Wednesday, July 10, 2019

Season 8, Episode 4 Probabilities - Live Blog

Welcome back! A very long episode tonight - we've got an extra half hour.

9:03: I just noticed the new slogan - "The one could be anyone." It's replacing the old one: "If your perfect match was standing right in front of you, would you even know it?"

9:04: Basit wants Jonathan, Jonathan wants Justin, Justin wants Max. A bunch of one directional interest, although Max really wanted Justin at the end of the last episode.

9:06: Amber and Nour bonding over not knowing how to share their identity with their dads.

9:07: Justin and Max just going for it.

9:08: Jonathan comes through and makes it awkward. He's mad and showing it... much differently than other guys have in previous seasons.

9:10: I'm not sure I understand Jenna's math. The same logic that makes it more likely that the couples repeated in the two matchup ceremonies are perfect matches make it more likely that she and Kai are a match.

9:11: Jenna is super petty and goes straight for Remy. He is very happy to be used!

9:15: Time for the date challenge. This is way more fun than last season's fate button.

They took a survey of who the most desirable people in the house are... Amber and Jenna. The other housemates get to run pickup lines by the two of them... best pickup line wins. Amber says she knows Nour's language. Kai picks the word "cake."

Amber picks Kari (liking that she used "lick" and "crazy") and Paige. Nour is not happy.

Jenna falls for the cake line, picking Kai and Remy.

The date is snorkeling at night with manta rays!

Out of the group on the date, Jenna and Kai (10.3%) are the most likely couple and Amber and Kari (2.4%) are the least likely couple.

9:25: Nour just starts threatening Paige. Extremely over the top. Just for winning a game!

9:26: Basit and Jasmine have decided to throw a queer prom that night after the group gets back from the snorkeling.

9:33: Jenna and Kai yelling at each other in the rain... this can only end one way... yep.

9:37: All the guys leaned right into the outfits. A couple of the guys got drag names... Brandon is Bianca, Jonathan is Beyond Good.

9:38: And it's time for Basit's Dionne Slay!

9:40: Amber is somewhat interested in Paige! But very aware of Nour's feelings. Very respectful.

9:41: And now Kylie and Nour are feeling each other... oh! Not as respectful as Amber and Paige.

9:42: OK Mark on Ex on the Beach seems to be just as entertained as us!

9:48: Jenna and Kai are on the floor. Guess who's going to be going to the Truth Booth...

9:56: Chicken in the house.

9:57: I like when people go up to the couple picker as a pair and discuss what they're thinking. Good TV!

9:59: Nour calls Paige an ostrich.

Truth Booth #3

As expected, it's Jenna and Kai.

10:07: No match means 24,133 combinations remain.

