I'd say that the lottery, specifically those with a variable number of winners, are the best bet. There's not a lot of emotional investment, unless the person expects themselves to win and a single winner is likely (and even then, if they believe > 90% odds that they'll win, they're quite probably a lost cause to begin with)

For those which rarely have winners and tend to just grow each week, "time until next winner" or the like would probably also work.

Sports/horses/gambling, by contrast, strike me as mind-killers for a lot of people.