(source)
From Tom Hanrahan, some big-money game show strategizing:
You are a contestant on “Who Wants to Be a Riddler Millionaire.” You have already made it to a late round: You could walk away right now with $250,000. But there are two potential questions still to go that you can try to answer. You could earn $500,000 if you get one right and then walk away, or $1 million if you nail them both. If you attempt any answer and miss, you go home with $10,000.
Luckily, you still have two of your lifelines:
- The 50/50: The host reduces the four possible answers to two; one of them is the correct one and the other is randomly chosen from among the other three answers.
- Ask the Audience: The studio audience submits their own guesses. You know historically that the correct answer will be chosen by the plurality 50 percent of the time; while 30 percent of the time the right answer finishes second; 15 percent third; and 5 percent last. Additionally, if there are only two answers available to the audience, they pick the correct one more often 65 percent of the time.
The problem: You’re burned out. All the pressure and questions you’ve already answered have made you a babbling mess. You assess that you would have no clue on the last two questions, so you’ll be guessing randomly.
What is your best strategy to play, or stop, or use your lifelines to maximize your expected winnings?