Tuesday, March 8, 2016

Wheel of Fortune Mystery Wedge Problem

The Wheel of Fortune Mystery Wedge Problem is my attempt at a slightly more modern spin (pun intended) on the classic Monty Hall problem, which is a probability puzzle based on an older game show. Most modern American (and many international, so I've learned) TV viewers are likely familiar with Wheel of Fortune, but this specific problem can be framed in a way that doesn't require complete knowledge of the rules of the game:

  • You have X dollars in the bank and it's your turn to spin the wheel
  • You spin the wheel and land on the $10,000 Mystery Wedge, make a correct guess to win Y dollars, and Pat Sajak, the host, then offers you two options:
  • The first option is to do nothing. It is still your turn and you will end up with X + Y dollars in the bank.
  • The second option is to flip over the Mystery Wedge for a 50/50 shot at winning $10,000. If you lose, you lose all your money plus your turn.

Should you flip over the Mystery Wedge or not? At what values of X and Y should you flip the wedge and take the risk?