Alright, made some dice-level changes to my home-brew game system and was trying to figure something out. If, for example, I am rolling a D12 with a difficulty of 4, that gives me a 25% chance of failure. What if its two dice? Three dice? I have never taken statistic classes so am at a bit of a loss as to how to figure this out.

Kane-

Since each dice roll is independent of the other you essentially just have to multiply the individual odds together.

Assuming you are counting succseses then the odds are:
2 Successes:
(The odds for die 1 a succcess) * (The Odds for die 2 a success) =
.75 * .75 = .5625 or 56.25%

0 Success:
(the odds for die 1 a failure) * (the odds for die 2 a failure) =
.25 * .25 = .0625 or 6.25%

1 Success:
(The odds for die 1 a failure) * (The odds for die 2 a success) =
.25 * .75 = .1857 or 18.75%

(The odds for die 1 a SUCCESS) * (The odds for die 2 a FAIILURE) =
.25 * .75 = .1857 or 18.75%

So the total odds for 1 succes will be 18.75% + 18.75% = 37.5%

-Pel (theoretical mathematics major)

Sad? Nay, brother! Rejoice in the beauty and majesty that is MATHEMATICS!

Worst thing for me is that back in school, I took algebra early, but was so flustered by a bad teacher for geometry and alII, I gave up on math. I even did math tutoring, but like so many coaches, I failed at the actual application.

If you want these probabilities for lots of dice, check out .

You also want and -- some baseline probability concepts good for doing such things calculating expected value outcomes when throwing a handful of different types of dice in D&D, Silent Death, etc.

Ah, I see the mistake in my math. Thanks. Now then, 10% will be the minimum chance (10 on a D10) so I suppose allowing up to 10 dice may not be a bad idea.

Just ran the chart for 10% and came up with just .1 repeating as you add more dice. Did I do something wrong here?

One Success Chances
D10s Diff +4(10%)
1 = 10%
2 = 11%
3 = 11.1%
4 = 11.11%
5 = 11.111%
6 = 11.1111%
7 = 11.11111%
8 = 11.111111%

Also, not sure how to plug that into Excel properly. Any tips?

Ugh...this is hurting my head. So, I can get the formula to work to find out if at least 1 die will come up high enough, but what about ALL dice?

Here is what it looks like from Excel

One Success Chances
D10s Diff +4(10%)
1 = 10%
2 = 19%
3 = 27%
4 = 34%
5 = 41%
6 = 47%
7 = 52%
8 = 57%
9 = 61%
10 = 65%

I have NO clue how that works if the chart for ALL dice to succeed is

All Succeed Chances
D10s Diff +4(10%)
1 = 10%
2 = 1%
3 = 0.1%
4 = 0.01%
5 = 0.001%
6 = 0.0001%
7 = 0.00001%
8 = 0.000001%
9 = 0.0000001%
10 = 0.00000001%

Or did I do that wrong too? 10% x 10%= 1%, 1% x 10%=0.1%...brain melting...ing...ing...

Yeah. it gets really hairy doing it by hand because you have to consider a lot of different combinations of successes and failures.