So if you're trying to roll higher than a D4, which is better? What if you're trying to roll higher than a D10? Or D20?
Isn't it just 2D6 every time? It rolls 7 on average, while 1D12 rolls only 6.5 on average.
But you have a better chance of rolling a 12 (or 11, I think) with a D12, so doesn't that give you a better chance of beating a D20, since its average is 10?
It's true that D12 has a better chance of beating 10, but a D20 only averages at 10, it doesn't roll it every time. To make it easier to wrap your head around the issue, imagine that you play the game 20 times and the D20 rolls each of its numbers exactly once.
I wrote a Python script to simulate this because it was easier than doing the math and it looks like 2D6 wins about 30% of the time, while 1D12 only wins about 27.5% of the time.