Season 3, Episode 6 Probabilities

I won't be around for tonight's episode, so probabilities will come later in the week. If you post the truth booth and matchup ceremony results in the comments, I can get to posting here faster. Thanks!

Update: Thank you for being patient and for helping out!

The Truth Booth revealed that Chuck and Kiki were no match and 708 combinations remain.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	11.3%	20.3%	16.8%	X	12.3%	9.0%	X	9.2%	8.6%	12.4%
Britni	3.2%	12.3%	X	X	14.5%	49.9%	X	11.7%	8.3%	X
Chelsey	X	X	X	Match	X	X	X	X	X	X
Cheyenne	4.8%	9.2%	18.4%	X	15.4%	10.5%	11.0%	X	13.6%	17.2%
Hannah	9.5%	12.7%	X	X	12.0%	12.3%	13.0%	8.8%	10.9%	20.9%
Kayla	6.6%	11.6%	16.8%	X	13.1%	7.3%	13.0%	7.9%	10.2%	13.4%
Kiki	17.5%	X	X	X	X	X	32.1%	21.9%	28.5%	X
Melanie	5.8%	12.6%	19.4%	X	X	X	12.7%	21.6%	13.0%	15.0%
Rashida	4.5%	10.6%	14.8%	X	24.0%	11.0%	9.5%	13.1%	X	12.4%
Stacey	36.7%	10.7%	13.8%	X	8.6%	X	8.8%	5.8%	6.9%	8.6%

Matchup Ceremony

• Chuck - Amanda
• Tyler - Hannah
• Zak - Kayla (repeat from episodes 1 and 5)
• Austin - Cheyenne
• Hunter - Britni (repeat from episodes 1 and 3)
• Alec - Stacey (repeat from episodes 1, 3, and 5)
• Nelson - Kiki
• Devin - Rashida (repeat from episode 3)
• Mike - Melanie

In the matchup ceremony, the pairings selected guaranteed no blackout, because they repeated Zak-Kayla, Hunter-Britni, and Alec-Stacey (1 of whom is a match). It also guaranteed a non-winning combination for the same reason. The number of possible lights ranged from 2 to 7.

The ceremony's 3 perfect matches brought the number of possible combinations down to 275.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	11.3%	18.9%	17.8%	X	10.2%	9.5%	X	10.2%	10.2%	12.0%
Britni	2.5%	12.0%	X	X	14.9%	50.9%	X	11.6%	8.0%	X
Chelsey	X	X	X	Match	X	X	X	X	X	X
Cheyenne	4.7%	10.5%	19.6%	X	16.0%	8.0%	10.5%	X	12.7%	17.8%
Hannah	9.1%	13.1%	X	X	8.4%	13.5%	12.7%	10.2%	11.3%	21.8%
Kayla	7.3%	11.6%	17.5%	X	14.2%	6.5%	12.7%	8.4%	8.4%	13.5%
Kiki	18.5%	X	X	X	X	X	33.1%	21.8%	26.5%	X
Melanie	6.5%	12.7%	21.8%	X	X	X	10.2%	18.9%	14.9%	14.9%
Rashida	4.4%	9.5%	11.6%	X	28.4%	11.6%	11.6%	11.6%	X	11.3%
Stacey	35.6%	11.6%	11.6%	X	8.0%	X	9.1%	7.3%	8.0%	8.7%

I don't think they're moving quickly enough.

Season 3, Episode 5 Probabilities - Live Blog

10:06: Gross challenge. Not excited about this.

10:07: OK, thought they would have to eat the squid.

10:10: OK, I was right.

10:11: Chelsey wins!

10:16: Chelsey goes with Connor and Rashida gets Nelson! Who doesn't like the fish chum all that much. Chelsey-Connor (53.8%) is the obvious pick. Rashida-Nelson (11.4%) is a distant second, but it's better than other options they've had so far.

10:18: Damn, that is a LOT of hair.

10:27: Why are there no sheets on these beds??

Truth Booth

Chelsey and Connor are a perfect match! 2,613 combinations remain.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	7.1%	15.6%	12.4%	X	15.0%	8.7%	X	13.1%	12.9%	15.2%
Britni	3.5%	9.2%	X	X	10.3%	54.2%	8.6%	6.1%	8.2%	X
Chelsey	X	X	X	Match	X	X	X	X	X	X
Cheyenne	9.6%	13.5%	12.6%	X	17.3%	8.4%	13.1%	X	13.0%	12.5%
Hannah	10.3%	13.8%	X	X	11.6%	9.3%	13.1%	13.7%	14.8%	13.5%
Kayla	7.1%	12.2%	11.9%	X	14.6%	5.4%	9.8%	11.4%	12.2%	15.3%
Kiki	12.6%	X	29.5%	X	X	X	20.1%	18.4%	19.5%	X
Melanie	9.8%	13.7%	12.7%	X	X	8.5%	13.4%	14.9%	9.1%	17.9%
Rashida	9.5%	13.3%	11.5%	X	18.9%	5.6%	11.9%	12.8%	X	16.5%
Stacey	30.6%	8.7%	9.3%	X	12.2%	X	10.0%	9.7%	10.4%	9.1%

This confirms that one of Britni-Hunter, Kayla-Zak, and Stacey-Alec are a match.

