Our other sibling is 12 years younger than me, and as much as I love them and we get along well the bond isn't the same because we didn't grow up together.

My sister is 2 years younger than me. We got along decently during our early years and then had a pretty big breach of trust at like 6-8 years old probably. We turned that into a major bonding experience and we've been best friends and confidants ever since. My life wouldn't be the same without her.

then the odds of the d20 rolling whatever you rolled on the d12 is a 1 in 20. But it is entirely possibly there's more complex math involving statistics or something that I don't know.

I'm not sure. Since you just care about both dice rolling the same number, not the same specific number, I don't think it does though. Like, the chance of both dice rolling specifically an 11 is a 1 in 240. But since we only care about them rolling any same number, you roll d12, it is whatever it is

I'm sure there's a way more complicated way of doing it, but I look at it as there being a 1 in 20 chance. Cause even though you roll them at the same time, whatever you roll on the d12 is essentially the target, and there's a 1 in 20 chance of rolling any specific face of a d20.

On the form you say you'll be getting back to people within a couple days of the application window closing, how long is the application window?