 Through this discussion, Pascal and Fermat not only provided a convincing, self-consistent solution to this problem, but also developed concepts that are still fundamental to probability theory.The starting insight for Pascal and Fermat was that the division should not depend so much on the history of the part of the interrupted game that actually took place, as on the possible ways the game might have continued, were it not interrupted.It is intuitively clear that a player with a 7–5 lead in a game to 10 has the same chance of eventually winning as a player with a 17–15 lead in a game to 20, and Pascal and Fermat therefore thought that interruption in either of the two situations ought to lead to the same division of the stakes.