Wednesday, January 25, 2017

Season 5, Episode 3 Probabilities - Live Blog

9:02: Grief and shell shock. Who died? Several relationships and $500,000 of the prize.

9:06: They have to go fishing for dating profile words in the inter nets. One of the most interesting segments in history of the show!

9:10: How did they do this? Put the names on top after the couples pair up?

9:15: Up for the date are Hayden-Kathryn (8.8%), Joey-Kari (9.6%), and Ozzy-Carolina (9.4%). No great possibilities... a Truth Booth hit would be big, but it's probably worth giving up the Truth Booth this time around in exchange for the prize.

9:16: Some friction as Joey had been paired with Carolina and Ozzy had been paired with Kathryn earlier.

9:17: I always find it strange when someone in the house is upset about someone else moving on quickly. Don't they all enter the house super excited to find out they they're with a bunch of hot women/men?

9:28: Joey managing to sink both his date and Carolina's date with Ozzy!

Truth Booth

9:31: Ozzy and Carolina head to the Truth Booth... but Ryan once again offers the house the option to trade.

Estimated value of forfeiting truth booth for $150,000: $2.60
Estimated value of going to the truth booth: $2.41
Estimated value of losing the truth booth: $2.21
It's worth trading the truth booth for approximately: $102,647

Based on my loose math, I think it's worth making the trade here.

9:33: The house declines the trade! For love purposes, it's probably best not to make the trade even when the money comes close to break-even, because then the couple will sit together at every subsequent Truth Booth.

9:36: Are You The One? Fantasy League? Anyone here playing? Sound off in the comments...

9:37: No match! 1,808,808 possibilities remain.

AndreDerrickEdwardHaydenJaylanJoeyMichaelMikeOsvaldoOzzyTyler
AliciaXX10.7%11.7%10.7%12.3%10.8%10.7%10.7%11.7%10.7%
Carolina13.6%10.9%10.6%11.6%10.6%X10.7%10.6%10.6%X10.6%
Casandra10.7%8.4%8.1%8.8%21.2%9.7%8.1%X8.1%8.8%8.1%
Gianna11.5%8.8%8.5%X8.5%10.4%X8.5%8.5%26.6%8.5%
HannahX8.6%8.3%9.0%8.4%9.9%21.7%8.4%8.4%9.1%8.3%
Kam10.7%8.4%21.2%8.8%X9.7%8.1%8.1%8.1%8.8%8.1%
Kari10.7%8.4%8.1%8.8%8.1%9.7%8.1%21.2%X8.8%8.1%
Kathryn10.8%21.7%8.1%8.8%8.2%9.7%8.2%8.2%8.2%X8.1%
Shannon10.5%8.1%X23.7%7.9%9.5%7.9%7.9%7.9%8.6%7.9%
Taylor10.8%8.4%8.2%X8.2%9.7%8.2%8.2%8.2%8.9%21.4%
Tyranny10.7%8.4%8.1%8.8%8.1%9.7%8.1%8.1%21.2%8.8%X

9:38: Kathryn pretty smug.

9:39: And now it's Joey and Kathryn! He's all over the place.

9:40: Tyranny ready for Osvaldo.

9:45: Are Kam and Eddie a #perfectmatch?

9:48: Tyler and Kari hooked up. Cue dramatic music!

9:53: Taylor devastated about Tyler's handjob from Kari!

9:54: Michael with a surprisingly mature statement about communicating better. Classy!

Matchup Ceremony
  • Kathryn - Joey
  • Tyranny - Osvaldo (repeat from episode 1)
  • Hannah - Derrick
  • Casandra - Jaylan (repeat from episode 1)
  • Kam - Edward (repeat from episode 1)
  • Shannon - Tyler
  • Carolina - Hayden
  • Gianna - Ozzy (repeat from episode 1)
  • Alicia - Mike
  • Taylor - Michael
  • Kari - Andre
Blackout odds: 16.8% (304,145 out of 1,808,808)
Instant win possible: No, repeated more than two matchups from episode 1
Maximum number of lights: 9
Most likely number of lights: 1

Lots of repeats from episode 1. Decent strategy for avoiding a blackout, but not that helpful for whittling down possibilities.

