Wednesday, October 18, 2017

Season 6, Episode 5 Probabilities

No live blog tonight.

Truth Booth #4

Dimitri and Nicole got in the Truth Booth, and they are NO MATCH. But we knew this already! Still 105,376 possibilities.

Matchup Ceremony #4
  • Alexis - Dimitri
  • Diandra - Kareem
  • Zoe - Joe (repeat from ceremonies 1 and 3)
  • Uche - Clinton (repeat from ceremonies 1-3)
  • Audrey - Shad (repeat from ceremony 1)
  • Jada - Tyler
  • Keyana - Anthony
  • Nicole - Ethan
  • Geles - Michael
  • Nurys - Keith
  • Alivia - Malcolm

Blackout odds: 8.9% (9,411 of 105,376)
Instant win possible: Yes
Most likely number of lights: 2

3 beams of light mean 18,980 combinations remain.


Wednesday, October 11, 2017

Season 6, Episode 4 Probabilities - Live Blog

Another truth booth to lead us off tonight, with Malcolm and Nurys.

Truth Booth #3

No match! 328,840 possibilities left.


10:07: "She just murdered someone" WHAT!??

10:11: Geles sneaks off with Anthony for sex even though Ethan wants her.

Matchup Ceremony #3
  • Malcolm - Geles
  • Michael - Audrey
  • Joe - Zoe (repeat from ceremony 1)
  • Kareem - Alivia (repeat from ceremonies 1 and 2)
  • Tyler - Nicole (repeat from ceremony 1)
  • Shad - Keyana
  • Ethan - Alexis
  • Clinton - Uche (repeat from ceremonies 1 and 2)
  • Anthony - Jada
  • Keith - Diandra
  • Dimitri - Nurys (I seem to have missed the order on this one)
Blackout odds: 8.3% (27,313 of 328,840)
Instant win possible: No, more than 3 couples from ceremony 1 were repeated
Most likely number of lights: 2

2 matches leaves 105,376 combinations.

10:36: Diandra leaving Malcolm with an ultimatum. He seems conflicted.

10:40: The house is hoping to get the two three-peats into the truth booth. Little do they know they're not the highest probability couples!

10:43: Malcolm thinking the real Batman is Ben Affleck is insane.

10:44: Kareem and Alivia get knocked out. It comes down to this... is Clinton Team Bieber or Team Selena Gomez? Uche guesses Selena... and fails!

10:45: The couples advancing to the date are Nicole-Dimitri (inferred no match), Geles-Ethan (14.0%), and Zoe-Keith (5.6%).

11:01: Malcolm not happy with Nurys playing with the rest of the house... he explodes and Diandra takes advantage. Total love triangle right now, each taking what they can get.

Wednesday, October 4, 2017

Season 6, Episode 3 Probabilities - Live Blog

We're starting with a truth booth tonight!

Truth Booth #2

10:03: And starting with a no match between Anthony and Geles! 1,661,296 combinations remain.

(note: it seems like Anthony's numbers are off here, but it's just a rounding issue)

10:06: Keyana is closing in.

10:09: Ethan fired up the house!!

10:16: Michael is tired but Keyana can't handle him taking a nap without her.

10:18: Keyana doesn't have much self worth. Sad.

Matchup Ceremony #2

10:23: Never had a matchup ceremony this early in the episode before.

10:26: Keyana picks Michael anyway!

10:27: Ethan frustrated with so many repeats. In past seasons, it may have made sense to repeat fewer couples, but the blackout rule makes sense to try to avoid it...
  • Alivia - Kareem (repeat from ceremony 1)
  • Alexis - Keith (repeat from ceremony 1)
  • Uche - Clinton (repeat from ceremony 1)
  • Zoe - Tyler
  • Keyana - Michael (repeat from ceremony 1)
  • Jada - Ethan (repeat from ceremony 1)
  • Nurys - Malcolm (repeat from ceremony 1)
  • Nicole - Dimitri
  • Diandra - Anthony
  • Audrey - Joe
  • Geles - Shad
Blackout odds: 2.8% (47,342 of 1,661,296)
Instant win possible: No, more than 3 couples from ceremony 1 were repeated
Most likely number of lights: 2

10:34: 1 beam leaves 390,046 possibilities.


