You are given a ten sided die (values 1-10) and you are allowed to roll it either once or twice. After the first dice roll you note the score and have to make a decision whether you want to try a second roll or not. In case you decided to roll a second time you add the values from both dices to get your final score. If your score is less than or equal to 13 you will receive the equivalent amount in pounds as a payout. However if your score exceeds 13 you won't receive a payout. Find the optimal strategy and explain how you arrived at your answer.

Two players, flipping a coin until one player wins. A wins if the roll ends with HHT. B wins if the roll ends with HTT. What are the odds B wins the game.