You Only Need a Bit of Luck To Win MTVs Are You the One?
Author: Stanley R. Huddy & Nomin Sukhbaatar
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
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.
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