10:36: 1 beam is a pretty good outcome as it tells them that the following couples are very high probability of perfect matches: Joe - Zoe, Shad - Audrey, Tyler - Nicole, Dimitri - Diandra. It also eliminates three of this week's couples as inferred no matches: Dimitri - Nicole, Joe - Audrey, and Tyler - Zoe. The second ceremony is the earliest we've ever had inferred no matches!

Explaining the logic here...

If Joe and Audrey were a perfect match, that means that none of the 6 repeaters are a perfect match, and that 3 of the non-repeaters from Ceremony 1 are a match. However, there are only 4 non-repeaters from Ceremony 1 after Anthony and Geles went into the Truth Booth, and two of those couples include Joe and Audrey separately. Same for the other two couples.

10:41: Michael is gunning for Audrey, who is his worst possible pairing.

10:43: The eggs start slipping and dropping. Pretty dramatic elimination of couples.

10:44: The couples going on the date are... Ethan and Geles (13.9%), Malcolm and Nurys (15.7%), Michael and Audrey (5.9%). Malcolm and Nurys would be the most straight-forward pick - both the highest probability of a match, and a match would make it obvious that the repeaters from the second ceremony are no matches.

10:47: Diandra's still very hopeful, but Malcolm and Nurys got LUH.

10:51: Swamp date with alligators! Hawaii and the Dominican got nothing on this.

11:00: Malcolm and Nurys to the Truth Booth... and that's where we'll pick up next week.

Wednesday, September 27, 2017

Season 6, Episode 2 Probabilities - Live Blog

10:00: Welcome back to an episode that might start with a matchup ceremony!

10:03: Nope, we're revisiting Malcolm and "side piece" Nurys.

10:05: Geles is very attention-driven.

10:07: It's pirate party time... how spontaneous can this be, they just had pirate stuff hanging out everywhere? Meanwhile Diandra is spending an hour on her makeup and is gonna miss the whole party.

10:09: Diandra comes down and... not sure that she looks so much more polished that it was worth missing the whole party.

10:13: Still no sign of a matchup ceremony... what's happening?

10:14: Tyler is cooking! Lasagna?

Matchup Ceremony #1

10:16: Welcome back, Terrence J.

10:21: Malcolm struggling.

10:25: Audrey almost as mad as Diandra.

10:28: Ethan amazed by Clint.
  • Kareem - Alivia
  • Anthony - Geles
  • Malcolm - Nurys
  • Keith - Alexis
  • Joe - Zoe
  • Michael - Keyana
  • Ethan - Jada
  • Clinton - Uche
  • Shad - Audrey
  • Tyler - Nicole
  • Dimitri - Diandra
Blackout odds: 36.4% (13,216,113 of 36,288,000)
Instant win possible: Yes
Most likely number of lights: 1

It's 3 beams, meaning 2,269,449 possibilities remain.


10:31: Michael and Keyana get together... but are still hopeful that they might be a perfect match. Cute.

10:36: Zoe very practical to only bring workout clothes.

10:40: It's Shad and Uche winning the date... "I don't even know who that is."

10:41: Joe very excited to get Alexis for his date.

10:45: Anthony gets the date with Geles! Definitely the best Truth Booth candidate at 26.8%.

10:53: The date is a horse carriage driven by a mule.

10:54: Despite the excitement of the date, we focus back on Keith and Zoe.

10:57: Alexis is quitting Keith to think about Joe... are we not getting to another Truth Booth this episode? Strange to see a season going this slow...

Truth Booth

11:02: Big surprise, it's Anthony and Geles going to the truth booth... to be revealed next week.

Wednesday, September 20, 2017

Season 6, Episode 1 Probabilities - Live Blog

MTV's Are You The One? season 6 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.

