# 2d6 mechanic options

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Relexx
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Joined: 05/31/2010

For one of the games I am currently in the process of brainstorming, I am considering using 2d6 as a mechanic. I am planing on using it for skill test. The three options I have come up with are as follows

1. skill + 2d6 vs target# + 2d6
This creates a direct comparable result of skill vs target#

2. Skill + 2d6 vs target#
The difference here is the target# in 1 would need to be increased by 7 (average result of 2d6) and is no directly comparable to a skill level

3. Skill + 1d6 - 1d6 vs Target#
This way the skill is still directly comparable to the target#

So the question comes down to what would be prefereable, I still wish for the bellcurve that 2d6 offers.

red hare
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Joined: 11/09/2009
I don't know if i have an

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...

Relexx
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Joined: 05/31/2010
that is why I want to use

that is why I want to use 2d6, as while there is still an element of change, it is a bell curve so the results are more predictable, and a lot less random than linear dice (ie 1d6)

InvisibleJon
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Joined: 07/27/2008
Being a probability wonk for a moment...

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.

hulken
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Joined: 04/18/2009
Me personaly would not go

Me personaly would not go with dice at al. I played a game with a simular system but the skill, 4 difrent ones, was 1, 2, 3, 4 and you roled 1 dice and ad it vs. target + 1 dice. du to the fact that the skill was so low the impackt of the dice role was so high. And the game realy sucked becaus of this and other factors but this was a big part in it. Just think about it the best skill is 4 and the weekest one is 1 comeone then you do not realy have abest or worst skill.

We al agreed on that the impact of the dice was to big, so if you do decide to use dice be aware of this. Two ways to reduce the impact of the dice is to ither reduce the randomness of the dice (use a dice with 2,2,3,3,4,4 for an example) or to simply have the skill value very high so that the outcome of the diceroal onley gives it flavour.

But this is onley becaus I do not like this sort of randomness, I think it have to much impact on the game and the outcome. But that is just me. Good luck to you in youre future endevors and keep us posted here on which way you go.

Pastor_Mora
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Joined: 01/05/2010
4 sided dice

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

Keep thinking!

Relexx
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Joined: 05/31/2010
Since we have been somewhat

Since we have been somewhat distracted by the term bell curve. I would still like some opinion on which option for dice roles is preferable.

red hare
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Joined: 11/09/2009
some chance is good

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.

SiddGames
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Joined: 08/02/2008
#2

I think the second option is preferable, especially if players are rolling against "the game" and not against each other. Putting 2d6 on both sides of the equation just wastes time with superfluous rolling, IMO.

releppes
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Joined: 09/17/2010
similar dilemma

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.

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.

stubert
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Joined: 01/26/2009
Only the second option mimics a bell curve...

THE CHANCE THAT ONE 2d6 ROLL WILL BEAT ANOTHER...

If you roll a XX - you will have a XX% chance of winning...

2...0.00%
3...0.16%
4...0.71%
5...1.90%
6...3.97%
7...7.14%
8...8.33%
9...8.25%
10...7.14%
11...5.24%
12...2.78%

The reason that you only have a 2.78% chance of winning with a 12 is that you actually have to ROLL a 12, which has a 1/36 chance of happening. The sum of these (which accounts for all possibilities), is 45.63%.

This only accounts for one roll beating the other. There is actually a 4.37% chance that you will both roll the same number (making the odds 50-50). If you reroll on ties, the chance that you will win becomes 50%, which pretty much negates the reason you have a +2d6 function in the first place.

If you win on ties, the curve shifts only slightly in your favor, which culminates in a total that gives you a 57.22% chance of winning (with the following breakdown):

2...0.08%
3...0.48%
4...1.43%
5...3.17%
6...5.95%
7...10.00%
8...10.32%
9...9.52%
10...7.86%
11...5.56%
12...2.86%

Without making it a deviation from 7, there is no bell curve, and no way to make rolling something improbable like a 2 as good as something equally as improbable like a 12.

If you are adding the result to some static number and comparing it to another number, you must calculate the difference between these two numbers against your die roll.

This makes only half of a bell curve (high percentages with low deviation in the beginning, mid-range percentages with high deviation in the middle, and low percentages with low deviation at the end), whereby:

the chance of winning if the difference is XX is XX%

1...100%
2...97.2%
3...91.7%
4...83.3%
5...72.2%
6...58.3%
7...41.7%
8...27.8%
9...16.7%
10...8.3%
11...2.8%
12...0.0%

Adding 1d6, then subtracting 1d6 is not advisable, as it provides volatile results that over a long enough timeline negate their validity and purpose. The only reason I can see with NOT going with the second option is if there is a way to somehow negate the minus die in the third scenario under certain circumstances - but without knowing what the theme of the game is, I wouldn't know where to begin...

Long story short, go with the second option if you're looking for bell curve results.

releppes
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Joined: 09/17/2010
slightly simpler comparison

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.

Relexx
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Joined: 05/31/2010
Thanks

Thanks all for the stats and examples.

I think the final conclusion is Skill+2d6 vs Target as it gives a close approximation to 2d6 vs 2d6, with out the additional complication of two sets of rolls.

ps I love anydice now ...

releppes
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Joined: 09/17/2010
Relexx wrote:Thanks all for

Relexx wrote:
Thanks all for the stats and examples.

I think the final conclusion is Skill+2d6 vs Target as it gives a close approximation to 2d6 vs 2d6, with out the additional complication of two sets of rolls.

ps I love anydice now ...

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.

pelle
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Joined: 08/11/2008
What I dislike, as a player,

What I dislike, as a player, about 2d6 + skill vs target (the system used in Conflict of Heroes) is that there is too much information to keep in my poor old brain. I prefer to shuffle the numbers around so that you can calculate a hit number (skill - target, most likely) and hit by rolling that or lower. You can get exactly the same probability, but the player only need to keep one number at a time in mind. It also makes it a bit quicker to see how likely a hit is (ok, not much, but if you have many options to consider it still helps).

Maybe that's just me though? CoH is a very successful and popular game, so I guess it isn't much of a problem. I'm probably in a minority. :)

pelle
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Joined: 08/11/2008
The big problem with multiple

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...).

Relexx
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Joined: 05/31/2010
pelle wrote:The big problem

pelle wrote:
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.

You are correct, but then again as a game designer you need to be aware of these. In the 2d6 case, you need to remember that 7 is the natural average, and percentages of rolling higher or lower values.

I do have motives for having multiple dice, player progression is based upon probabilities, in fact the whole game is based upon probabilities.
One of the options I am looking at is awarding advancement points. Each advancement point allows you to see if you can advance one of your skills. Roll the dice (2d6) if it is higher than your current skill level, increase your skill 1 level. This way, low skills advance fast, and higher skills are more difficult. Hopefully increasing game longevity.