I was wondering: if we roll opposed 2d6 rolls, what are the chances of beating your opponent? It must be around 50% but somewhat less, because both rolling a seven – the most likely result – is undecided, that is: you didn’t beat your opponent.
And what about your chances when you get a +1 and your opponent doesn’t? I started wondering but I also didn’t want to dive back into the introduction to statistics I must have in my bookshelf somewhere. And I also didn’t want to look it up on AnyDice.
I started thinking: with just 2d6, it should be possible to explain it all using tables and counting... and I did it! I wrote a little three page PDF about it: Understanding 2d6 Math.