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.
| Andre | Derrick | Edward | Hayden | Jaylan | Joey | Michael | Mike | Osvaldo | Ozzy | Tyler | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Alicia | X | X | 10.7% | 11.7% | 10.7% | 12.3% | 10.8% | 10.7% | 10.7% | 11.7% | 10.7% |
| Carolina | 13.6% | 10.9% | 10.6% | 11.6% | 10.6% | X | 10.7% | 10.6% | 10.6% | X | 10.6% |
| Casandra | 10.7% | 8.4% | 8.1% | 8.8% | 21.2% | 9.7% | 8.1% | X | 8.1% | 8.8% | 8.1% |
| Gianna | 11.5% | 8.8% | 8.5% | X | 8.5% | 10.4% | X | 8.5% | 8.5% | 26.6% | 8.5% |
| Hannah | X | 8.6% | 8.3% | 9.0% | 8.4% | 9.9% | 21.7% | 8.4% | 8.4% | 9.1% | 8.3% |
| Kam | 10.7% | 8.4% | 21.2% | 8.8% | X | 9.7% | 8.1% | 8.1% | 8.1% | 8.8% | 8.1% |
| Kari | 10.7% | 8.4% | 8.1% | 8.8% | 8.1% | 9.7% | 8.1% | 21.2% | X | 8.8% | 8.1% |
| Kathryn | 10.8% | 21.7% | 8.1% | 8.8% | 8.2% | 9.7% | 8.2% | 8.2% | 8.2% | X | 8.1% |
| Shannon | 10.5% | 8.1% | X | 23.7% | 7.9% | 9.5% | 7.9% | 7.9% | 7.9% | 8.6% | 7.9% |
| Taylor | 10.8% | 8.4% | 8.2% | X | 8.2% | 9.7% | 8.2% | 8.2% | 8.2% | 8.9% | 21.4% |
| Tyranny | 10.7% | 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
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.
| Andre | Derrick | Edward | Hayden | Jaylan | Joey | Michael | Mike | Osvaldo | Ozzy | Tyler | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Alicia | X | X | 7.8% | 9.1% | 7.6% | 8.4% | 8.7% | 34.1% | 7.8% | 7.7% | 8.9% |
| Carolina | 8.5% | 8.2% | 7.2% | 37.2% | 7.1% | X | 8.1% | 7.9% | 7.2% | X | 8.6% |
| Casandra | 7.7% | 7.2% | 5.4% | 7.3% | 40.3% | 7.1% | 7.1% | X | 5.4% | 5.2% | 7.3% |
| Gianna | 7.8% | 7.1% | 5.3% | X | 5.1% | 7.0% | X | 6.5% | 5.2% | 49.0% | 7.1% |
| Hannah | X | 31.8% | 7.3% | 8.7% | 7.1% | 8.2% | 5.8% | 8.2% | 7.3% | 7.1% | 8.5% |
| Kam | 7.6% | 7.0% | 40.5% | 7.2% | X | 7.0% | 6.9% | 6.5% | 5.3% | 5.0% | 7.0% |
| Kari | 34.1% | 8.2% | 6.7% | 8.4% | 6.5% | 7.7% | 8.0% | 5.8% | X | 6.4% | 8.2% |
| Kathryn | 8.8% | 6.2% | 6.9% | 8.8% | 6.7% | 30.9% | 8.4% | 8.0% | 6.9% | X | 8.4% |
| Shannon | 8.8% | 8.4% | X | 6.0% | 7.1% | 8.3% | 8.7% | 8.2% | 7.1% | 7.0% | 30.2% |
| Taylor | 8.9% | 8.7% | 7.4% | X | 7.2% | 8.2% | 31.2% | 8.2% | 7.4% | 7.2% | 5.7% |
| Tyranny | 7.8% | 7.2% | 5.5% | 7.3% | 5.4% | 7.2% | 7.1% | 6.7% | 40.6% | 5.2% | X |
In the moment, I can see how the possibility of a Truth Booth match is too tempting to give it up for money. Plus can you imagine how hard it would be to tear these couples apart if they weren't confirmed no match? And as a viewer, I don't care about their winnings and just like getting more information!
