Andrew Moreton
Adventurer
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))
(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))