I found this question from Ian Hacking's book on probability and induction.
Diogenes is a cynic. He thinks the Maple Leafs will come in last in their league next year. His betting rate that they will come in last (proposition B) is 0.9. His betting rate that they not come in last (proposition ~B) is 0.2. Make a sure-loss contract against Diogenes.
It seems that a sure-loss contract is one wherein Diogenes loses every time. I don't understand how to make one from the given information though. Are you supposed to simply state prices that would provide Diogenes with a net loss every time?
If we're the bookmaker and Diogenes is a customer (as clarified in comments), then offer him two bets
In the first bet he pays in \$89 and we promise to pay him \$100 if $B$ happens. Since he thinks the probability of $B$ is $0.9$ he should think the chance of winning \$100 is worth \$90 to him, so he would take the bet.
In the second bet he pays in \$19 and we promise to pay him \$100 if $\neg B$ happens. Since he thinks the probability of $\neg B$ is $0.2$ he should think the chance of winning \$100 is worth \$20 to him, so he would take the bet.
If he takes both bets, he will be paying us \$108 in total, and we must pay him \$100 no matter what happens -- a sure profit for us.