I saw a fascinating talk from Christopher Bishop, author of Pattern Recognition and Machine Learning at MLADS (Microsoft's internal machine learning and data science conference) yesterday. He introduced me to the concept of non-transitive dice, which demonstrate how unintuitive probability can be sometimes.
Let's play a game with these four dice (invented by none other than Bradley Efron). I'll let you pick any die you choose, and then I'll choose mine. Then we'll both roll our dice, and the person with the highest roll wins. (By design, there can't be ties.) To make things less random, let's make it a best of 9 competition.
The thing about these die is that whatever die you choose, I can always choose a die that will statistically beat yours. There is no best die, and yet evey die has another that will outperform it. You can see it by running the numbers on all the faces below. In the long run, yellow beats red; blue beats yellow; green beats blue; and red beats green. What's more, each die beats the other at a rate of 2:1.
It just goes to show that when it comes to probalities, it's dangerous to rely on your intuition.
That's all from us here at the blog for this week. Have a good weekend, and we'll see you back here on Monday.