Wow - 4 beams of light! Big win for the house, which gets down to 80,795 combinations left.

AndreDerrickEdwardHaydenJaylanJoeyMichaelMikeOsvaldoOzzyTyler
AliciaXX7.8%9.1%7.6%8.4%8.7%34.1%7.8%7.7%8.9%
Carolina8.5%8.2%7.2%37.2%7.1%X8.1%7.9%7.2%X8.6%
Casandra7.7%7.2%5.4%7.3%40.3%7.1%7.1%X5.4%5.2%7.3%
Gianna7.8%7.1%5.3%X5.1%7.0%X6.5%5.2%49.0%7.1%
HannahX31.8%7.3%8.7%7.1%8.2%5.8%8.2%7.3%7.1%8.5%
Kam7.6%7.0%40.5%7.2%X7.0%6.9%6.5%5.3%5.0%7.0%
Kari34.1%8.2%6.7%8.4%6.5%7.7%8.0%5.8%X6.4%8.2%
Kathryn8.8%6.2%6.9%8.8%6.7%30.9%8.4%8.0%6.9%X8.4%
Shannon8.8%8.4%X6.0%7.1%8.3%8.7%8.2%7.1%7.0%30.2%
Taylor8.9%8.7%7.4%X7.2%8.2%31.2%8.2%7.4%7.2%5.7%
Tyranny7.8%7.2%5.5%7.3%5.4%7.2%7.1%6.7%40.6%5.2%X

Wednesday, January 18, 2017

Season 5, Episode 2 Probabilities - Live Blog

Welcome back Nicole for a guest blog!

9:03 N: Mike is getting very real right away

9:04 A: Seems like they didn't get their partying on enough during the first week, so the guys are getting the party started!

9:04 N: It's Ozzy's birthday tomorrow, I wonder if he gets the same birthday present that Mike got

9:05 N: MTV casting fail, people that don't want to party and act trashy? Tyler and Taylor, kind of feel like their names are too similar

9:07 N: Confessional boner!!!

9:07 A: Andre and Alicia headed to the Boom Boom Room... lots of chemistry going on

9:10 N: It's challenge time!

9:12 A: The guys are going to be tied to posts and the girls are going to tie them up and find them by smell.

9:13 N: Tyler looks SOOOO disappointed that Hannah (8.2%) liked his scent.

9:14 A: Alicia finds Andre (17.8%) because he smells like Fritos!

9:15 N: Kari studied neuroscience in college, clearly took notes... that's why she won this get away date with Joey (8.2%).

9:18 N: Shower show and tell time. Kam, you are looking.

Truth Booth

9:28 N: Not shocking that it's Andre and Alicia headed to the Truth Booth. These two are going to be DEVASTATED if they are not a match.

9:30 A: No offer this week to trade the truth booth for an extra $150,000 added to the prize. Let's run those numbers anyway...

Estimated value of forfeiting truth booth for $150,000: $1.54
Estimated value of going to the truth booth: $1.89
Estimated value of losing the truth booth: $1.62
It's worth trading the truth booth for approximately: $413,691

9:34 A: No match! Brings us down to 5,540,084 combinations remaining.

AndreDerrickEdwardHaydenJaylanJoeyMichaelMikeOsvaldoOzzyTyler
AliciaX9.9%9.9%10.8%9.9%9.9%9.9%9.9%9.9%9.8%9.9%
Carolina9.9%7.8%7.8%8.4%7.8%19.6%7.8%7.8%7.8%7.6%7.8%
Casandra9.9%7.8%7.8%8.4%19.6%7.8%7.8%7.8%7.8%7.6%7.8%
Gianna10.8%8.4%8.4%X8.4%8.4%8.4%8.4%8.4%21.7%8.4%
Hannah9.9%7.8%7.8%8.4%7.8%7.8%19.6%7.8%7.8%7.6%7.8%
Kam9.9%7.8%19.6%8.4%7.8%7.8%7.8%7.8%7.8%7.6%7.8%
Kari9.9%7.8%7.8%8.4%7.8%7.8%7.8%19.6%7.8%7.6%7.8%
Kathryn9.9%19.6%7.8%8.4%7.8%7.8%7.8%7.8%7.8%7.6%7.8%
Shannon9.8%7.6%7.6%21.7%7.6%7.6%7.6%7.6%7.6%7.5%7.6%
Taylor9.9%7.8%7.8%8.4%7.8%7.8%7.8%7.8%7.8%7.6%19.6%
Tyranny9.9%7.8%7.8%8.4%7.8%7.8%7.8%7.8%19.6%7.6%7.8%

