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 20 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 $25,000 each (in addition to a shot at finding their perfect match and getting some weekly face time on MTV).The number of possible permutations in the original game is 10 factorial = 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800. Put simply, a random guess would have a 1 in 3,628,800 chance of winning (0.00002756%). The calculations done here throughout the season evaluate all of those 3,628,800 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.
Live Blog
10:00: I'm back tonight with a live blog, despite the sour taste from last season's pretty clear indication that AYTO is rigged. 84% of readers agree - even if the cast members had the ability to go through all of the possible permutations, they would have only had a 1 in 4 chance of getting it right.10:05: The first truth booth will add $250,000 to the final prize. The odds of any pairing right off the bat is 1 in 10.
10:08: This season's twist is adding the foreign guy? Israeli with the fake Italian accent?
10:15: 6 years without dating? How old is this guy?
10:27: A lot of these people believe in horoscopes. Is that still a thing?
Truth Booth
10:32: Tori and Prosper to the Truth Booth, over Kaylen-Stephen and Alyssa-Tyler.
No match, leaving 3,265,920 combinations. They're all surprised to see this outcome which had a 90% chance of happening.
| Asaf | Cam | Cameron | Giovanni | John | Morgan | Prosper | Sam | Stephen | Tyler | |
|---|---|---|---|---|---|---|---|---|---|---|
| Alyssa | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Camille | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Emma | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Francesca | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Julia | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Kaylen | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Mikala | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Nicole | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
| Tori | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% | X | 11.1% | 11.1% | 11.1% |
| Victoria | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% |
Matchup Ceremony
10:44: The blackout rule is back this season - get no lights other than truth booths, and the prize goes down by $250,000. The chance of this first matchup ceremony resulting in a blackout is...
Blackout odds: 36.3% (1,186,632 possible blackout combinations out of 3,265,920)
Instant win possible: Yes
Most likely number of lights: 1
10:55: Cameron, Cam, and Sam makes it very hard to follow the results just by listening...
- Kaylen - Giovanni
- Victoria - Cam
- Francesca - Asaf
- Emma - John
- Camille - Prosper
- Alyssa - Sam
- Mikala - Cameron
- Julia - Morgan
- Nicole - Stephen
- Tori - Tyler
| Asaf | Cam | Cameron | Giovanni | John | Morgan | Prosper | Sam | Stephen | Tyler | |
|---|---|---|---|---|---|---|---|---|---|---|
| Alyssa | 7.8% | 7.8% | 7.8% | 7.8% | 7.8% | 7.8% | 8.4% | 29.4% | 7.8% | 7.5% |
| Camille | 7.5% | 7.5% | 7.5% | 7.5% | 7.5% | 7.5% | 32.5% | 7.5% | 7.5% | 7.2% |
| Emma | 7.8% | 7.8% | 7.8% | 7.8% | 29.4% | 7.8% | 8.4% | 7.8% | 7.8% | 7.5% |
| Francesca | 29.4% | 7.8% | 7.8% | 7.8% | 7.8% | 7.8% | 8.4% | 7.8% | 7.8% | 7.5% |
| Julia | 7.8% | 7.8% | 7.8% | 7.8% | 7.8% | 29.4% | 8.4% | 7.8% | 7.8% | 7.5% |
| Kaylen | 7.8% | 7.8% | 7.8% | 29.4% | 7.8% | 7.8% | 8.4% | 7.8% | 7.8% | 7.5% |
| Mikala | 7.8% | 7.8% | 29.4% | 7.8% | 7.8% | 7.8% | 8.4% | 7.8% | 7.8% | 7.5% |
| Nicole | 7.8% | 7.8% | 7.8% | 7.8% | 7.8% | 7.8% | 8.4% | 7.8% | 29.4% | 7.5% |
| Tori | 8.4% | 8.4% | 8.4% | 8.4% | 8.4% | 8.4% | X | 8.4% | 8.4% | 32.5% |
| Victoria | 7.8% | 29.4% | 7.8% | 7.8% | 7.8% | 7.8% | 8.4% | 7.8% | 7.8% | 7.5% |
So glad you're posting again! I already have my excel sheet filled out with my names to cross off as we go along.
ReplyDeleteSame! I made my own table as well. So happy this show (and blog) are back.
DeleteI just made mine as well. I also LOVE the timed commentary, Alex. Who are you? Your "Complete Profile" doesn't offer many clues. I have followed your blog since Season 1.
DeleteI'm just a guy! Software developer in Boston, MA who likes probability and reality TV.
DeleteI love this! Alex, you're my hero & I excited to make my spreadsheet to play along!
DeleteDoes anyone else watch So You Think You Can Dance? Because Asaf was a contestant on the show last season. I was so upset to see him on AYTO because I enjoy this show and don't need him ruining it for me. He's so annoying! At this point I'm hoping him and Francesca are a perfect match and leave the house ASAP. I don't want to have to watch him for weeks on end.
ReplyDeletethanks for starting the blog up for S4!
ReplyDeletebest blog
ReplyDeleteJust so you know, the probability of matches is not 10 factorial. There are 100 different match options. 10 options per person. 10 X 10 =100.
ReplyDeleteThe number of possible combinations is 10 factorial. To confirm this, try counting the combinations with 2 men and 2 women (only 2 possible combinations) or 3 men and 3 women (6 possible combinations).
DeleteMan, I hope you aren't really a statistics and probability teacher!
DeleteTrying to make an excel file as well... Could someone share theirs with me or throw me some equations for determining how many permutations are eliminated with each event? Thanks!
ReplyDeleteThis is awesome! I am geeking out on the statistics too and am glad I am not alone lol. It all started when I just watched season 3. They were terrible! So before I watched the final match up ceremony, I tried to see if I could figure out the right combo. And like you, I figured that they were unable to get the correct combo before the ceremony. And then when they won I googled "Are You The One rigged" and found your blog lol. Now I'll happily be keeping track with season 4.
ReplyDeleteHey Alex- cool blog :)
ReplyDeleteHow do you update the probabilities after the matchup ceremony? Like I understand that you need to scale 3/10 based on the existing probabilities, but I don't understand exactly where 29.4% and 32.5% come from. Thanks!
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ReplyDeleteJust getting into this show for the first time and just found your blog. This is amazing. You've saved me a lot of time. Your live coverage is a riot also. You're a true hero.
ReplyDelete