Question: On the television show Jeopardy contestants in the final round must choose some part of their winnings to bet on their answer to an upcoming question, and the winner's bet is added to the amount he has already won on that day. Only the winner takes home cash, and the other contestants get prizes like vacation trips that they cannot trade for their cash values.

a. Why would the producers not allow losers to make themselves better off when there is no extra cost to them of allowing it?

b. Is your answer to the previous question consistent with the following fact: Scattered through the earlier rounds are Daily Doubles, on which a contestant can bet any amount up to her then-current winnings. The typical contestant gets a Daily Double question right about 80 percent of the time. Nevertheless, the average bet is usually only about 30 percent of the amount possible.