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.
| Anthony | Clinton | Dimitri | Ethan | Joe | Kareem | Keith | Malcolm | Michael | Shad | Tyler | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Alexis | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Alivia | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Audrey | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Diandra | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Geles | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Jada | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Keyana | 10.0% | 10.0% | 10.0% | X | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% |
| Nicole | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Nurys | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Uche | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
| Zoe | 9.0% | 9.0% | 9.0% | 10.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% | 9.0% |
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!
So happy to see you're back. I'm a bit bummed there wasn't a matchup ceremony - I was hoping some of these early couples would find out they're not a match. I didn't realize the last time that happened, the cast won early - thanks for the insight. Looking forward to the blog this season. :)
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteGlad to see you are back as well!
ReplyDeleteI have to say the guys from this season seem to be a lot lower on the douche-bag index, than in seasons past.
ReplyDeleteAlthough I have to wonder what they are looking for in terms of the cast. Almost all of the guys, with "E-money" being the notable exception, have washboard abs and look as if they could double as underwear models. And usually have the personality and mental agility of small soap dish.
You don't see that on the girls' side. They are all attractive, but none of them look like they are triathletes or anything. And the girls usually seem to have much more in the personality department than the guys.
Hey Alex, what program did you use to generate your probability table?
ReplyDeleteHi Amanda, I wrote the code myself.
DeleteI'm trying to create a similar chart on Excel - and then I found your blog and it's amazing! Do you think it's possible to formulate a chart that just takes into account probabilities based on found no matches (not numbers of beams at each match up ceremony)?
DeleteDefinitely possible, just much harder to get to the right answer if you're ignoring all that extra information.
DeleteI totally agree, I'm just not sure how to factor in everything in an Excel formula. I'm having trouble just figuring out the formula that takes into account found No Matches only - are you familiar with Excel formulas? I would so appreciate ANY help!!!
Delete@Alex - give us some clues! Also stuck trying to replicate in excel. Any hints? :P
DeleteI don't think Excel is the right tool to solve this problem. The method I use would not be replicable in Excel since it would require creating 39,916,800 rows and Excel appears to have a maximum around 1,000,000 rows.
DeleteYour blog is the shit!!!!
ReplyDeletedoesn't 11 factorial include female/female couples and male/male couples...? it also counts (for example:) Jada and Michael as one... and Michael and Jada as another.
ReplyDelete