The Detroit Lions football team weren’t having a great season. After their first twelve games they had one win, one tie and ten losses. But an article in the paper said that they had actually been a great team to bet on! In their first twelve games, they beat the point spread eight times out of twelve.

This made me wonder, what if you knew that fact ahead of time? What if you knew with certainty, before the season started, that they would go eight and four against the spread in their first twelve games? Could you use that fact to make money betting on the team?

Let us assume you start with a bankroll of 100 dollars, and each week you get to bet any amount, from zero dollars up to your entire bankroll, on the Lions. Each week if the Lions win, your bankroll will grow, and the number of remaining wins will decrease by one. If the Lions lose, your bankroll will shrink, and the number of remaining losses will decrease by one.

What is your best strategy to guarantee maximum winnings after twelve games, no matter what order the wins and losses occur? We’re not interested in the expected value of different outcomes here; we just want to maximize the amount we can be sure of. How much should you bet each week, always knowing the number of wins and losses remaining, and how big will your bankroll be after twelve weeks?

Extra credit:

Surely, a true Lions fan would never be caught betting against their own team, but what if you were one of those fair-weather fans, and you were okay with betting in favor of the Lion’s opponent. Now what is your best strategy, and how much will you win?