10:35: Wow, Nelson went from chill to crazy in a matter of minutes. Chuck is hilarious.

10:37: They're having fun watching out the window.

10:42: I like the men and women coordinating their outfits. Great idea.

10:43: 5 weeks in the honeymoon suite can't be too bad.

10:44: Melanie with an early disruptive pick, taking the most likely couple off of the board.

10:51: Alec hasn't reciprocated Stacey's pick despite the fact that they're the second-most likely couple.

10:55: So no additional lights still means a blackout? Interesting angle. That means a blackout is far more likely than my earlier logic, which assumed a truth booth perfect match eliminated blackouts. (UPDATE: See the new logic.)

Matchup Ceremony

• Melanie - Hunter
• Britni - Mike
• Stacey - Alec (repeat from episodes 1 and 3)
• Kayla - Zak (repeat from episode 1)
• Rashida - Nelson
• Cheyenne - Devin
• Hannah - Austin
• Kiki - Chuck (repeat from episodes 3 and 4)
• Amanda - Tyler

Under these conditions, the chances of a blackout are 654 out of 2,613 (25%). This combination is not a winning combination, as it was eliminated in a previous episode. It's 2 perfect matches - the worst possible result, as it still leaves 818 combinations. They're actually worse off than the far harder season 2. We have our first inferred non-match, as Melanie and Hunter are not a couple. (UPDATE: This is an easier explanation than most inferred matches/non-matches, see below.)

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	9.8%	17.6%	14.5%	X	17.0%	7.8%	X	12.1%	7.5%	13.7%
Britni	2.8%	10.6%	X	X	12.6%	56.6%	X	10.1%	7.2%	X
Chelsey	X	X	X	Match	X	X	X	X	X	X
Cheyenne	8.3%	13.1%	15.9%	X	13.3%	9.0%	13.7%	X	11.7%	14.9%
Hannah	10.1%	11.0%	X	X	10.4%	10.6%	13.2%	11.2%	15.3%	18.1%
Kayla	7.2%	11.5%	14.5%	X	15.0%	6.4%	11.2%	9.8%	12.7%	11.6%
Kiki	15.2%	X	13.4%	X	X	X	27.8%	18.9%	24.7%	X
Melanie	7.9%	14.3%	16.7%	X	X	X	13.9%	18.7%	11.2%	17.1%
Rashida	6.8%	12.6%	12.8%	X	20.8%	9.5%	11.1%	11.4%	X	14.9%
Stacey	31.8%	9.3%	12.0%	X	10.9%	X	9.0%	7.7%	9.7%	9.7%

(Programming note: No live blog next week, and the matchup post may be delayed.)

Season 3, Episode 4 Probabilities - Live Blog

10:02: Alec is technically right, if they accrue an extra light each week, they'll get 10 lights during week 10.

10:06: Melanie's boob just hanging out.

10:07: OK, more boobs from Britni.

10:09: "Cutting tension with scissors" isn't exactly the quote.

10:09: This is one of the funniest looking challenges yet.

10:15: Cheyenne / Zak (12.5%) and Britni / Chuck (5.1%) aren't great choices for the competition. Smart of Connor to go for Chelsey but it didn't make it.

10:15: WTF is a manta ray?

10:30: Hannah is awfully confident about Chuck leaving the house even though there's a 95% chance he sticks around.

10:40: No match between Chuck and Britni! 13,410 combinations remain. This is one of the worst truth booth picks in the history of this show, by the way.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	6.7%	19.3%	11.5%	6.6%	14.1%	5.8%	X	11.8%	11.8%	12.5%
Britni	1.6%	6.2%	X	2.0%	6.9%	65.5%	6.4%	5.7%	5.7%	X
Chelsey	X	6.5%	6.2%	53.8%	7.4%	2.0%	7.1%	6.4%	6.4%	4.3%
Cheyenne	6.6%	12.2%	11.5%	6.6%	14.0%	5.8%	12.9%	X	17.8%	12.5%
Hannah	7.3%	13.3%	X	7.2%	15.0%	6.7%	13.6%	12.6%	12.6%	11.8%
Kayla	4.0%	11.1%	10.5%	X	12.8%	2.9%	8.8%	10.5%	10.5%	28.9%
Kiki	8.8%	X	30.9%	8.7%	X	X	18.3%	16.7%	16.7%	X
Melanie	6.8%	12.5%	11.9%	6.7%	X	5.8%	13.2%	18.3%	12.0%	12.8%
Rashida	6.4%	12.0%	11.2%	6.4%	22.1%	5.5%	12.5%	11.4%	X	12.3%
Stacey	51.8%	6.8%	6.4%	2.0%	7.7%	X	7.3%	6.6%	6.6%	4.9%

10:44: This is the earliest they've done the matchup ceremony in a while, so something is up.

