Wednesday, January 25, 2023

Season 9, Episode 3 Probabilities

Truth Booth #2

Hamudi and Anissa go into the Truth Booth and are not a match.

AqelBrendanClayEduardoHamudiLeoMikeyNathanOllieSamuelWill
Anissa11.0%11.0%11.0%11.0%X11.0%11.0%12.3%X11.0%11.0%
Brooke9.7%9.7%9.7%9.7%11.1%X9.7%11.0%9.9%9.7%9.7%
CC9.7%X9.7%9.7%11.1%9.7%9.7%11.0%9.9%9.7%9.7%
CourtneyX9.7%9.7%9.7%11.1%9.7%9.7%11.0%9.9%9.7%9.7%
Danielle9.7%9.7%9.7%9.7%11.1%9.7%X11.0%9.9%9.7%9.7%
Dew9.7%9.7%X9.7%11.1%9.7%9.7%11.0%9.9%9.7%9.7%
Jordanne9.7%9.7%9.7%9.7%11.1%9.7%9.7%11.0%9.9%9.7%X
Julia Ruth9.7%9.7%9.7%9.7%11.1%9.7%9.7%11.0%9.9%X9.7%
Mijntje9.9%9.9%9.9%9.9%11.2%9.9%9.9%X10.0%9.9%9.9%
Roz9.7%9.7%9.7%X11.1%9.7%9.7%11.0%9.9%9.7%9.7%
Taylor11.1%11.1%11.1%11.1%X11.1%11.1%X11.2%11.1%11.1%

11,895,985 possibilities remain.

Matchup Ceremony #2
  • Anissa - Aqel
  • CC - Clay
  • Danielle - Eduardo
  • Mijntje - Hamudi
  • Brooke - Ollie
  • Roz - Mikey
  • Dew - Samuel
  • Julia Ruth - Nathan
  • Jordanne - Brendan
  • Taylor - Will
  • Courtney - Leo

Blackout probability: 32.5% (3,865,932 of 11,895,985)
Instant win possible: Yes
Most likely number of lights: 1

2 beams. 2,441,740 combinations left.

AqelBrendanClayEduardoHamudiLeoMikeyNathanOllieSamuelWill
Anissa19.5%9.9%10.0%10.0%X10.0%10.0%11.0%X9.9%9.8%
Brooke8.9%9.0%9.0%9.0%10.0%X9.0%9.9%17.5%9.0%8.8%
CC8.9%X17.3%9.0%10.0%9.0%9.0%9.9%9.1%9.0%8.8%
CourtneyX9.0%9.0%9.0%10.0%17.3%9.0%9.9%9.1%9.0%8.8%
Danielle8.9%9.0%9.0%17.3%10.0%9.0%X9.9%9.1%9.0%8.8%
Dew8.9%9.0%X9.0%10.0%9.0%9.0%9.9%9.1%17.3%8.8%
Jordanne8.8%17.3%9.0%9.0%10.0%9.0%9.0%9.9%9.1%9.0%X
Julia Ruth8.7%8.8%8.9%8.9%9.9%8.8%8.9%19.5%8.9%X8.7%
Mijntje8.8%8.9%8.9%8.9%20.0%8.9%8.9%X9.0%8.9%8.8%
Roz8.9%9.0%9.0%X10.0%9.0%17.3%9.9%9.1%9.0%8.8%
Taylor9.9%10.1%10.0%10.0%X10.0%10.0%X10.1%10.0%19.8%

Wednesday, January 18, 2023

Season 9, Episodes 1 & 2 Probabilities

MTV's Are You The One? season 9 features 11 men and 11 women looking for their perfect match. If they manage to guess the exactly right combination, they'll split $1,000,000. Season 9 is streaming on Paramount+, although the first episode will also air tonight on MTV.

