#### Andrew Moreton

##### Adventurer

(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))