9:35 A: Now Hannah trying to talk Alicia out of Andre.

9:36 N: What's a "mandle"?

9:37 N: Alicia is not a happy camper.  So many female eye rolls

9:37 A: Hannah was just trying to move in on Andre as soon as she could.

Matchup Ceremony

9:45 A: Lots of people choosing differently... this actually is a great strategy for narrowing a lot of possibilities, but risk of a blackout is high.

9:47 A: Hilarious bit by Michael (who looks a bit like Kevin Love?) and Hannah calling Gianna Trump.
  • Osvaldo - Kari
  • Ozzy - Kathryn
  • Jaylan - Kam
  • Edward - Shannon
  • Derrick - Alicia
  • Hayden - Taylor
  • Andre - Hannah
  • Michael - Gianna
  • Joey - Carolina (repeat from episode 1)
  • Mike - Casandra
  • Tyler - Tyranny
Blackout odds: 36.0% (1,997,186 out of 5,540,084)
Instant win possible: No, did not repeat two matchups from episode 1
Maximum number of lights: 9
Most likely number of lights: 1

10:00 A: Blackout!!! They lose half a million dollars and still have 1,997,186 possibilities left.

AndreDerrickEdwardHaydenJaylanJoeyMichaelMikeOsvaldoOzzyTyler
AliciaXX10.8%11.9%10.9%12.3%10.9%10.9%10.9%10.6%10.8%
Carolina12.3%9.9%9.6%10.5%9.6%X9.7%9.6%9.6%9.4%9.6%
Casandra10.9%8.4%8.2%8.9%21.5%9.6%8.2%X8.2%8.0%8.2%
Gianna11.9%9.2%8.8%X8.8%10.5%X8.8%8.8%24.1%8.8%
HannahX8.7%8.4%9.2%8.4%9.9%22.1%8.4%8.4%8.2%8.4%
Kam10.8%8.4%21.5%8.9%X9.6%8.2%8.2%8.2%8.0%8.2%
Kari10.9%8.4%8.2%8.9%8.2%9.6%8.2%21.5%X8.0%8.2%
Kathryn10.8%21.8%8.1%8.8%8.1%9.6%8.2%8.1%8.1%X8.1%
Shannon10.6%8.2%X24.1%8.0%9.4%8.0%8.0%8.0%7.8%8.0%
Taylor10.9%8.5%8.2%X8.2%9.7%8.2%8.2%8.2%8.0%21.8%
Tyranny10.8%8.4%8.2%8.9%8.2%9.6%8.2%8.2%21.5%8.0%X


We had hundreds of readers following along live tonight - thank you! Would you be interested in watching a live stream after the show?

Would you watch an Are You The One? Math after-match live stream?

Yes
No

Wednesday, January 11, 2017

Season 5, Episode 1 Probabilities - Live Blog

MTV's Are You The One? season 5 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

9:00: Welcome back for Season 5! As mentioned above, this season now has 22 contestants, and getting all of the perfect matches is now 11 times harder. Is MTV setting us up for the first failure, or will they rig it again?

9:01: They've moved from Hawaii to the Dominican Republic!

9:03: The parents are playing matchmaker, selecting three dates for the getaway date: Joey - Carolina, Hannah - Osvaldo, and Gianna - Hayden.

9:04: The parents are setting up couples where the girl is not in to the guy at all!

9:06: Casandra can count!

9:07: Haircut, Eyebrows, And a Tan.

9:08: A girl who loves animals??

9:09: Also, Hayden, her mom picked you!

