Ash and Bree are playing a simple game of chance:
They fill a bag with small marbles coloured red or blue. They take turns to draw a marble from the bag without looking, then:
- If Ash draws a red marble, she wins the game
- If Bree draws a blue marble, she wins
- If either player draws the opposite colour, the marble is returned to the bag, and the next player takes their turn.
Ash is set to take her turn first, but Bree complains that gives her a disadvantage. In order to balance out this disadvantage, they decide to add extra blue marbles to the bag until the chance of either player winning is equal.
What ratio of blue marbles to red should they use for optimal fairness?