, it makes no difference which as long as it's always the same. Allowing the player to shoose which to re-roll and leave the other alone would be much more powerful.

The chance of success, and how the chance is changed by the choice of die size, depends on the result needed for success. But in general, the chance of success will always be greater when larger dice are used. Therefore, what I'd suggest is a system where success is just success (or a single level of critical success may be allowed at a pretty high threshhold) but failures have badness in proportion to the amount missed by. So for the jumping off a cliff example, and let's say it's rather a low and easy cliff today, to land safely requires a roll of 5 or more with the Dex mod applied (comparable to a DC 15 Dex check.) The character has a Dex mod of +2, so needs 3 on the dice. If he gets the 3 he lands safely and that's that, but if he fails he takes damage equal to what he missed by. Rolling 2d4-5 gives a 1 in 16 (6.25%) chance of success and maximum possible damage of 6 points. (Worst possible roll is -3, which misses the required 3 by 6.) Rolling 2d8-9 gives 23.44% chance of success, but maximum possible damage of 10, and 2d20-21 gives a 38.25% success chance and 21 possible damage. (Thanks, Kree West, for the AnyDice link, which gave me these success chances real quick. To calculate the average damage in the event of a miss will take me a bit longer.)

EDIT:
FWIW, I calculated the average damage for the example above.


Dice Rolled

Chance of Success

Chance of Failure

Max Damage

Avg. Damage on Failure

Ave. Damage Overall



2d4-5

6.25%

93.75%

6

3.20

3.00



2d8-9

23.44%

76.56%

10

4.33

3.32



2d20-21

38.25%

61.75%

21

8.16

5.04




So, in this case, the player would probably be best off choosing the middle risk (or not jumping.)

SECOND EDIT: The chance of success for a DC 15 check with a +2 ability modifier is 40%. That means my method of subtracting 10 for the DC on this modified system is not so good. Lunch hour is over, so I'll have to get back to this later.

[Doorhandle]

The way you can get a swingy result is that you roll two dice (one negative, one positive), but the result is the more extreme value rather than the sum of the two. Ties can be zero. Adding more dice but always taking the most extreme value (e.g. 2 positive, 2 negative) will push the distribution even further towards the edges.

Hmmm... you may be onto somthing there.

I think perhaps normal and safe should remain with a normal distribution (because they're well, NORMAL.) And I use this system instead for risky.