9:10: Spreading seed to see what bites?

9:11: Michael with a good line: "I dated a lot of girls with holes [in their hearts] but none of them got the surgery."

9:13: Kathryn and Mike going for it - in front of everyone!!!

9:18: Might not be the indecision that's making your stomach hurt...

9:20: Hayden freaking out Gianna. Too weird for her!

9:21: The AfterMatch is back!

9:26: The getaway is riding a truck through a forest and river.

9:28: "I would never cheat on a girl." "I like that about you." (Cue happy music and a kiss!)

Truth Booth

9:29: Hayden and Gianna to the Truth Booth!

9:30: Twist!! "What is the truth booth worth to you?"

9:34: Ryan offers the house a deal - give up the truth booth and the right to ever send that couple to the truth booth, get an extra $150,000 added to the prize.

9:35: Derrick knows what's up - the first episode, where they know nothing (9.1%), is probably the best time to add this money. And yet they choose not to take the trade!

9:36: No match means 36,288,000 combinations remain.


AndreDerrickEdwardHaydenJaylanJoeyMichaelMikeOsvaldoOzzyTyler
Alicia9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Carolina9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Casandra9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Gianna10.0%10.0%10.0%X10.0%10.0%10.0%10.0%10.0%10.0%10.0%
Hannah9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Kam9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Kari9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Kathryn9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Shannon9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Taylor9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%
Tyranny9.0%9.0%9.0%10.0%9.0%9.0%9.0%9.0%9.0%9.0%9.0%

Some very loose estimates on expected values on the truth booths... the estimate here is based on the expected number of combinations produced by the truth booth, multiplied by the prize and number of matchup ceremonies remaining. It does not account for the value of future truth booths, blackouts, or that each subsequent matchup ceremony reduces the number of combinations remaining - all of which could significantly impact the calculation!

Estimated value of forfeiting truth booth for $150,000: $1.53
Estimated value of going to the truth booth: $1.61
Estimated value of losing the truth booth: $1.47
It's worth trading the truth booth for approximately: $198,020

Matchup Ceremony

The new blackout rule is the prize gets cut in half - not just losing $250,000!
  • Kam - Edward
  • Taylor - Tyler
  • Kari - Mike
  • Casandra - Jaylan
  • Carolina - Joey
  • Tyranny - Osvaldo
  • Gianna - Ozzy
  • Hannah - Michael
  • Alicia - Andre
  • Kathryn - Derrick
  • Shannon - Hayden
Blackout odds: 36.4% (13,216,113 of 36,288,000)
Instant win possible: Yes
Most likely number of lights: 1

Two matches mean 6,741,548 possibilities remain.

AndreDerrickEdwardHaydenJaylanJoeyMichaelMikeOsvaldoOzzyTyler
Alicia17.8%8.2%8.2%8.9%8.2%8.2%8.2%8.2%8.2%8.0%8.2%
Carolina8.2%8.2%8.2%8.9%8.2%17.8%8.2%8.2%8.2%8.0%8.2%
Casandra8.2%8.2%8.2%8.9%17.8%8.2%8.2%8.2%8.2%8.0%8.2%
Gianna8.9%8.9%8.9%X8.9%8.9%8.9%8.9%8.9%19.8%8.9%
Hannah8.2%8.2%8.2%8.9%8.2%8.2%17.8%8.2%8.2%8.0%8.2%
Kam8.2%8.2%17.8%8.9%8.2%8.2%8.2%8.2%8.2%8.0%8.2%
Kari8.2%8.2%8.2%8.9%8.2%8.2%8.2%17.8%8.2%8.0%8.2%
Kathryn8.2%17.8%8.2%8.9%8.2%8.2%8.2%8.2%8.2%8.0%8.2%
Shannon8.0%8.0%8.0%19.8%8.0%8.0%8.0%8.0%8.0%7.9%8.0%
Taylor8.2%8.2%8.2%8.9%8.2%8.2%8.2%8.2%8.2%8.0%17.8%
Tyranny8.2%8.2%8.2%8.9%8.2%8.2%8.2%8.2%17.8%8.0%8.2%