AashaAmberBasitBrandonDannyJasmineJennaJonathan
AashaX3.7%4.0%17.1%5.7%6.6%7.4%4.0%
Amber3.7%X2.2%4.5%3.4%3.7%4.5%2.2%
Basit4.0%2.2%X4.8%3.6%4.0%4.8%46.8%
Brandon17.1%4.5%4.8%X6.6%7.3%8.6%4.8%
Danny5.7%3.4%3.6%6.6%X5.8%6.7%3.6%
Jasmine6.6%3.7%4.0%7.3%5.8%X16.8%4.0%
Jenna7.4%4.5%4.8%8.6%6.7%16.8%X4.8%
Jonathan4.0%2.2%46.8%4.8%3.6%4.0%4.8%X
Justin7.4%4.5%4.5%8.2%6.8%11.6%7.7%4.5%
Kai7.1%4.5%4.8%8.4%16.8%7.2%X4.8%
Kari4.0%2.2%2.4%4.8%3.6%4.0%4.8%2.4%
Kylie4.0%2.2%2.4%4.8%3.6%4.0%4.8%2.4%
Max6.6%4.0%4.3%7.8%6.6%6.6%7.7%4.3%
Nour4.1%49.8%2.4%5.0%3.7%4.1%5.0%2.4%
Paige11.1%4.1%4.4%7.3%6.5%7.1%7.9%4.4%
Remy7.1%4.5%4.8%X16.8%7.1%8.5%4.8%
JustinKaiKariKylieMaxNourPaigeRemy
Aasha7.4%7.1%4.0%4.0%6.6%4.1%11.1%7.1%
Amber4.5%4.5%2.2%2.2%4.0%49.8%4.1%4.5%
Basit4.5%4.8%2.4%2.4%4.3%2.4%4.4%4.8%
Brandon8.2%8.4%4.8%4.8%7.8%5.0%7.3%X
Danny6.8%16.8%3.6%3.6%6.6%3.7%6.5%16.8%
Jasmine11.6%7.2%4.0%4.0%6.6%4.1%7.1%7.1%
Jenna7.7%X4.8%4.8%7.7%5.0%7.9%8.5%
Jonathan4.5%4.8%2.4%2.4%4.3%2.4%4.4%4.8%
JustinX8.0%4.5%4.5%12.0%X7.5%8.2%
Kai8.0%X4.8%4.8%7.8%5.0%7.8%8.1%
Kari4.5%4.8%X46.8%4.3%2.4%4.4%4.8%
Kylie4.5%4.8%46.8%X4.3%2.4%4.4%4.8%
Max12.0%7.8%4.3%4.3%X4.5%11.1%7.9%
NourX5.0%2.4%2.4%4.5%X4.5%5.0%
Paige7.5%7.8%4.4%4.4%11.1%4.5%X7.6%
Remy8.2%8.1%4.8%4.8%7.9%5.0%7.6%X

10:18: Brandon is proud of Jonathan's pronoun usage!

Matchup Ceremony #3
  • Jonathan - Brandon
  • Aasha - Max
  • Paige - Amber
  • Kai - Danny (repeat from ceremony 1)
  • Jenna - Justin
  • Remy - Basit
  • Kylie - Kari (repeat from ceremonies 1 and 2)
  • Jasmine - Nour
Blackout probability: 33.8% (8,154 of 24,133)
Instant win possible: No, repeated 1 couple from ceremony 2
Maximum number of lights:: 6
Most likely number of lights: 1

2 beams means there are 4,383 possibilities left.
AashaAmberBasitBrandonDannyJasmineJennaJonathan
AashaX4.8%4.9%15.1%5.5%6.2%7.3%4.8%
Amber4.8%X3.6%6.0%3.5%4.6%5.7%3.8%
Basit4.9%3.6%X5.2%3.4%5.5%5.9%32.2%
Brandon15.1%6.0%5.2%X6.0%7.3%8.1%13.1%
Danny5.5%3.5%3.4%6.0%X6.0%6.0%3.5%
Jasmine6.2%4.6%5.5%7.3%6.0%X7.8%5.5%
Jenna7.3%5.7%5.9%8.1%6.0%7.8%X5.8%
Jonathan4.8%3.8%32.2%13.1%3.5%5.5%5.8%X
Justin6.2%5.2%5.2%7.0%6.2%14.4%20.1%5.2%
Kai6.2%4.5%4.5%7.1%33.2%6.5%X4.6%
Kari1.6%1.1%1.0%2.0%0.4%1.6%1.8%0.9%
Kylie1.6%1.1%1.0%2.0%0.4%1.6%1.8%0.9%
Max17.1%5.0%4.8%6.9%5.8%6.3%7.3%4.8%
Nour5.1%34.1%4.3%6.5%4.0%11.7%6.2%4.4%
Paige6.0%10.9%5.3%7.6%6.3%6.8%7.7%5.3%
Remy7.7%5.9%13.1%X9.7%8.3%8.6%5.1%
JustinKaiKariKylieMaxNourPaigeRemy
Aasha6.2%6.2%1.6%1.6%17.1%5.1%6.0%7.7%
Amber5.2%4.5%1.1%1.1%5.0%34.1%10.9%5.9%
Basit5.2%4.5%1.0%1.0%4.8%4.3%5.3%13.1%
Brandon7.0%7.1%2.0%2.0%6.9%6.5%7.6%X
Danny6.2%33.2%0.4%0.4%5.8%4.0%6.3%9.7%
Jasmine14.4%6.5%1.6%1.6%6.3%11.7%6.8%8.3%
Jenna20.1%X1.8%1.8%7.3%6.2%7.7%8.6%
Jonathan5.2%4.6%0.9%0.9%4.8%4.4%5.3%5.1%
JustinX6.9%1.5%1.5%5.9%X6.7%7.9%
Kai6.9%X0.7%0.7%6.6%5.0%6.8%6.7%
Kari1.5%0.7%X80.8%1.5%1.0%1.7%2.3%
Kylie1.5%0.7%80.8%X1.5%1.0%1.7%2.3%
Max5.9%6.6%1.5%1.5%X5.2%13.7%7.4%
NourX5.0%1.0%1.0%5.2%X5.1%6.5%
Paige6.7%6.8%1.7%1.7%13.7%5.1%X8.4%
Remy7.9%6.7%2.3%2.3%7.4%6.5%8.4%X

