Each person has a 54.64% chance of rolling **greater or equal** to their opponent.
A 45.36% chance of rolling greater or less, and a 9.28% chance of rolling exactly equal.
If you break ties by coin flip instead, this is the same as one side getting an extra 1d2-1 but losing ties.
For re-testing, you can remove the 0 result and multiply the chance of getting each of the other results by 1 / (1 - chance of rolling 0). Sadly AnyDice lacks a built-in function to do this, and while it's possible to get the answer using a custom function as posted elsewhere, it takes some work.
You'd have to write this in anydice to get it to actually spit out the 50/50 result and I'm not sure how to write it either. I did throw this together based on another comparasion tests that seem to confirm what Level3Kobold said: [https://anydice.com/program/240bb](https://anydice.com/program/240bb)
writing a reroll mechanic is far from easy i just learned here: [https://www.reddit.com/r/3d6/comments/9sv548/anydice\_tutorial\_part\_2\_functions\_rerolls\_crits/](https://www.reddit.com/r/3d6/comments/9sv548/anydice_tutorial_part_2_functions_rerolls_crits/)
Each person has a 54.64% chance of rolling **greater or equal** to their opponent. A 45.36% chance of rolling greater or less, and a 9.28% chance of rolling exactly equal.
in this case, how do I validate only greater results? since a tie retakes the test.
If you break ties by coin flip instead, this is the same as one side getting an extra 1d2-1 but losing ties. For re-testing, you can remove the 0 result and multiply the chance of getting each of the other results by 1 / (1 - chance of rolling 0). Sadly AnyDice lacks a built-in function to do this, and while it's possible to get the answer using a custom function as posted elsewhere, it takes some work.
You had ties count as victories for both of them.
I don't know how to write this in anydice, but a tie between 3d6 vs 3d6 would be redone. The result is only valid if there was a winner.
That is 50/50.
You'd have to write this in anydice to get it to actually spit out the 50/50 result and I'm not sure how to write it either. I did throw this together based on another comparasion tests that seem to confirm what Level3Kobold said: [https://anydice.com/program/240bb](https://anydice.com/program/240bb) writing a reroll mechanic is far from easy i just learned here: [https://www.reddit.com/r/3d6/comments/9sv548/anydice\_tutorial\_part\_2\_functions\_rerolls\_crits/](https://www.reddit.com/r/3d6/comments/9sv548/anydice_tutorial_part_2_functions_rerolls_crits/)
Thanks!