Diciest Probability!

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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