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, cuts the prize in half 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.

Previous seasons have used 20 contestants - by adding another couple to the house, MTV has made this season 11 times harder than the four previous seasons.

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

10:00: Welcome back for Season 6! It's a new host and a new location for the house (New Orleans). Hard to beat Hawaii/DR and Ryan Devlin, but they'll try!

10:03: It's Terrence J from the After-Match. Ryan has disappeared from Twitter entirely!

10:04: Kareem is pretty excited to be the first from his hometown to get one million dollars, even though he's only going to get 1/22th of an annuity worth one million dollars.

10:05: Michael is huuuuge

10:06: Audrey and Malcolm are the first couple going on a date! I like the new bylines that talk about the love troubles each contestant has, instead of their city.

10:07: Keyana gets Ethan, who's a bit dorky and definitely scaring off a few of the contestants.

10:08: Clinton strikes out... none of the women want to go on a date even if it's him.

10:09: Jada dives in ... and ends up with Shad, even though she'd rather have Clinton.

10:11: I also like the names hanging on the shoulders - good way to intro us to the cast.

10:12: Surprising to see some guys with significantly less success with even getting to relationships this season in Ethan and Joe. Meanwhile, Keyana wants in on Michael... and she knows him from Instagram!

10:19: Clinton having difficulty as people didn't like the wristbands... but all the girls like his body. And he's a nude model!

Uche bringing the funny: "So you're January, but also July? At the end of February, you turn the page and it's still you?"

10:23: Alexis firing shots at West Virginia. Keith trying to get her to stop smoking.

10:24: Keith and Alexis the first couple going into the Boom Boom Room and really enjoying each others' company.

10:29: For the fifth straight season, we got a Tyler, and he's rattling off celeb lookalikes in the house. Is he JR Smith?

10:32: Ethan is bumming me out with his sad stories about sabotaging his own relationships.

Truth Booth

10:40: It's Ethan and Keyana going into the Truth Booth... no way these guys fit, right?

10:45: No match and Keyana is thrilled! Ethan is so devastated. 36,288,000 combinations remain.


10:47: This situation escalated like crazy. Keith is NOT happy, but Clinton a great sport for getting the shower kiss.

10:55: Pretty contentious sandwich going on right now.

10:58: We're getting pretty close to the end of the episode with no matchup ceremony. Last time they didn't have a truth booth and matchup ceremony in the same episode, they won early...

10:59: Diandra and Malcolm going on in the shower. A little early with the boyfriend call...

11:00 Then after Diandra goes to bed... Nurys sneaks in and goes for it!

11:01: Boner alert!

11:02: No matchup ceremony... see you next week!

Wednesday, March 22, 2017

Second Chances Open Thread

Not sure yet if Are You The One? Second Chances will have any interesting math, but I want to leave this open for the AYTO? Math community to comment on the new show. If there's any math, I'll take it on here!

9:55: Looks like The Choice is a modified Prisoner's Dilemma.

Wednesday, March 15, 2017

Season 5, Episode 10 Probabilities - Live Blog - The Matches Are In!

9:01: Season finale!

As a quick reminder, here are your perfect matches so far:
  • Kam - Eddie (Week 5 truth booth)
  • Carolina - Hayden (Week 8 truth booth)
  • Alicia - Mike (Week 8 matchup ceremony)
  • Gianna - Ozzy (Week 8 matchup ceremony)
  • Kari - Michael (Week 8 matchup ceremony)
  • Kathryn - Andre (Week 9 matchup ceremony)
  • Taylor - Osvaldo (Week 9 matchup ceremony)
  • Tyranny - Jaylan (Week 9 matchup ceremony)

We're hoping one of these six couples go to the Truth Booth:
  • Casandra - Derrick
  • Casandra - Tyler
  • Hannah - Tyler
  • Hannah - Joey
  • Shannon - Joey
  • Shannon - Derrick

9:03: Derrick also shares with us that he knows this exact information. So that means they've managed to figure out the same information as running the possibilities through a computer program. Could you have figured that all out without this blog? (I couldn't - but it's definitely possible!) If they send one of those couples to the Truth Booth, they know the answer. It seems really likely that this house will pull off a win.

