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