ReplyDeleteJoey: "I wasn't disrespectful to her! I called her disgusting, and she IS disgusting!"
ReplyDeleteApparently, respectfulness is in the eye of the very drunk beholder.
DeleteI think this episodes major drama is sorta indicative of the dating culture we live in now. These people cant handle "dating" it seems to be all or nothing for them. And maybe thats just bc they have to watch the other "move on" but you gotta let them play the game!!
ReplyDeleteCan you explain how you are calculating/computing the odds of a blackout? (ie, when you say "Blackout odds: 36.0% (1,997,186 out of 5,540,084)") How are you getting the 1,997,186 number without knowing the correct matches? If you knew the actual CORRECT matches you could compare each of the 5,540,084 possibilities to the correct answer to see if it's a blackout. Since you don't know the correct answer, you'd have to think:
ReplyDeleteIf there are 5540084 remaining possibilities, then to compute the odds of a blackout you'd have to compute 5540084*5540084 possibilities... 30,000,000,000,000 possibilities. Basically you'd have to assume that each of the 5540084 remaining possibilities is equally likely to be chosen and each of the 5540084 possibilities is equally likely to be the correct answer, so you'd have a grid of 5540084 x 5540084 and you'd have to calculate whether each of the 30,000,000,000,000 grid squares is a blackout.
If you knew the actual correct matches, the odds of a specific matchup ceremony being a blackout are 0% or 100%, because you'd know whether or not the perfect matches were selected or not.
DeleteWhat I'm doing here is looking at each of the possibilities remaining and calculating how many lights would show up if that possibility were the correct answer. So, in this case, 304,145 of the remaining 1,808,808 possibilities would have shown 0 lights for the week 3 matchup ceremony.
All of my calculations assume that each of the remaining possibilities are equally likely, because there's no information available to suggest otherwise.
Ah OK, you're computing the odds of a blackout after the week's matches are known. That makes sense now.
DeleteI was thinking about calculating the odds of a blackout if YOU DID NOT KNOW who was going to sit with who for the ceremony, and you instead assumed that any permutation is possible as long as the perfect matches are together and the no matches aren't together (and maybe the inferred no matches from a blackout because those are obvious). Then you could theoretically calculate the odds of a blackout before the matches are known. Of course it will always be CLOSE to 36% (derangement), but presumably the knowledge of the no matches would improve their odds.
The difficulty of trying to solve the question "what are the odds that they pick a matchup that ends up being a blackout", then the denominator is "any matchup they could pick," i.e. basically anything other than failed truth booths or blackouts - and in fact in Season 3, Episode 8, the matchup ceremony included a blackout couple, so you're basically back to the 39,916,800 denominator that only moves when there is a perfect match truth booth. I don't think that ends up being very informative.
DeleteSo since there were 4 beams and 4 repeats as episode 1... All four of those couples are confirmed matches? Right??
ReplyDeleteNope! Only two lights showed up in episode 1. In fact, it's possible that none of the 4 repeats are perfect matches.
DeleteDoes the program eliminate results based on the fact that at least two of the four repeats are wrong?
DeleteSo I have a conspiracy theory that they don't actually decide the matches until a few weeks in. I think that in the first few weeks, they just randomly choose the truth booth results/number of beams based on the drama that's going on in the house, then run a program like yours to see what matches are still possible. Then, a few weeks in, they have a smaller number of possible combinations, and they pick the one they think will be the most dramatic. Thoughts?
ReplyDeleteI don't think they would do that because it's too much work.
DeleteMy conspiracy theory is that there are no experts or algorithms, etc. They cast 20 (or 22) people and just match them based on the information they get from the auditions.
I think both conspiracy theories are correct. There are no rules here, if the producers want to rig it, they can rig it. This has been pretty obvious in the last couple of seasons (especially season 3, where they got TWO matches in week 3, and then magically figured out 10 matches the next week).
