Enough of the Monty Hall Dilemma! Let's move on to a more modern game show and a new dilemma.

You're on the TV game show, "Who Wants To Be A Millionaire". You are about to be asked a question which, if answered, will win you $16,000, and the only lifeline you have left is the 50/50 lifeline. You're asked the question, and you have no idea of the correct answer. You use your 50/50 lifeline, and you now have two answers from which to choose, with still no idea of which of the two is the correct answer.

If you answer the question correctly, you win the $16,000 and can proceed to the next question. If you answer incorrectly, you will leave the show with only $1,000. If you decline to answer the question after seeing it, you keep the $8,000 you've previously won and leave the show.

What is the move with the best potential payoff?
1) Guess randomly between the two choices.
2) Decline to answer and leave with the $8,000.
3) Do either, as the payoff is the same either way.

Number 1 ?

BTW, I should have phrased the question as to which has the greatest expected payoff.

Are you sure, Slim? What is the expected payoff for choice #1?

Good, "trick question"!

If you choose to answer, even assuming you have no idea as to the correct choice of answer, your chance of winning is 50%. If you are correct, you win $16,000, and if you are incorrect, you win $1,000. Therefore, your expected payoff is 1/2 of ($16,000 + $1,000) = $8,500.

Therefore, you're expected to do better if you answer rather than walk away and take $500 less by keeping the $8,000.

Good job, Slim & Arnon! You both got it!