what is a formula for working out dice chance percentages? I am not a student or a maths type person. Instead I play a lot of board games and one in particular. Arkham Horror / Eldritch Horror. It uses a dice system to calculate successful rolls and I would love to know a formula for that which I could make into a simple app for my phone. 
Basically a successful roll is a 5 or a 6 from a 6 sided die. Though there are ways to modify the dice pool and the test may ask for more than one success. 
Example : Roll 3 die and gain 2 successes.
Example : Roll 8 die and gain 4 successes.
I was hoping there would be some formula I could use to plug in the die number and the amount of success needed to past the test.
In addition, you can be "blessed" (success is now 4-6) or "cursed" (success is now only on a 6).
So if it is possible to either have the formula define the value needed for a success as well or a different formula for those 3 options.
Finally.. if at all possible sometimes there are spell cards that can "add 1" to a rolled value. So rolling a 4 is a fail, but as you get +1 from the card it is now a success but that +1 can only be applied to a single die of all the die rolled.
Here is laymans sudo outline....
success range = "a-z" So. roll "DieCount" to acquire "x" successes then add "y" to a single die that is not already a success = Percentage chance of passing die test
I hope that makes sense to you as I am not a maths guys I am bad at expressing this stuff.
Thanks in advance for any help you can provide
--Jynks
 A: For a regular die, the probability of success is $2/6 = 1/3$.
For a "blessed" die, the probability of success is $3/6 = 1/2$.
For a "cursed" die, the probability of success is $1/6$.
If you apply a spell card, the probabilities of success for a regular, blessed, and cursed die are $1/2, 2/3,$ and $1/3,$ respectively.
Basically, count up the number of values that will give you success under the appropriate conditions, and divide by the number of all possible outcomes (6), and that gives you your probability for that die, which is somewhere between $0$ and $1$.
If you're looking for a formula,
$$P = \frac{2 + b + s}{6},$$
where $P_i$ is the probability of success for the $i$th die, $b$ is a "blessing factor" that is $+1$ for blessed, and $-1$ for cursed, and $s$ is a "spell factor" that is $0$ if there is no spell on the die, and $1$ if there is.
So if you roll $n$ dice with no spells, you should get, on average, $nP$ successes.  This will be a fraction unless $n$ is a multiple of $6$, so you have to figure out how to handle the fractions.
But, you could also just use a random number generator, and count up the number of successes directly.  And, once you know the outcomes, then you can choose to cast a spell on one of the dice to bump up the number of successes by one.
Hope that helps!  Good luck.
