A new twist on the Monty Hall problem, described as arguably the greatest mathematics puzzle of all time, asks contestants to reverse their objectives. In the traditional version, a contestant on the game show Let's Make a Deal chooses one of three doors: one conceals a car, and two conceal goats. The host, Monty Hall, then opens one door known to contain a goat and offers the contestant the chance to switch.
The puzzle's counterintuitive solution holds that switching improves the odds of winning the car from one-third to two-thirds. However, the new variant changes the desired prize. A contestant who secretly knows that one of the two goats is the former pet of an eccentric billionaire willing to pay far more than the car's value must decide whether to switch after the host reveals the ordinary goat.
The host remains unaware of the contestant's true goal and has only opened a door known not to contain the car. The question asks whether the contestant should switch doors under these altered circumstances.