2d6 mechanic options

I don't know if i have an answer for you, but how comparable are the numbers between the skill and target# ? If their values are very similar, then wouldn't you be leaving most of the outcome to chance? This may or may not be your intention...

Howdy all,

I'm going to be a pedantic wonk for a moment:

The distribution you get with an infinite number of 2d6 rolls is not a bell curve. It's more like a pyramid.

* 2
** 3
*** 4
**** 5
***** 6
****** 7
***** 8
**** 9
*** 10
** 11
* 12

You need to use at least 3d6 to start approximating a bell curve.

This is actually relevant, though. There's a difference between a "pryamoidal" distribution and a bell curved distribution. So if you're really looking for a bell curve, consider shifting to 3d6. If you're looking for a center-weighted distribution with evenly sloping decreased odds toward the extremes, then 2d6 will work fine.

Sorry to wonk out like that. Thanks for listening.

3d4 will give you more "bell" than 2d6, just in case you want to stick with the 12 max output.

Keep thinking!

Not knowing the game's theme or how the mechanic fits into the game, it would be hard to say which of the three methods is better.

I'm not sure of the effect you're looking for. Are you trying to normalize your results to be in a specific range (ie: 1-6, 2-12, 3-18, ...), or is it that you want to evenly match skill to target?

When you mention bell curve, is it that you only want to eliminate the 1d6 situation where all outcomes have equal probabilities, or do you really want that warping effect you get from a bell curve? Bad question, but I hope you know what I'm driving at.

Here's a generalized answer that might satisfy the questions above. But first we need to nail down some of the things you're looking for. You mentioned 2d6, so I'm going to assume you want an outcome in the range 2-12. Let's say SKILL is the BONUS number of dice you add to the base 2 dice you're rolling. So if you had a SKILL of 1, you would roll 3 dice total (2DICE + 1BONUS). For you're outcome, you only count the top 2 DICE. That way you'll always normalize the result to be in the range 2-12. As you may guess, the more BONUS dice you add, the higher the probability is of getting a better score.

As for balance with TARGET, modify the process above by subtracting TARGET dice from the BONUS. So the total dice you roll will be DICE + SKILL - TARGET and you'll count the top number of DICE in that roll.

If you want a quick visual, clink on this link:

http://anydice.com/program/2d8

You'll see how the higher BONUS will shift the bell curve.

Now for some tweaking. If you want a slightly more granular curve, change the DICE parameter to 3.

You'll notice that I only looped over the possibility of adding up to 4 extra dice. That means I only considered the situation where that largest difference between SKILL and TARGET will be 4. If you're designing for a larger range, then tweak this setting to get your effect.

Lastly, you'll note I have a POINTS setting. Let's assume you want to really limit your outcome values. Between 2-12 is to much. One solution is to use d4 dice instead of d6. Replace the POINTS range of {1..6} with {1..4}. This will give an outcome range of 2-8.

Still not good enough? Now you're getting into the tweaking I did with my game. Try a weighted dice mechanic. I wanted the effect of a 3 sided die (ie: d3). Here's an interesting example of using 3+ dice to achieve an outcome in the range of 0..6 with an average outcome being 3:

http://anydice.com/program/2da

As a final example of tweaking: If you want to minimize deviation from an expected outcome, try weighting the dice more. Take the first graph in the last example. It's a bell curve with an average outcome of 3. What if you want that bell curve to be more pointy. Meaning you want less deviation from that average of 3. The solution is to weight the d3 more towards the center. Since we're really using a d6 die to achieve this effect, try weighting the values as:

POINTS: {0:1, 1:4, 2:1}

Basically saying you have 1/6 chance of getting 0 points, 4/6 chance of getting 1 point and 1/6 chance of getting 2 points. It's a nice effect:

http://anydice.com/program/2db

Another favorite weight scheme is 3/6 chance of 0 points, 2/6 chance of 1 point, and 1/6 chance of 2 points. This of course doesn't give even point distribution, but it's an easy way to shift outcome without adding tons of dice and crazy mechanics.

I'm not sure I followed the last example well, but here's my take on comparing options #1 and #2:

http://anydice.com/program/2dd

If the link didn't work, just go to http://anydice.com/ and Calculate this:

output 2d6 - 2d6
output 2d6 - 7

From the two tables, you can see the distribution. As pointed out, the 2d6 vs 2d6 is just a comparison of one roll beating another. However, the distribution is pretty good.

What's interesting is comparing the two mechanics. As also pointed out, reducing the roll for defense will simplify the game and make it less tedious. As you can see from the tables, you don't sacrifice much.

In a 2d6 vs 2d6 match, there's an 11.27% chance you'll get a tie. You can either give the tie to the skill or the target. It's not much, but it does have influence. If you want exact even odds, then do a re-roll on ties.

In a 2d6 vs (target - 7) situation, there a 16.67% chance of a tie.

What gets interesting is when you change the "Odds" output to display "At Least". Now you can really compare the results. You can see that 2d6 vs (target - 7) is a pretty good estimate for the 2d6 vs 2d6 scenario.

Yes, that was the same conclusion I came to with my game.

Something else you may want to consider is the choice of using 2d6 vs 1d12. The 2d6 will give that bell curve. That's great if you interpret the results as, "If I get an X, I win". But if you want to interpret the results as, "If I get an X or less, I win", then I strongly suggest looking into a single d12 or even a d20.

AnyDice being your friend now, compare these results:

output 1d12
output 2d6
output 3d4

Put it on graph and change the view to "At Least". The results are pretty obvious to some, but I was surprised. I never thought of the multiple dice vs single die situation.

The big problem with multiple dice is that die roll modifiers act so strange. If you need to roll a 12 to hit a +2 drm will make a small difference in absolute numbers (still very unlikely). If you need to roll 8 or higher to hit a +2 drm will make a huge difference. The same of course goes for target numbers in this example, that if the difference between the target number and skill is around 7 a small change will have a big effect.

A nice variation is to roll two d6 as a d66, reading one die as 10s. But it might only work well if you can easily look up the target number somewhere and there are no modifiers, since it is no fun to do addition or subtraction on those numbers (16 + 1 = 21...).