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A Game of Dice

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #43901 Fun: (2.45) Difficulty: (2.66) Category: Probability Submitted By: javaguru Corrected By: krishnan

Your friend offers to play a game of dice with you. He explains the game to you.

"There are two dice and the goal is to have the highest total of two dice. You roll first. If you don't like your roll, then you can roll both dice again. If you roll a second time, you must keep the second roll. I'll roll second. I have to keep my first roll, but if we both roll the same number, I win."

On your first roll you roll a 7. Should you roll again or keep the 7?

Bonus question: if you play the optimal strategy, what is the probability that you will win?

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