How can I calculate the distribution of 3d6, keep and rerolling any 1s and 2s, once? [duplicate]

Question

The way my DM wants to try is roll 3d6 and reroll any 1's or 2's once. If you roll a 2 and the reroll ends up being a 1 you have to take the 1.

Answer 1

You can do it like this, using the helper function from this answer:

function: ROLL:n replace FILTER:s with REROLL:d {
  if ROLL = FILTER { result: REROLL }
  result: ROLL
}

X: [d6 replace {1,2} with d6]
output 3dX named "3d6, reroll 1 and 2 once" 

Note that I'm first defining a custom die X that represents a single d6 with 1s and 2s rerolled once, and then rolling three of these custom dice. Especially with large pools of dice this is significantly more efficient than rolling the whole pool at once and feeding the results into a custom function as sequences, since in that case AnyDice isn't smart enough to realize that the individual dice in the pool cannot affect each other.

Answer 2

https://anydice.com/program/1d573

This should do what you are wanting with a single d6, its a modified great weapon fighting script. I have updated the program to follow common practices better.

function: reroll R:n under N:n {
   if R < N { result: d6 } else {result: R}
}
output 3d[reroll 1d6 under 3]

Answer 3

You just need a 36 sided dice

output 3d{1:2,2:2,{3..6}:8}

See https://rpg.stackexchange.com/a/104780/6203