10:33: Our end shot - Basit is out on Jonathan.

Wednesday, July 3, 2019

Season 8, Episode 3 Probabilities

Unfortunately, I'm not able to watch the show tonight. I've opened up the comments for tonight's episode, feel free to comment away and let me know what happened at the Truth Booth and Matchup Ceremony - I'll have the probabilities up in the morning. I'll return for the Live Blog next week.

Update (10:15 PM) - Here's the update based on what was shared in the comments:

Truth Booth #2

Brandon & Remy - no match leaves 120,800 combinations left.
AashaAmberBasitBrandonDannyJasmineJennaJonathan
AashaX4.7%4.8%7.1%4.8%4.8%4.8%4.8%
Amber4.7%X4.7%6.9%4.7%4.7%4.7%4.7%
Basit4.8%4.7%X7.1%4.8%4.8%4.8%28.0%
Brandon7.1%6.9%7.1%X7.1%7.1%7.1%7.1%
Danny4.8%4.7%4.8%7.1%X4.8%4.8%4.8%
Jasmine4.8%4.7%4.8%7.1%4.8%X28.0%4.8%
Jenna4.8%4.7%4.8%7.1%4.8%28.0%X4.8%
Jonathan4.8%4.7%28.0%7.1%4.8%4.8%4.8%X
Justin5.0%5.0%5.0%7.5%5.0%5.0%5.0%5.0%
Kai4.8%4.7%4.8%7.1%28.0%4.8%4.8%4.8%
Kari4.8%4.7%4.8%7.1%4.8%4.8%4.8%4.8%
Kylie4.8%4.7%4.8%7.1%4.8%4.8%4.8%4.8%
Max4.7%4.5%4.7%6.9%4.7%4.7%4.7%4.7%
Nour5.0%30.0%5.0%7.5%5.0%5.0%5.0%5.0%
Paige28.0%4.7%4.8%7.1%4.8%4.8%4.8%4.8%
Remy7.1%6.9%7.1%X7.1%7.1%7.1%7.1%
JustinKaiKariKylieMaxNourPaigeRemy
Aasha5.0%4.8%4.8%4.8%4.7%5.0%28.0%7.1%
Amber5.0%4.7%4.7%4.7%4.5%30.0%4.7%6.9%
Basit5.0%4.8%4.8%4.8%4.7%5.0%4.8%7.1%
Brandon7.5%7.1%7.1%7.1%6.9%7.5%7.1%X
Danny5.0%28.0%4.8%4.8%4.7%5.0%4.8%7.1%
Jasmine5.0%4.8%4.8%4.8%4.7%5.0%4.8%7.1%
Jenna5.0%4.8%4.8%4.8%4.7%5.0%4.8%7.1%
Jonathan5.0%4.8%4.8%4.8%4.7%5.0%4.8%7.1%
JustinX5.0%5.0%5.0%30.0%X5.0%7.5%
Kai5.0%X4.8%4.8%4.7%5.0%4.8%7.1%
Kari5.0%4.8%X28.0%4.7%5.0%4.8%7.1%
Kylie5.0%4.8%28.0%X4.7%5.0%4.8%7.1%
Max30.0%4.7%4.7%4.7%X5.0%4.7%6.9%
NourX5.0%5.0%5.0%5.0%X5.0%7.5%
Paige5.0%4.8%4.8%4.8%4.7%5.0%X7.1%
Remy7.5%7.1%7.1%7.1%6.9%7.5%7.1%X


