Oli and Pip are playing a game with two fair dice, where the winner is the first person to throw a double. However, if a throw has a total of 3, the person throwing gets another go.

Oli throws first.

What is the probability that Oli wins on the first or second throw of the game?

What is the probability that someone has won the game after 2 throws? Or after 3 throws?

What is the probability that Oli wins the game without Pip ever getting a chance to throw the dice?