Football Betting Problem

• 1. If you bet on three teams at a time, and if all three teams win by more than the given margin of victory, you will receive 5 points.
• 2. If you bet on four teams at a time to win by more than the parlay card margin, you will receive 10 points if you are correct.

• ... and so on as indicated by the odds listed on the parlay card.

If, however, you are incorrect about the margin of victory or if you pick the wrong team to win, you lose your one point. You only need be incorrect on one of the games to lose your point.

You decide that you really only have knowledge (inside information) on five of the games listed on the card. You feel confident that you can not only pick the winners in these games but that you can also "beat" the point spread. You have quantified the probability of picking the winner by the appropriate margin in the following manner:

1. You are 70% sure that Rice will defeat Texas A&M by the appropriate margin (in this case, by just one point).
2. You are 60% sure that Syracuse will beat West Virginia by the appropriate margin.
3. You are 80% sure that UCLA will beat Washington by the appropriate margin.
4. You are 80% sure that Wake Forest will beat North Carolina State by the appropriate margin.
5. You are 60% sure that Ohio State will beat Purdue by the appropriate margin.

Your Assignment:

1) How would you bet your one point to maximize your return?

2) How would you bet your one point to minimize your risk?

Note carefully that the answer to this second question will probably be different than the answer to the first question.

A commercial parlay card example can be viewed. This particular card is from a Las Vegas Sports Book.