Here I'll be keeping track of the possible remaining perfect match combinations (with the help of a computer), and looking into the potential strategy of playing this game. The math work here will be independent of the romance and excitement that comes with the pairings. Unless noted otherwise, assume the probabilities of a matchup here being successful are random, ignoring chemistry and all the parts of the show that are actually fun.

Prize and Probability of Winning


All 22 winners will split a 30-year annuity that will pay out $1,000,000. That means if they elect to take the present day "lump sum," they'll end up with around $22,000 each (in addition to a shot at finding their perfect match and getting some weekly face time on MTV).

The blackout rule, introduced in season 3, drops the prize by $250,000 if a matchup ceremony results in no lights other than truth booths.

The number of possible permutations in the original game is 11 factorial = 11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800. Put simply, a random guess would have a 1 in 39,916,800 chance of winning (0.00000002505%). The calculations done here throughout the season evaluate all of those 39,916,800 possibilities against the information that's been shared through truth booths and matchup ceremonies to figure out the set of perfect matches. The easy way of saying it: I use a computer program to do a process of elimination in seconds.

The show has multiple challenges where additional information is provided, reducing the number of possible combinations. The contestants only have 10 episodes to find the perfect match, so they'll need to reduce it quickly to have a chance.

Probabilities

Truth Booth

Taylor and Nathan go into the Truth Booth at the end of Episode 1. The start of Episode 2 shows... no match.

AqelBrendanClayEduardoHamudiLeoMikeyNathanOllieSamuelWill
Anissa9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Brooke9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
CC9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Courtney9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Danielle9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Dew9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Jordanne9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Julia Ruth9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Mijntje9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Roz9.0%9.0%9.0%9.0%9.0%9.0%9.0%10.0%9.0%9.0%9.0%
Taylor10.0%10.0%10.0%10.0%10.0%10.0%10.0%X10.0%10.0%10.0%

36,288,000 possibilities remain.

Matchup Ceremony
  • Nathan - Mijntje
  • Leo - Brooke
  • Mikey - Danielle
  • Brendan - CC
  • Aqel - Courtney
  • Hamudi - Taylor
  • Ollie - Anissa
  • Samuel - Julia Ruth
  • Eduardo - Roz
  • Clay - Dew
  • Will - Jordanne

Blackout probability: 36.4% (13,216,113 of 36,288,000)
Instant win possible: Yes
Most likely number of lights: 1

It's a blackout! 0 beams. 13,216,113 combinations left.

AqelBrendanClayEduardoHamudiLeoMikeyNathanOllieSamuelWill
Anissa9.9%9.9%9.9%9.9%10.0%9.9%9.9%11.1%X9.9%9.9%
Brooke9.9%9.9%9.9%9.9%10.0%X9.9%11.1%9.9%9.9%9.9%
CC9.9%X9.9%9.9%10.0%9.9%9.9%11.1%9.9%9.9%9.9%
CourtneyX9.9%9.9%9.9%10.0%9.9%9.9%11.1%9.9%9.9%9.9%
Danielle9.9%9.9%9.9%9.9%10.0%9.9%X11.1%9.9%9.9%9.9%
Dew9.9%9.9%X9.9%10.0%9.9%9.9%11.1%9.9%9.9%9.9%
Jordanne9.9%9.9%9.9%9.9%10.0%9.9%9.9%11.1%9.9%9.9%X
Julia Ruth9.9%9.9%9.9%9.9%10.0%9.9%9.9%11.1%9.9%X9.9%
Mijntje10.0%10.0%10.0%10.0%10.1%10.0%10.0%X10.0%10.0%10.0%
Roz9.9%9.9%9.9%X10.0%9.9%9.9%11.1%9.9%9.9%9.9%
Taylor11.1%11.1%11.1%11.1%X11.1%11.1%X11.1%11.1%11.1%


For an explanation on why Mijntje and Hamudi have slightly higher probabilities than everyone else (i.e. the difference between 9.9%, 10.0%, and 10.1%), please see the comments section.