Consortium for Mathematics and its Applications

Product ID: Articles
Supplementary Print
Undergraduate

You Only Need a Bit of Luck To Win MTVs Are You the One?

Author: Stanley R. Huddy & Nomin Sukhbaatar


Introduction

Are You the One? is an MTV reality show in which a cast of single women and single men try to discover their "perfect" opposite-sex matches within the cast and earn money for doing so. MTV claims to use an extensive match-making process to determine which couples are "perfectly" matched, and the cast has 10 episodes for the cast to discover all of these (designated "perfect") matches.

During each episode, there are two events when the cast learns information about the matches. MTV calls these events a truth booth and a matching ceremony. If the cast is able to use these events to find all of the perfect matches, they head home with their shares of $1 million; otherwise, they leave alone and empty-handed.

MTV aired seven seasons of Are You the One? between the beginning of 2014 and the end of 2018, and they plan to air an eighth season in 2019. Each of the first four seasons of Are You the One? featured a cast of 10 couples. After viewing these seasons, we were surprised by the 100% success rate of each cast because they did not appear to use any strategy to discover the matches. In fact, of the first seven seasons, season five was the only one in which the cast failed to determine all of the perfect matches and win money.

In modeling the show, we find that even the most basic approach results in determining all 10 matches approximately 90% of the time, and that finding them 100% of the time just requires a few lucky guesses along the way. We model the show as an n-couple game with n rounds (shown in n TV episodes), and we develop three algorithms to pair the cast:

• The first takes a na®ƒ±ve approach, randomly choosing (from cast members remaining in play) pairings for each truth booth and matching ceremony.
• The second improves on the first version by choosing (from cast members remaining in play) a pairing for each truth booth that has the greatest probability of being a perfect match.
• The third incorporates the improvement from the second version and additionally, at each matching ceremony, calculates all possible outcomes for that ceremony using the cast members remaining in play. It then randomly chooses, for the matching ceremony, pairings that remove the maximum number of couples from play.

We find that each algorithm can win a very high percentage of games for n = 2, 3, . . . , 10 couples. Along the way, we obtain a number of combinatorial results that provide insight into the complexity of the game.

©2019 by COMAP, Inc.
The UMAP Journal 40.1
16 pages

Mathematics Topics:

Application Areas:

  • Combinatorics

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