WOIN probabilities of success

[Andrew Moreton]

The principle of how to combine the two ways of succeeding is easy basic stats. The actual implementation is going to be complicated and fiddly

(P Success by rolling more than the target) + ((P Chance of Failure by Rolling less than the Target)*(P Chance of success by rolling 3 6's on some of the dice combinations that failed))

For 22 on 10d6 though the chance of success by rolling 3 6's on some of the dice combinations that failed is 0. If 3 of the dice add up to 18 the minimum total is 25 if all the other dice roll 1's

Which means for any number of dice N and target T Where T <= 18 + N-3 then you can ignore the chance of success from 3 6'S
Likewise whne T>6N then you can ignore the chance of success from rolling more than T (That one is obvious I admit)
The inbetween cases are tricky as not all results containing 3 6's matter due some of them being normal successes, It may be easier to calculate as

(P Chance of success by rolling 3 6's on some of the dice combinations that failed)
+ ((P Chance of Failure by Rolling less than the Target)*(P Success by rolling more than the target))

 

[TheHirumaChico]

Maybe this is the right formula?

The probability of the union of two events can be obtained by adding the individual probabilities and subtracting the probability of their intersection: P(A∪B)=P(A)+P(B)−P(A∩B). [Additive and Multiplicative Rules for Probability]

Seems the tricky part is calculating P(A∩B), while P(A) and P(B) seem pretty straightforward. I'm no math whiz, so I haven't figured out how to determine P(A∩B) yet.

 

[Andrew Moreton]

I don't think thats quite the right set of maths. However this is nearly 40 years to late for me to do the maths for this, back when I left school this would have been about half an hours work.Know I would have to relearn everything I have forgotten

 

[TheHirumaChico]

Hi folks. Sorry for the post-necro, but I updated the original table in this post to account for attribute & skill checks, for which triple-6's are not an auto success. I used the "at least" function at Anydice.com and generally stuck to 2 significant digits or one decimal place for values less than 1%. The >99% means these values are not auto-successes, but the values round up to 100% using 2 significant digits. Similar for the <0.1% values. Hope this is useful. Please let me know if any corrections are required and I'll try to update in a timely manner.

 

[lichmaster]

Hi folks. Sorry for the post-necro, but I updated the original table in this post to account for attribute & skill checks, for which triple-6's are not an auto success. I used the "at least" function at Anydice.com and generally stuck to 2 significant digits or one decimal place for values less than 1%. The >99% means these values are not auto-successes, but the values round up to 100% using 2 significant digits. Similar for the <0.1% values. Hope this is useful. Please let me know if any corrections are required and I'll try to update in a timely manner.

There's a typo for the odds of DC 32 when rolling 7d6, it should be 6.1%, not 36.1%

 

[TheHirumaChico]

There's a typo for the odds of DC 32 when rolling 7d6, it should be 6.1%, not 36.1%

Good catch, thanks @lichmaster! I've edited my post above with an updated version with the typo fixed.