Brain Game: McLanderstone's Offer

McLanderstone & Associates is an odd place to work. Old Man McLanderstone was once a high-school teacher, and he likes to quiz and challenge his employees as if they were his students. This morning, via inter-office memo, he made an offer to his four key employees - Ron, Don, Jon, and Lon. The question is: Should they accept his offer?

NEW WEEKLY EMPLOYEE GAME OPPORTUNITY At the end of each week, I'll shuffle a regular deck of 52 cards. You'll pay $1 to pull a single card from the deck, and if it happens to be the Ace of Spades, you'll win $50! A random dice roll will determine who gets to draw the first card from the deck, followed by the second, third, and fourth. If you're the fourth person to draw, the odds are with you, since there will only be 49 cards left in the deck. So the one of you who draws fourth will have a 1 in 49 chance of winning at any given time. Now think about it: If you played 49 times, it would cost you $49, but the odds are that you'd win at least once, which is $50. So you'd be $1 ahead. And remember, there are 52 weeks in the year, not 50, so how could you lose? What do you say? I need your answer ASAP.

Financially, is this a smart opportunity for the employees?

Here is the SOLUTION.

THE SOLUTION:

NO, it's not.

(The Old Man isn't trying to rip off his employees, mind you. He offered the contest to help keep his employees thinking. He likes it when people think.) 

McLanderstone's statement about the one-in-49 odds is true, but it ONLY applies to the person who picks the fourth card from the deck. And his mention of their being "52 weeks in a year, not 50" does nothing to change the odds; he's simply employing that number to confuse things and make it sound as if one's chances of winning are even greater.

Here's the basic breakdown:

Each employee would pay $52 a year to play, or $208 total for the four of them. But the overall odds that the Ace of Spades would be drawn over that year is 92.3 percent. The prize is $50, so averaged over time, the annual payout would be only $46.15.

So, given enough time, and barring a string of (good or bad) luck, McLanderstone would make an average of $3.85 a year operating this "contest."

Want the math? I'll leave that to one of our readers to post in a comment. Thanks!