Reality TV Math Explained

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In Survivor seasons 41 and 42, Jeff introduced the “Do or Die Twist”, a thinly veiled version of the Monty Hall Problem. In Jeff’s version, 41’s Deshawn and 42’s Lindsay both came last in an immunity challenge and had to select one of three boxes looking for safety/an image of fire. The twist was that the other two boxes had skulls, meaning the player would be eliminated and tribal council would be cancelled if they selected a skull. Both times, Jeff revealed one of the skulls, and Deshawn and Lindsay had the opportunity to switch their boxes. They both chose to stick with their original box and both times, they were safe.

Both times their math was wrong. Like the original Monty Hall problem on the classic show hosted by Monty Hall, Let’s Make a Deal, the move is always to switch after the host reveals one of the wrong answers, because it actually doubles your odds. But you already know that because you’re a wise confessional reader… and if you don’t it’s completely unintuitive so check out the Wikipedia page.

One of our guilty pleasures here is Deal or No Deal Island (DONDI), a game of black widows, golden gods, and doctors of dermatology who are trying to compete for large sums of money in a game of strategy, a lot of luck, and some complex math.

This week, we aired one of RHAP’s greatest recurring podcasts, “Ask Dr. Christian Hubicki”, where we asked the aforementioned Survivor: David vs Goliath star if DONDI logic is similar to The Monty Hall Problem.

Deal or No Deal is largely a game of chance; for those of you who haven’t watched DONDI, every episode ends with a game of Deal or No Deal where the goal is to make a good deal with the banker. The game begins with a bunch of dollar amounts in closed briefcases - come on, you had to watch with Howie at least once - and then the player chooses one case for themselves and progressively selects other cases to open and remove from the game. Based on those amounts, the banker will then make a variety of offers to try to save themselves money while leaving contestants happy.

If the player doesn’t accept any deals by the end of the game, the player has the option to swap their original sealed briefcase with the final sealed briefcase left in the game. So we asked Christian, is this the same as the Monty Hall Problem? Should players always switch if they’re in that position?

According to Dr. Hubicki, DONDI is fundamentally different. With the Monty Hall/Jeff Probst Problem, the host always makes sure they don’t open the winning door or winning box. This increases the odds of the player selecting the winning door because the probability of winning shifts to the closed door or box that the player didn’t originally select. With DONDI, the player might open the highest value case which would lower the banker’s offer. This couldn’t happen on Let’s Make a Deal or New Era Survivor.

There it is. The math says you don’t have to switch, even if the math is a probability, not a guarantee. Just ask Deshawn or Lindsay.

Have a great week, and try not to throw your other Traitors under the bus - if you can!

-The Confessional

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