D5. Triple Fever

Contributed by Ian Stewart, University of Warwick

Caught up in the excitement of the Derby and the Preakness, a buddy of yours heads to the track, and discovers that today is the running of the Medium-Rare Stakes. Only three horses have been entered: Tee Bone, New York Strip, and Rib Eye. Your buddy then notices the posted odds: Tee Bone is paying 4-1, New York Strip is at 3-1, and Rib Eye at 2-1.

“Hmm,” thinks your friend, “that sounds too good to be true!” Knowing your math prowess, your pal manages to get you on the phone and tells you the situation, wrapping up with “And I only have $94 on me and no time to get more before the windows close. I want to make sure I get this right. Tell me how I should place my wagers!”

Assuming your friend can only buy tickets to win, but can back any or all of the entrants with any amount as long as the bets total $94 or less, how should the money be placed to maximize the winnings in the worst-case scenario? In other words, what bets will guarantee the most winnings, regardless of which horse wins the race?

This problem originally appeared in the Prisoner’s Dilemma in the 2022 Summer issue of the PMP Newsletter. Solutions will be accepted through 2022 Sep 1.