Without getting too much into game rules or strategies, it will be enough to know that a 7 on your first role (summing a white and any other die) is bad.
K: "What are the chances that you get a 7 on the first role?"
I'm super excited that she's even asking a probability related question, though I immediately recognize this would be a really tough one to answer.
Me: "Well first we have to know how many different outcomes are possible and then decide how many of them have 7s in them. I think there are going to be some pretty big numbers. Can we figure out how many outcomes there are first?"
K: "Sure"
Me: "Any thoughts on how many outcomes there are for six dice?"
K: "No."
Me: "How about 1 die?"
K: "6"
Me: "How about 2 dice?"
K: "11"
Me: "How did you get that?"
K: "Is it right?"
Quick aside here. For years of our mathematical conversations, I haven't been telling K if her answers are right or wrong until after she answers "How did you get that?". Lately I've dropped the question for arithmetic that I'm confident that she's mastered. I almost said, no, but thankfully, this time I told her that I wanted her to explain where she got 11 from.
K: "Well you could roll a 2, a 3, a 4 and so on up to a 12. So there are 11 possibilities"
I'm so glad that I took a moment to ask where she got 11 from. Based on her understanding of the word outcome and the types of questions she was asking 11, makes total sense.
We continued to talk about how many outcomes there were for 2 dice, which had me acknowledging her answer as correct and offering another, different definition related to the actual dice as opposed to just their sum. Then we did lots of thinking and listing, eventually working up to a general formula and an answer to how many outcomes exist for 6 dice. We did not however answer the original question, but that's OK too!
