There are 200 one-dollar coins, each with an equal probability of going into a pot. You can bid for the pot (the winner gets all the coins, but does not know exactly how many coins are in it). The person who offers the highest bid wins the auction. What would your optimal bid be if there is 1 competitor? What about with 10 competitors? Now, suppose only two people are bidding and both are using their best strategies, but I have the advantage of knowing how many of the first 10 coins are in the pot. What bidding strategies should we each use, how much should you bid, and what is your expected payoff?