The evil twin

Saturday's Los Angeles Times described a strategy for a football pool discovered at Dartmouth College in their weekly football pool at Emmys - the math department pub. In this football pool, department members are asked to pick the winners in, say, in a list of ten games to be played over the weekend. A point spread is provided. For example, if the list has Dallas Cowboys favored to beat the Washington Redskins by 5.5 points and you choose Dallas, Dallas must win by at least 6 points for your choice to be correct. The point spread is chosen to make the bet as even as possible, so most people in the pool are, in effect, tossing a coin for their choices. Each participant puts in a dollar and the winner gets the entire pot or an equal share of the pot if there is more than one winner.

One day, a graduate student asked if he could pay 2 dollars and put in two entries. We agree that this would be fine. The student then used the strategy of making random choices for one entry; for the other he made the choice opposite of that which was made made in his first entry. He called this the evil twin strategy. We want to see if his strategy is any good.

Discussion

1. Divide up into groups of three. Specify one person as the odd person out and the other two as the evil twins. In each of ten weeks your aim is to guess the outcome of three tosses of a coin. For each week the odd person just tosses a coin to determine his guesses. One of the evil twins does the same but the other guesses exactly the opposite for each outcome. Each person puts in 1 dollar and those that guess the outcome correctly divide the three dollars equally. Once the guesses are made, toss a coin three times and see how each person made out. Carry out this experiment for ten weeks and keep track of the total winnings of the odd person and the combined winnings of the evil twins.

Journal assignment

1. Determine how much the evil twins should win over the long run by their strategy if there is only one game each week. Do the same for the case there are three games each week.