Matchup Ceremony #2
  • Kai - Jenna
  • Basit - Jonathan (repeat from ceremony 1)
  • Justin - Jasmine
  • Amber - Nour (repeat from ceremony 1)
  • Kylie - Kari (repeat from ceremony 1)
  • Brandon - Aasha
  • Remy - Danny
  • Max - Paige
Blackout probability: 24.3% (29,410 of 120,800)
Instant win possible: No, repeated 3 couples from ceremony 1
Maximum number of lights: 6
Most likely number of lights: 1

2 beams means 26,907 possibilities remain.
AashaAmberBasitBrandonDannyJasmineJennaJonathan
AashaX3.8%4.1%15.3%5.9%6.6%6.6%4.1%
Amber3.8%X2.4%4.9%3.8%4.1%4.1%2.4%
Basit4.1%2.4%X5.2%4.1%4.4%4.3%45.2%
Brandon15.3%4.9%5.2%X7.2%7.8%7.7%5.2%
Danny5.9%3.8%4.1%7.2%X6.4%6.0%4.1%
Jasmine6.6%4.1%4.4%7.8%6.4%X15.0%4.4%
Jenna6.6%4.1%4.3%7.7%6.0%15.0%X4.3%
Jonathan4.1%2.4%45.2%5.2%4.1%4.4%4.3%X
Justin6.6%4.5%4.5%8.1%6.8%10.4%6.9%4.5%
Kai6.4%4.1%4.3%7.5%15.0%6.5%10.3%4.3%
Kari4.1%2.4%2.6%5.2%4.1%4.4%4.3%2.6%
Kylie4.1%2.4%2.6%5.2%4.1%4.4%4.3%2.6%
Max6.0%4.0%4.3%7.6%6.5%6.5%6.9%4.3%
Nour4.2%48.2%2.6%5.4%4.2%4.5%4.4%2.6%
Paige15.0%4.1%4.3%7.3%6.4%6.9%7.1%4.3%
Remy7.3%4.9%5.2%X15.4%7.7%7.6%5.2%
JustinKaiKariKylieMaxNourPaigeRemy
Aasha6.6%6.4%4.1%4.1%6.0%4.2%15.0%7.3%
Amber4.5%4.1%2.4%2.4%4.0%48.2%4.1%4.9%
Basit4.5%4.3%2.6%2.6%4.3%2.6%4.3%5.2%
Brandon8.1%7.5%5.2%5.2%7.6%5.4%7.3%X
Danny6.8%15.0%4.1%4.1%6.5%4.2%6.4%15.4%
Jasmine10.4%6.5%4.4%4.4%6.5%4.5%6.9%7.7%
Jenna6.9%10.3%4.3%4.3%6.9%4.4%7.1%7.6%
Jonathan4.5%4.3%2.6%2.6%4.3%2.6%4.3%5.2%
JustinX7.2%4.5%4.5%16.3%X6.8%8.3%
Kai7.2%X4.3%4.3%7.0%4.4%7.0%7.3%
Kari4.5%4.3%X45.2%4.3%2.6%4.3%5.2%
Kylie4.5%4.3%45.2%X4.3%2.6%4.3%5.2%
Max16.3%7.0%4.3%4.3%X4.4%10.0%7.7%
NourX4.4%2.6%2.6%4.4%X4.4%5.4%
Paige6.8%7.0%4.3%4.3%10.0%4.4%X7.6%
Remy8.3%7.3%5.2%5.2%7.7%5.4%7.6%X

Wednesday, June 26, 2019

Season 8, Episodes 1 & 2 Probabilities - Live Blog

MTV's Are You The One? season 8 (Come One, Come All) features 16 individuals looking for their perfect match. If they manage to guess the exactly right combination, they'll split $1,000,000. In a twist from previous seasons, each house member is sexually fluid and can partner off with any of the possible partners.

