I used [Any Dice] website to work this out.
The code below is probably not the cleanest but I only learned this site today. The function below will count 1 success if at least one 5 and add to that how many sixes rolled. This is getting results of to 5d6.
function: contains VALUES:s in SEQUENCE:s {
FIVES: 0
SIXES: 0
loop P over {1..#VALUES} {
if (5 = SEQUENCE) {
if FIVES = 0 {
FIVES: 1
}
}
SIXES: SIXES + (P@VALUES = SEQUENCE)
}
result: FIVES + SIXES
}
output [contains { 6 } in d6]
output [contains { 6 } in 2d6]
output [contains { 6 } in 3d6]
output [contains { 6 } in 4d6]
output [contains { 6 } in 5d6]
These are the results that I've formatted to be a bit more readable than the anydice website gives me. If you roll 1d6 the chance of 1 success (A 6 or 5) is 33.3%
If you roll 3d6. the chance of 2 successes is 18.05% (that's either 2 6s and no 5s or one 6 and at least one 5)
1d6
0 success, 66.6666666667
1 success,33.3333333333
2d6
0 success, 44.4444444444
1 success, 47.2222222222
2 success,8.33333333333
3d6
0 success, 29.6296296296
1 success, 50.462962963
2 success, 18.0555555556
3 success, 1.85185185185
4d6
0 success, 19.7530864198
1 success, 48.225308642
2 success, 26.2345679012
3 success, 5.4012345679
4 success, 0.385802469136
5d6
0 success, 13.1687242798
1 success, 43.4799382716
2 success, 31.9573045267
3 success, 9.90226337449
4 success, 1.4146090535
5 success, 0.0771604938272