DeleteIn the end, the producers of MTV have always believed that drama equates to good television. Having the cast figure out the truth booth in Week 1 would be devastating for the show, because there would be no drama. Having a bunch of cast members run around all angst ridden because the "person of their dreams" who they just met 5 minutes ago, isn't their perfect match, is a dream for the producers.
I agree with both of you. I think the only "experts" involved are those who look at the video applications and determine how much drama a cast member would potentially cause. Similarly, the show can't be over in Week 3 or 4, so I am sure that the producers also rig the matches so that the show always drags out 10 "weeks".
My conspiracy theory is that the show doesn't take place over 10 weeks, but rather 10 days. Each "week" we see on the program is a single day, maybe two. Not a big deal, other than it makes the drama about broken relationships seem really insincere.
Jason - your final point is not so much a conspiracy theory but rather, how reality shows are filmed. Any producer can tell you so. No one is going to waste money feeding/housing/filming these people for 10 whole weeks. That would be absurd. So, yes, every "week" in AYTO is likely two or three days in reality. The same goes for The Bachelor franchise and pretty much every reality show you've ever watched. :)
DeleteHi Alex -
ReplyDeleteCould you talk us through your calculations/numbers for the truth booth tradeoff? I've tried to understand, but I just don't get what you're doing there.
Estimated value of forfeiting truth booth for $150,000: $0.2308
Estimated value of going to the truth booth: $0.2415
Estimated value of losing the truth booth: $0.2212
It's worth trading the truth booth for approximately: $205,295
Sure - first of all, thanks for your comment. I realized after reading it that I made a calculation error in real-time, so I've updated those numbers.
DeleteThe quick and short answer is, if the estimated value of forfeiting the truth booth exceeds the value of going to the truth booth, you should forfeit the truth booth. I'm saying "estimated value" instead of "expected value" because my estimations are very imperfect.
I'm calculating the estimated value = prize / num of possibilities remaining * number of matchup ceremonies remaining.
Here's an example calculation for this week:
1,997,186 possibilities remained
~187,735 (9.4%) of those had Ozzy and Carolina together
~1,809,451 (90.6%) did not have Ozzy and Carolina together
Lost truth booth = 500,000 / 1,809,451 * 8
Won truth booth = 500,000 / 187,735 * 8
Go to truth booth = (9.4% * won) + (90.6% * lost)
Trade truth booth = 650,000 / 1,997,186 * 8
Of course, there are many factors ignored here, including future truth booths and the fact that each matchup ceremony yields information that reduces the number of possibilities remaining. There's a lot of chaining there that is too hard for me to calculate!
Hi Alex!
ReplyDeleteI just wanted to say thank you for doing this!! I love being able to come here and read this after every episode to compare predictions! You're doing an awesome job!!!!!
Thanks for posting this. I started tracking all this about halfway through last season when there were a lot less permutations. My programming skills aren't quite up to par to do it from the beginning. So I was happy to see someone else had successfully done it.
ReplyDeleteIt won't post here, but I've got the expected value equations for the game worked out in a bit more detail. Shoot me an email and I'll send them your way (lockedown.jl@gmail.com).
Kam and Edward are a perfect match. In the official trailer, it shows the group celebrating after a truth booth and twenty people are visible.. minus Kam and Edward. Consistent with beams as well
ReplyDeleteWould make the most sense and the trailers last year predicted Emma and Prosper were a match as well when you could see them on the screen in the background
DeleteHi Alex! Would you mind sharing the formulas you use to calculate these tables? Do you use excel? I am so impressed and fascinated by this! I would love to use a spreadsheet like this with my kids at school. Thanks!
ReplyDeleteThere's no formula, I just have a computer program (not Excel) manually check whether each of the 39 million possibilities is possible based on what we know from truth booths and matchup ceremonies.
DeleteI've done it in Excel before. Starting with all the possibilities is a bit much for it to handle though. You could easily simplify it for a lesson. I could send you some examples.
DeleteI think the matches from week 1 are Taylor/Tyler and Eddie/Kam
ReplyDeleteBased on the power couple spinoff Carolina/Hayden, Cassandra/Derrick and Mike/Alicia are 100% perfect matches.
ReplyDelete