1. ## Probability

Hello All,
I was asked by a colleague to work out some probabilities (its been a good 20+ years since I have done any real probabilities mind), and I have worked out some but I know they are wrong I just can't fathom why.

We have X Dice, with Y Sides, and its possible two or more sides can have the the symbol (so these dice aren't simple 1-6 D6's).
So for example
Dice 1 (D8) = A A B B B C D

I need to work out combination of using multiple dice from various symbol layouts can effect the results of getting a "A" for example or getting two "A"'s.
Not to bad, the problem is if some dice "negate" other results, i.e.

Dice A (D8) = -A -A -AA B B B C D
As in two sides negate an A and one side negates one or two A's.

This is where my probabilities skills have become to rusty for me to work out, help would be much appreciated! (especially as we are dealing up with pools of 20+ dice with various (6+) variations on symbols)

Ta!

2. Originally Posted by pauljh
Hello All,
I was asked by a colleague to work out some probabilities (its been a good 20+ years since I have done any real probabilities mind), and I have worked out some but I know they are wrong I just can't fathom why.

We have X Dice, with Y Sides, and its possible two or more sides can have the the symbol (so these dice aren't simple 1-6 D6's).
So for example
Dice 1 (D8) = A A B B B C D

I need to work out combination of using multiple dice from various symbol layouts can effect the results of getting a "A" for example or getting two "A"'s.
Not to bad, the problem is if some dice "negate" other results, i.e.

Dice A (D8) = -A -A -AA B B B C D
As in two sides negate an A and one side negates one or two A's.

This is where my probabilities skills have become to rusty for me to work out, help would be much appreciated! (especially as we are dealing up with pools of 20+ dice with various (6+) variations on symbols)

Ta!
What game are you playing? Are you trying to calculate your odds of winning?

You're example of Dice 1 has eight sides so the probability of;

$\displaystyle Ap = \frac 28$

$\displaystyle Ap = \frac 14$

$\displaystyle Bp = \frac 38$

$\displaystyle Cp = \frac 18$

$\displaystyle Dp = \frac 18$

If you role the dice three times, you multiple the probabilities together ie

probability of rolling A,A,B in 3 dice is

$\displaystyle Ap^2 * Bp$

If you now have a side which is AA and this negates the effect of rolling an A ie you roll 3 dice AA,A,B then only the B is used then you use the same formula;

$\displaystyle AAp = \frac 18$

$\displaystyle Ap = \frac 18$

$\displaystyle Bp = \frac 38$

$\displaystyle Cp = \frac 18$

$\displaystyle Dp = \frac 18$

probability of rolling AA,A,B in 3 dice is

$\displaystyle AAp * Ap * Bp$

Does this help? What combinations are you attempting to calculate? A little more detail and I could help you build an excel spreadsheet to work everything out.