Opposing d6 Pools, # of higher dice

I’ve read dozens of posts here, and wrestled with with anyDice suggested code, but nothing matches quite what I am looking for. I think it is simple in concept: for opposing dice pools of 1..6d6, I want to figure the probability of of higher dice.

In my case, the count of higher dice includes a dice with a higher face than the opponents highest, and/or a higher count of the opponent’s highest face. A = 1234, B = 456: B nets 2 (5 and 6 > 4) A = 1233, B = 1223, A nets 1 (2 3s to 1 3) I want to analyze the probability of each 3 of higher dice for 2d6 versus 2..6d6. Any help would be appreciated.

The closest I’ve come is https://anydice.com/program/1f78d, but that just tells me the relative probability of X # of dice of the same face.

Thanks,

  • John