10:46: Nelson really mad that Cheyenne was taken from him.

10:48: Devin says fuck the math!

10:50: Rashida should be mad here, Devin is her highest-probability match.

10:56: Tyler wants an in with Rashida.

10:58: Connor wants nothing to do with Kayla.

Matchup Ceremony

• Alec - Amanda
• Tyler - Melanie
• Zak - Cheyenne
• Chuck - Kiki (repeat from episode 3)
• Devin - Hannah
• Mike - Kayla (repeat from episode 3)
• Connor - Chelsey (repeat from episodes 1, 3)
• Nelson - Britni
• Hunter - Rashida
• Austin - Stacey

The chances of a blackout with this specific combination is 18% (2,406 of 13,410). This combination was previously ruled out as a game-winning combination.

2 right means 3,702 combinations remain.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	8.0%	16.3%	10.0%	4.7%	14.5%	7.4%	X	13.1%	13.0%	13.0%
Britni	2.5%	7.6%	X	1.5%	8.1%	59.3%	7.6%	6.8%	6.6%	X
Chelsey	X	4.3%	2.1%	70.6%	5.0%	1.5%	4.9%	4.8%	4.6%	2.2%
Cheyenne	8.0%	13.2%	10.3%	4.8%	14.7%	7.1%	13.2%	X	14.0%	14.8%
Hannah	8.2%	13.3%	X	4.6%	17.7%	7.4%	13.2%	13.1%	13.0%	9.5%
Kayla	5.0%	10.5%	9.3%	X	12.3%	3.8%	11.7%	10.5%	10.6%	26.3%
Kiki	8.9%	X	41.2%	3.0%	X	X	15.6%	15.4%	15.9%	X
Melanie	7.8%	13.2%	10.5%	4.8%	X	6.9%	13.3%	15.5%	14.1%	13.9%
Rashida	7.9%	13.1%	9.9%	5.0%	18.1%	6.6%	12.6%	12.9%	X	13.9%
Stacey	43.8%	8.4%	6.7%	1.0%	9.5%	X	8.0%	7.9%	8.2%	6.4%

This is the worst performance of any season so far. They're almost as far away from succeeding as season 2, which was much harder with the 11th girl. They really don't know what's going on.

Season 3, Episode 3 Probabilities - Live Blog

If you're curious about the chances of a blackout happening, as happened last week, see this post: "What are the odds of a blackout?"

10:04: Oh, she's not wearing a bra.

10:06: OK, Devin has a pretty good point. They all jumped on him for hooking up with a confirmed no match, and now all the couples have to deal with being confirmed non-matches.

10:08: Why wouldn't the smartest guy just stand next to a pole with a tire and let the other guys do the running?

10:09: Wait... if there are only 60 tires, a guy can't stack up his own name 6 times anyway. So the guys who are carrying over their own tires to the poles are doing it wrong.

10:16: WHO IS THIS NERD?

Some relatively weak couples here. Chuck-Amanda (13.3%) is the best choice, with Zak-Kiki (9.6%), and Mike-Britni (6.8%) behind.

10:25: Helicoptering. Bold move.

10:27: Wow, 6 figures at age 22? I guess he's a pretty credible nerd.

10:28: Nerds everywhere!!

10:29: Did Zak just raise the price of prescription drugs 5,000%?

Truth Booth

No match between Zak and Kiki! 57,160 combinations remaining.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	7.5%	13.9%	12.9%	7.5%	16.1%	8.2%	X	12.9%	12.9%	8.2%
Britni	2.2%	7.1%	6.5%	2.5%	8.3%	53.7%	6.5%	6.5%	6.5%	X
Chelsey	X	8.0%	7.6%	46.3%	9.4%	3.1%	7.6%	7.6%	7.6%	2.7%
Cheyenne	7.5%	13.9%	12.9%	7.5%	16.1%	8.2%	12.9%	X	12.9%	8.2%
Hannah	7.5%	13.9%	X	7.5%	16.1%	8.2%	12.9%	12.9%	12.9%	8.2%
Kayla	2.5%	7.2%	6.6%	X	8.4%	2.2%	6.6%	6.6%	6.6%	53.2%
Kiki	10.6%	X	19.7%	10.6%	X	X	19.7%	19.7%	19.7%	X
Melanie	7.8%	14.2%	13.3%	7.8%	X	8.4%	13.3%	13.3%	13.3%	8.4%
Rashida	7.5%	13.9%	12.9%	7.5%	16.1%	8.2%	12.9%	12.9%	X	8.2%
Stacey	46.8%	8.0%	7.5%	2.7%	9.3%	X	7.5%	7.5%	7.5%	3.1%

It's not always a great strategy to keep going down the line, sending the same person into the truth booth repeatedly. You only have a limited number of guesses, so trying to solve one person can be a rabbit hole. In general, the highest probability guess is usually the best one.

