# Diciest Probability!

Discrete Mathematics Level 5

Satvik proposes a game of dice to Agnishom.

He says, "There are $$2$$ standard six-sided dice and the aim is to have the highest total of two dice. First you will throw $$2$$ dice. If you are happy with your total, that's great!

If you aren't happy with the total you have thrown, you can roll both dice again. However if you roll a second time, then whatever total you get, you must keep.

Now I will roll both dice. I have to accept the total I throw the first time, however if we both have rolled the same total then I win."

Given optimal strategy by Agnishom, what is the probability for Agnishom winning this game?

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