Trying to get this formula has been puzzling me for a bit...
In certain sports, winning a game requires a lead of two points. That is, if the score is tied you have to score two points in a row to win.
In tennis, a point is scored every play. Suppose your probability of scoring the next point is always p. Then, your opponent's probability of scoring the next point is always 1 - p.
Give a formula for your probability w of winning a tied game.