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.

We'll have to watch closely as some of the rules may be different this season...

Prize and Probability of Winning

All 16 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 $32,000 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, reduces the prize by $250,000 if a matchup ceremony results in no lights other than truth booths.

The number of possible permutations in this season's game is 2,027,025 - read this post for an explanation of why!

Put simply, a random guess would have a 1 in 2,027,025 chance of winning (0.00000049333%). The calculations done here throughout the season evaluate all of those 2,027,025 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.

Live Blog

Double episode tonight, so we'll need to catch up on the presidential debate on YouTube tomorrow...

Welcome to Season 8 - Come One, Come All.

We have fewer possible combinations this season than any other season - BUT - each contestant has 15 possible matches, which is harder for each individual to figure out.

9:04: Jonathan is a bank manager! Don't judge a book by its cover... great hair.

9:06: Looks like I have to keep track of pronouns... Basit is they / them (but prefers Basit). Kai is nongender, he / him / they / them.

9:10: Paige is coming out for the first time on the show. Amber kept her girlfriend a secret from her dad for 6 years!

9:12: Danny's claiming this game is 345 times harder than any previous season? Wondering where he came up with that number... maybe he thought there were 20 contestants? That would have had 16 times more possibilities. Maybe he did some math on win probability?

9:22: Jenna and Kai's kiss on the cheek escalates quickly!

9:24: Is Nour the first divorcee on the show?

9:27: Remy introduces himself as this season's drama leader... he is looking to be involved with everyone... wants to slide in between Jenna and Kai and make it messy.

9:31: Amber and Nour are the next week 1 couple. Justin sad he isn't getting a shot at Nour, but Jonathan is ready for him. I get Jonathan as the bank manager now with the hair up.

9:32: Danny is a software developer and data analyst. I guess this is as close as you'll get to me being on the show??

9:39: Welcome to the show, Dr. Frankie!

9:40: This might be the most complicated challenge ever. Overcome literal hurdles of relationships (or go under if you haven't). Pick up bags of dirt representing baggage. Tandem walking through a relationship minefield. Feels like this could have been three separate challenges!

9:41: Justin has boxed Amber out of Nour.

9:42: Basit and Kylie are in sync, but a lot of other contestants are eating it.

9:43: Your first challenge winners - Basit and Kylie, Jasmine and Paige, Justin and Nour.

9:51: The getaway this week is a kayaking adventure. Looks like a lot of fun!

9:54: Basit's drag name is Dion Slay. Nice!

Truth Booth #1

10:01: No surprise, it's Justin and Nour. As the first couple going into the Truth Booth they have a 6.7% (1 in 15) chance of being a perfect match.

10:03: Jonathan says this single truth booth is going to solve everything... riiight...

10:08: No match! 1,891,890 possibilities remain.

Doing split tables this year to try to fit better on the screen, let me know how you like it. Because of the way this season works, you can read the table either left-to-right or up-and-down.

