AnyDice code for rolling pools of dice, ignoring all 6s, and adding up the remainder; whoever rolls highest wins

Question

I'm trying to ascertain the probabilities of the following pool system. If anyone could crunch some numbers in AnyDice so much the better.

Two opponents roll a pool of d6. These pools vary from 1-10. Both pools ignore all 6s and add up all the remaining dice. Whoever rolls highest wins. With ties, victory goes to the defender or target of the action.

Example 1

Josh wants to seduce Mary. His Charm is 3. Mary is just resisting with her Mind of 4. Josh rolls 1, 4 and 6. Ignoring the 6, Josh adds 1 and 4 totalling 5. Mary rolls 3, 1, 2 and 6. Ignoring the 6, Mary adds 3, 1 and 2 for a total of 6.

Josh 5 vs Mary 6, she successfully resists.

Example 2

Troy wants to sneak by a bunch of zombies. He rolls his Dexterity 4 vs the zombies' Mind 2. Troy rolls 1, 4, 6 and 4. He ignores the 6, adds the rest for a total of 9. The zombies roll 5 and 3 for a total of 8.

Troy sneaks by the zombies undetected.

Answer 1

Here is an anydice program that should do that.

D: {1,2,3,4,5,0}

loop N over {1..10}{
   loop M over {1..10}{
      output NdD - MdD > 0 named " Attacker [N] vs Defender [M]"
   }
}

This redfines the 6 on the die to count as zero.

I had no good way to summarize the output across this huge matrix, but thanks to @Ilmari Karonen there is a nice script for it in his answer here. Here is the output, the percentage is the chance of the attacker to win:

The more dice you use, the more they average out and the same number of dice on both sides gets closer to 50%, but of course, as overall ties win for the defender the attacker never quite gets to 50% in those cases.

The chances for the side with fewer dice go down pretty quickly.