How many sides of dice do you need to see to accurately characterize their position?

(Note: the singular form of dice is die–but it sounds funny to talk about one die.)

Let me rephrase the question: **Can you tell from looking at this photo what number is on top?** (Because that’s how we normally score the toss of a pair of dice.)

What if I told you that the number four was also “showing”? Can you deduce what number is on top from those two pieces of information?

How much information do you need in order to deduce what number is on top?

Is this the same question as the very first that I asked, at the outset of this post?

I bet you wish you had some dice right now to help you with this thought experiment. (If you send me a self-addressed stamped envelope, I will send you a pair of dice. No, seriously, I will.)

The probability of a 3 on a toss of the die is 1/6.

What is the probability that a 3 will appear on the side, as it does here?

Knowing that I just tossed a 3, does that affect the chances of me tossing a 3 on the next one?

How many tosses of dice would it take to *ascertain* that the dice are fair?

What if it cost a million dollars every time you tossed the dice?

**Sometimes in order to make the right decision–especially when there is an element of uncertainty or risk–we just need to ask the right question.**

The answer to the first question is not trivial by the way.

*ATOMs is a monthly column that introduces analytical tools of mathematics and statistics and illustrates their application. To read more about ATOMs, you can read Where Do We Go From Here, or view the online workbook here.*