AashaAmberBasitBrandonDannyJasmineJennaJonathan
AashaX6.6%6.6%6.6%6.6%6.6%6.6%6.6%
Amber6.6%X6.6%6.6%6.6%6.6%6.6%6.6%
Basit6.6%6.6%X6.6%6.6%6.6%6.6%6.6%
Brandon6.6%6.6%6.6%X6.6%6.6%6.6%6.6%
Danny6.6%6.6%6.6%6.6%X6.6%6.6%6.6%
Jasmine6.6%6.6%6.6%6.6%6.6%X6.6%6.6%
Jenna6.6%6.6%6.6%6.6%6.6%6.6%X6.6%
Jonathan6.6%6.6%6.6%6.6%6.6%6.6%6.6%X
Justin7.1%7.1%7.1%7.1%7.1%7.1%7.1%7.1%
Kai6.6%6.6%6.6%6.6%6.6%6.6%6.6%6.6%
Kari6.6%6.6%6.6%6.6%6.6%6.6%6.6%6.6%
Kylie6.6%6.6%6.6%6.6%6.6%6.6%6.6%6.6%
Max6.6%6.6%6.6%6.6%6.6%6.6%6.6%6.6%
Nour7.1%7.1%7.1%7.1%7.1%7.1%7.1%7.1%
Paige6.6%6.6%6.6%6.6%6.6%6.6%6.6%6.6%
Remy6.6%6.6%6.6%6.6%6.6%6.6%6.6%6.6%
JustinKaiKariKylieMaxNourPaigeRemy
Aasha7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
Amber7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
Basit7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
Brandon7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
Danny7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
Jasmine7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
Jenna7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
Jonathan7.1%6.6%6.6%6.6%6.6%7.1%6.6%6.6%
JustinX7.1%7.1%7.1%7.1%X7.1%7.1%
Kai7.1%X6.6%6.6%6.6%7.1%6.6%6.6%
Kari7.1%6.6%X6.6%6.6%7.1%6.6%6.6%
Kylie7.1%6.6%6.6%X6.6%7.1%6.6%6.6%
Max7.1%6.6%6.6%6.6%X7.1%6.6%6.6%
NourX7.1%7.1%7.1%7.1%X7.1%7.1%
Paige7.1%6.6%6.6%6.6%6.6%7.1%X6.6%
Remy7.1%6.6%6.6%6.6%6.6%7.1%6.6%X

10:15: Apparently Kai is also trying to move on everyone in the house. Not a bad strategy, honestly!

10:19: Jenna takes advantage of Kai's attention fraying to escalate... and we have our first visit to the Boom Boom Room!

10:24: Kari starting to feel out Kylie, who's feels like she's spent more time with Basit... some people feel like they're not making moves, but they haven't been in the house very long.

10:28: Remy and Kai hook up!! Kai is back in the Boom Boom Room with someone different in 2 hours... is this a record? And then he goes back to hold Jenna while she sleeps!

10:43: Dr. Frankie time.

Matchup Ceremony #1
  • Nour - Amber
  • Kari - Kylie
  • Max - Justin
  • Basit - Jonathan
  • Aasha - Paige
  • Remy - Brandon
  • Jasmine - Jenna
  • Kai - Danny
10:45: New stage for this year since nobody starts seated!

10:55: This tea!

10:56: Danny's matchup outfit ðŸ˜‚ - so square. He's excited for Kai but not vice-versa. No man-woman matches!

10:57: This year's blackout rule is that your prize is cut by $250,000. Lighter penalty for the first blackout, harder for the third. And Max gets it right - the odds of a blackout are higher than ever before. In fact, it's more likely to be a blackout than not. And a blackout tells them the least amount of information since it's the most likely outcome.

Blackout probability: 58.4% (1,105,624 of 1,891,890)
Instant win possible: Yes
Most likely number of lights: 0 (blackout)

11:02: 2 beams means 160,060 combinations left.

