I’m searching for information (or a model) that can give me accurate percentages concerning dice pools or related articles that display the proper math involved, (and %) that display skill check modifiers (or success/failure) per number. This sort of material would take into account not just a base number for success/failure, but cover material that maps the likely combinations of dice to reach a certain total. For instance, a dice pool concerning 2D6 would take into account the likely combinations of dice impact the results of a percentage towards a specific total:
Example: 2D6 Combinations.
2; total: One combination (one and one) possible.
3; total: One combination (two and one) possible.
4; total: Two combinations (one and three, two and two) possible.
5; total: Two combinations (one and four, two and three) possible.
6; total: Three combinations (one and five, two and four, three and three) possible.
7; total: Three combinations (one and six, two and five, three and four,) possible.
8; total: Three combinations (two and six, three and five, four and four) possible.
9; total:Two combinations (three and six, four and five) possible.
10; total: Two combinations (four and six, five and five) possible.
11; total: One combination (five and six) possible.
12; total: One combination (six and six) possible.
To clarify:
Rolling a single D6 has 1/6 numerical probabilities or values: 1,2,3,4,5, and 6. And no combinations in order to achieve these numbers: it’s a raw one in six chance to hit a specific number.
For example (to keep it simple) rolling a 1 (specific total) has a 1 in 6 chance.
However, rolling a 2D6 has 11 possible values, but 21 combinations to reach these specific values, which changes the math needed to accurately gauge the correct (%)chance when facing a specific number (skill check etc.)
Now for example rolling a 2 (specific total) does not have a 1 in 11 chance, but a 1 in 21 because of the possible combinations.
This is what I’m thinking, and by no means I’m-I a math guy. If I’m not thinking about this correctly, please set me straight and provide references where you can to support your thoughts.
Thanks-
Actually, when you roll 2d6, you have 36 (6 x 6) possible outcomes.
You can list them out: (1,1), (1,2), etc, then do the same thing with (2,1), (2,2) etc.
The chance of rolling snakeyes (two 1's) is 1/36.
The chance of rolling a sum of 3 is 2/36
A sum of 4 is 3/36...when you get to rolling a 7, it's 6/36.
Just write it out and you can get the whole distribution, then you can set up the probabilities properly, if that's your thing.
There are some online tools like anydice (http://anydice.com/program/20) that do what you are trying to do, the link is for 2d6.
Just to follow up the other posts, there are 36 diffierent combinations of result you can roll on 2D6. The number of combinations for each possible total are:
Total / Number of Combinations
2 / 1
3 / 2
4 / 3
5 / 4
6 / 5
7 / 6
8 / 5
9 / 4
10 / 3
11 / 2
12 / 1
So the chance of rolling a 12 is 1 out of 36, while the chance of rolling a 7 is 6 out of 36 (which rounds down to 1 in 6).
If you wanto to equal or beat a value, add up all of the combinations for the target value and higher. So, the chance off rolling 10+ is 3+2+1 = 6 out of 36, and so on.
To convert stuff into percentages, just divide the number of combinations by 36 and then multiply the result by 100. So the chance of rolling a 7 = (6/36)*100 = 16.666666 %
To work out the effect of a modifier, compare the number of combinations before and after the modifier is added. For example, needing to roll a 10+ has 6 combinations that will give a success (see earlier example). If you need to roll a 10+ but have a +2 modifier, then the combinations for rolls of 8 or 9 will also give a success, adding 5+4 = 9 combinations to the 6 you already had, for a total of 15 successful combinations altogether. Putting that into percenatages, the +2 modifier increases your chances of success from 16.6666% to 41.6666%.
Hope that helps!
Thanks for all the helpful input.
Appreciated.
Quote from: snooggums;732473There are some online tools like anydice (http://anydice.com/program/20) that do what you are trying to do, the link is for 2d6.
This is awesome!
The thing that you have to remember doing it this way is that each dice is separate, so for some of the combinations you're undercounting.
Think of having a red and blue D6. You will score a total of 6 on 2D6 if you roll:
Red 1 Blue 5
Red 2 Blue 4
Red 3 Blue 3
Red 4 Blue 2
Red 5 Blue 1
giving 5 combinations out of 36.
Anydice is great, and there are lots of fantastic tutorials on basic probabilities. For multiple events, a fruitful place to start is the probability tree, a nice graphical representation of all the possible outcomes. Look it up.
So a probability tree for 2D6 would have 6 options branches on the first roll, then the second roll gives each of those another 6 branches - total of 36 possible outcomes. You can then count up the number of times each sum result appears.
Probability trees also help with things like rolling over a threshold, or the number of times a value is rolled, or the probability of a certain number being the highest value rolled. They are also a good start to "getting" more complicated notions like Binomial Distributions and combinatorics. Look up Pascal's triangle as another good intro topic.
Quote from: J.L. Duncan;732527This is awesome!
One thing I only caught on from other people's examples was that you can do more than one at a time (http://anydice.com/program/356b).
The At Least button is really helpful for figuring out how likely it is for someone to hit a target number on a given roll as well.
Why is this here? It has fuck all to do with my forum. I'm moving it.
Quote from: RPGPundit;732697Why is this here? It has fuck all to do with my forum. I'm moving it.
Thank you.