9:06: Kathryn and Ozzy going at it. Even though they know their perfect matches are someone else.

9:10: Good to see some people questioning how they got to the conclusion. Wish they would have shown us a fast-forward version of them trying to figure it out!

Truth Booth

9:16: It's Joey and Casandra going to the Truth Booth, and Derrick and Tyranny going on the date but ineligible for the truth booth. So with the house knowing what we know... they have a 50-50 shot at it.

9:25: They have to be hoping for a trade at this point.

9:28: Trade offer is out! Derrick pushing the team to take the offer.

9:29: What we can infer from what's been shown... Derrick has come to the right conclusion somehow, but hasn't done a good enough job showing his work to the rest of the group, especially the women.

9:32: Trade accepted! The prize goes up another $150,000 to $800,000.

Matchup Ceremony

9:39: Why is Michael so sweaty?

9:41: Ryan skeptical about Mike and Alicia. Mike sounds like a cover letter when he's talking about Alicia.

9:48: Kathryn thinks Andre is her perfect match... because of the way he treats Taylor? Not a lot of faith in the process. The team is dedicated to the numbers.
  • Michael - Kari (inferred perfect match, repeat from episodes 4, 5, 6, and 9)
  • Ozzy - Gianna (inferred perfect match, repeat from episodes 1, 3, and 9)
  • Mike - Alicia (inferred perfect match, repeat from episodes 3, 5, 6, and 9)
  • Joey - Hannah (repeat from episode 9)
  • Osvaldo - Taylor (inferred perfect match, repeat from episodes 4, 7, 8, and 9)
  • Jaylan - Tyranny (inferred perfect match, repeat from episodes 4, 7, 8, and 9)
  • Tyler - Casandra
  • Andre - Kathryn (inferred perfect match, repeat from episode 9)
  • Derrick - Shannon (repeat from episode 8)

9:49: It comes down to this. If they're right... 11 beams. If they're wrong, 8 beams.

9:52: Not very lucky for the show to already be going to beams this early...

9:56: And... they LOSE! This house was sacrificed at the altar for the luck of previous seasons. Here are your confirmed perfect matches:
  • Kam - Eddie (Week 5 truth booth)
  • Carolina - Hayden (Week 8 truth booth)
  • Alicia - Mike (Week 8 matchup ceremony)
  • Gianna - Ozzy (Week 8 matchup ceremony)
  • Kari - Michael (Week 8 matchup ceremony)
  • Kathryn - Andre (Week 9 matchup ceremony)
  • Taylor - Osvaldo (Week 9 matchup ceremony)
  • Tyranny - Jaylan (Week 9 matchup ceremony)
  • Casandra - Derrick (Week 10 matchup ceremony)
  • Hannah - Tyler (Week 10 matchup ceremony)
  • Shannon - Joey (Week 10 matchup ceremony)

9:58: Shots being fired all across the stage. Guys mad at each other. Kari and Derrick taking it hard. Great final shot of a devastated Derrick. Let's go to the reunion.

10:00: In case you were curious - the spoilers that leaked earlier in the season turned out to be accurate. With those spoilers, we were able to figure out the perfect matches after week 8.

10:02: Derrick still feels the strategy worked. About half of the house agrees with him.

10:09: Feels like the women's outfits looked better on the island than tonight at the reunion.

10:12: If Shannon had chosen Derrick Week 9... and Hannah picked Joey, Casandra and Tyler - they would have had 8 beams and known the 11 perfect matches.

10:16: Tyranny and Alicia escalating quickly and then exploding.

10:18: Alicia is with Eddie after the season, and Kam is with Gio from a previous season.

10:50: Gianna has an "appreciation ring" from Hayden.