AashaAmberBasitBrandonDannyJasmineJennaJonathan
AashaX5.2%5.4%5.4%5.4%5.4%5.4%5.4%
Amber5.2%X5.2%5.2%5.2%5.2%5.2%5.2%
Basit5.4%5.2%X5.4%5.4%5.4%5.4%24.5%
Brandon5.4%5.2%5.4%X5.4%5.4%5.4%5.4%
Danny5.4%5.2%5.4%5.4%X5.4%5.4%5.4%
Jasmine5.4%5.2%5.4%5.4%5.4%X24.5%5.4%
Jenna5.4%5.2%5.4%5.4%5.4%24.5%X5.4%
Jonathan5.4%5.2%24.5%5.4%5.4%5.4%5.4%X
Justin5.7%5.7%5.7%5.7%5.7%5.7%5.7%5.7%
Kai5.4%5.2%5.4%5.4%24.5%5.4%5.4%5.4%
Kari5.4%5.2%5.4%5.4%5.4%5.4%5.4%5.4%
Kylie5.4%5.2%5.4%5.4%5.4%5.4%5.4%5.4%
Max5.2%5.1%5.2%5.2%5.2%5.2%5.2%5.2%
Nour5.7%26.4%5.7%5.7%5.7%5.7%5.7%5.7%
Paige24.5%5.2%5.4%5.4%5.4%5.4%5.4%5.4%
Remy5.4%5.2%5.4%24.5%5.4%5.4%5.4%5.4%
JustinKaiKariKylieMaxNourPaigeRemy
Aasha5.7%5.4%5.4%5.4%5.2%5.7%24.5%5.4%
Amber5.7%5.2%5.2%5.2%5.1%26.4%5.2%5.2%
Basit5.7%5.4%5.4%5.4%5.2%5.7%5.4%5.4%
Brandon5.7%5.4%5.4%5.4%5.2%5.7%5.4%24.5%
Danny5.7%24.5%5.4%5.4%5.2%5.7%5.4%5.4%
Jasmine5.7%5.4%5.4%5.4%5.2%5.7%5.4%5.4%
Jenna5.7%5.4%5.4%5.4%5.2%5.7%5.4%5.4%
Jonathan5.7%5.4%5.4%5.4%5.2%5.7%5.4%5.4%
JustinX5.7%5.7%5.7%26.4%X5.7%5.7%
Kai5.7%X5.4%5.4%5.2%5.7%5.4%5.4%
Kari5.7%5.4%X24.5%5.2%5.7%5.4%5.4%
Kylie5.7%5.4%24.5%X5.2%5.7%5.4%5.4%
Max26.4%5.2%5.2%5.2%X5.7%5.2%5.2%
NourX5.7%5.7%5.7%5.7%X5.7%5.7%
Paige5.7%5.4%5.4%5.4%5.2%5.7%X5.4%
Remy5.7%5.4%5.4%5.4%5.2%5.7%5.4%X


11:03: No live blog next week.

Tuesday, June 25, 2019

Season 8 - Counting Combinations

Season 8 is almost here! This season has the biggest changes yet: all 16 housemates are sexually fluid, meaning anyone else in the house could be a perfect match.

I'm going to explain how to figure out how many possible combinations of contestants there are for the matchup ceremonies this season.

(all images from MTV website, used for informational purposes only)

Two Housemates


Let's start with an easy thing to prove. If there are only two housemates, you only have one possible combination:


2 housemates = 1 combination

Four Housemates


Now let's add two new housemates, Max and Nour:

4 housemates = ? combinations

We know that Nour could be perfect matches with any one of the three other housemates. When we pair up Nour with a housemate, we know that there are two housemates left over that only has one combination. So there are only three possible combinations for four housemates:

2 housemates = 1 combination

2 housemates = 1 combination

2 housemates = 1 combination
4 housemates = 3 combinations


Six Housemates


Now let's add two more and go to six:


6 housemates = ? combinations

Let's focus on the two new additions, Kylie and Justin. If we were to assume they were a perfect match, then the four housemates left over are the same as before:


4 housemates = 3 combinations

If they weren't a perfect match, though, Kylie's partner could be anyone. Each time we partner Kylie with someone, we see that there are four housemates remaining:

4 housemates = 3 combinations

4 housemates = 3 combinations

4 housemates = 3 combinations

4 housemates = 3 combinations
So Kylie has 5 possible partners, and whenever she's partnered with a housemate, the four remaining housemates can form 3 combinations. 5 x 3...
6 housemates = 15 combinations


The Proof


Did you notice the pattern? Whenever you add two new housemates, all you have to do is pair off one of those housemates with each person in the house, and then multiply that by the number of combinations of the leftover people.

The way we might express this mathematically is in the format f(n), where f() stands for a mathematical function and n is the number of housemates. The formula is thus:

f(n) = (n - 1) x f(n - 2)

You also have to pair this with the base we started with, that two people can only form one combination of couples:

f(2) = 1

Then, if you follow this formula all the way out... you find that 16 housemates can make 2,027,025 possible matchup combinations. This process is what's called a proof by induction.

Housemates
Combinations
2
1
4
3
6
15
8
105
10
945
12
10,395
14
135,135
16
2,027,025