Computer Science interviews at Oxford and Cambridge are most likely to contain questions on relevant maths content, including probability and recursion. While improvising possible questions, I came up with this one. I think it’s a little too hard to get through in a successful interview.

**Alice and Bob play a dice game. **They take it in turns to roll a (fair, six-sided) die.

*Alice’s first roll – no matter what Alice rolls, the game continues.Bob’s first roll – if he rolls more than Alice’s most recent turn, he immediately wins, and the game ends. Alice’s second roll – if she rolls more than Bob’s most recent turn, she wins.*

*The game continues until a player rolls more than the previous roll.*

**a) Describe how some typical games will play out. **

**b) Calculate the probability that Alice will win.**

**c) If you get to a solution (or not), how would you like to check it?**

In an interview, it’s not necessarily expected that you’ll get to the answer. Your exploration of the idea, with directed guidance from a tutor, is more important.

*Would you like to do some interview practice with me for Computer Science and Mathematics for Oxford, Cambridge and other university courses?* *The questions will be challenging, but not this difficult!*

*Get in touch to arrange some sessions online: ronald@mathswithronald.com, WhatsApp +31682589013*

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