# What are the odds of rolling seven dice and all coming up equal?

What are the odds of rolling seven, six sided dice one time and getting all the same number?

I just rolled seven dice one time and got all ones in that one roll. I am wondering what the odds are or what is the probability of rolling this type of roll.

Thank you.

• $46655:1$, pretty unlikely. – vadim123 Jul 18 '15 at 1:09
• The title is pretty unfortunate. It seems to be asking what the probability is that you would go find seven dice and roll them. – Matt Samuel Jul 18 '15 at 1:18
• It is very unlikely, vadim123. That's why I was wondering what the odds were. My husband and I were playing a game called 10,000, which uses 7 dice. In one roll I rolled all 1's. I was pretty excited because this roll won me the game and I was really behind. lol – Andrea Jul 18 '15 at 1:38

This may help: the chance of getting a 1 is $\frac{1}{6}$, so the chance of getting seven 1s is $(\frac{1}{6})^7$.
However, we also want to count getting seven 2s, seven 3s, etc. There are six numbers, so now we have a chance of $6\cdot(\frac{1}{6})^7$ which is $(\frac{1}{6})^6$
Think about one die to start. The probability that all the numbers will be the same if you roll one die is (obviously) $100\%$. With two dice, there are $6^2=36$ possibilities, and only six of them are the same number twice, so the probability is $1/6$. With three dice, there are $6^3=216$ possibilities, and again, six ways to get all the same number, so $6/6^3=1/6^2=1/36$ is the probability. If we continue this process, it's not hard to see that with seven dice, the probability of getting all the same number is $1/6^6$.