Brainteaser - Coin Flipping Game

Abby and Ben are engrossed in a coin flipping game. Abby's coin isn't like most coins. It shows heads with a probability \( p \) on every flip. Ben, on the other hand, possesses a regular coin that's fair. The game goes like this: Abby flips her coin first, followed by Ben, and they take turns in this manner. The game ends when one of them flips a heads. The first one to achieve this feat is declared the winner.

Here's the intriguing part: it's known that both Abby and Ben have equal chances of winning this game. Based on this, can you determine the value of \( p \)?