Here's a game. In front of you are two urns. The small urn contains 1 white ball and 1 red ball. The big urn contains 1 million white balls and 2 red balls. You choose one of the urns and pull a ball. If the ball is white, you get $1. TWO white balls are then returned to the urn, and the game continues. If the ball is red, the game ends.

Suppose you want to maximize EXPECTED money. Which urn should you choose? And a bonus question: how much should you be willing to pay to get your chosen urn?