Card Auction (Introducing dependence)

Last month, Nat Banting described a fantastic task on his website called the Dice Auction. You should really just read the original post, but I will summarize it as best as I can here.

Cfh3p4sUsAEk2Wj.jpg_largeThe premise is that you are invited to an auction, and given a budget of $10 [I changed the budget to $15 for my students to encourage a bit more risk taking]. Everyone at the auction has the same budget. The participants are all bidding on certain events that may occur when two 6-sided dice are rolled (e.g., both numbers are greater or equal to 5; a single 2 is rolled; both numbers are odd; etc.). After all the events have been auctioned off to the highest bidders, the two dice are rolled 20 times. Each time the event that you purchased occurs, you collect a prize. Bidding always begins at $1 and goes up in increments of $1. You cannot bid against yourself. The order of the events up for auction is known beforehand. If you choose not to spend (some, or all of) your money, the auctioneer will sell you prizes at a cost of $2 per prize after the bidding has ended. Your task is to get as many prizes as possible.
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