10:36: It's hard enough for me to tell the difference between these people at the start of a season, but adding glasses makes it twice as hard.

10:37: Stage 5 clinger.

10:39: These Sour Patch Kid commercials are awful. (But effective?)

10:42: The team can guarantee no blackout by putting forth the 4 people who were matched up in the first episode but not in the second. It's a pretty low-risk strategy.

10:45: Ryan is getting really unusually involved here! SHOTS FIRED

10:52: Devin unleashing the truth!

Matchup Ceremony

• Chelsey - Connor (repeat from Episode 1)
• Kiki - Chuck
• Amanda - Austin
• Rashida - Devin
• Cheyenne - Tyler
• Melanie - Nelson
• Hannah - Zak
• Kayla - Mike
• Stacey - Alec (repeat from episode 1)
• Britni - Hunter (repeat from episode 1)

Guaranteed not to be a blackout since they repeated 3 of the 4 pairs from episode 1 - they know at least one of these is still a match. Also guaranteed not to be a winning combination. Getting 1 or 2 correct here is probably much more useful than getting 3, 4, 5, or 6 right.

3 correct means 14,129 combinations remain.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	6.5%	20.0%	10.9%	6.5%	14.0%	6.4%	X	11.7%	11.7%	12.4%
Britni	1.5%	5.8%	5.1%	1.9%	6.6%	62.2%	6.0%	5.4%	5.4%	X
Chelsey	X	6.4%	5.9%	54.9%	7.2%	2.2%	7.0%	6.2%	6.2%	4.1%
Cheyenne	6.4%	12.2%	10.9%	6.4%	14.0%	6.3%	12.9%	X	18.3%	12.5%
Hannah	7.1%	13.3%	X	7.1%	15.0%	7.2%	13.6%	12.5%	12.5%	11.7%
Kayla	3.8%	11.1%	10.0%	X	12.8%	3.2%	8.8%	10.4%	10.4%	29.7%
Kiki	8.7%	X	29.3%	8.7%	X	X	19.0%	17.2%	17.2%	X
Melanie	6.6%	12.5%	11.3%	6.6%	X	6.4%	13.2%	18.8%	11.9%	12.8%
Rashida	6.2%	12.0%	10.6%	6.2%	22.9%	6.1%	12.4%	11.3%	X	12.3%
Stacey	53.3%	6.7%	6.1%	1.9%	7.5%	X	7.1%	6.4%	6.4%	4.6%

Season 3 - What are the odds of a blackout?

Are You The One? Season 3's twist is that if the matchup ceremony results in 0 perfect matches, the prize is reduced by $250,000. They're calling this a blackout, although the mathematical term is a derangement.

UPDATE: In episode 5, host Ryan Devlin indicates that at least one non-truth-booth match is necessary to avoid a blackout. That increases the chances of a blackout - my guess is that the odds approximately double. Strikeout text below indicates calculations that assumed that a truth booth eliminated the possibility of a blackout, underlined text is what was added after episode 5.

1,334,961 out of the 3,628,880 (36.8%) possible combinations have zero perfect matches. We won't know exactly which 1,334,961 are the zero perfect matches until later in the season, of course.

The probability of a blackout in the first episode is 36.4% are slightly below 1 in 3 at 32.7%. There's a 90% chance of the first truth booth being no match, and then the odds of a blackout in the subsequent matchup is 1,186,632 in 3,265,920 = 36.3%. Add on the 10% chance of a perfect match, then the odds of striking out on the other 9 picks is 133,496 out of 362,880 = 36.8%. That combines to 36.4%.

Note that it's not possible to calculate the odds of a blackout during any subsequent matchup ceremony prior to a perfect match. This is because the contestants don't know which combinations are correct before they go into the matchup ceremony, so oftentimes they will pick a combination that already has been eliminated. The contestants are usually trustworthy enough to not pair up in possibilities that have already been eliminated in truth booths or blackouts, but they don't have the time or tools to ensure that their guess hasn't already been invalidated through other rules.

Overall, though - we know that the chances of a blackout in any given season is more than the 36.4% 32.7% mentioned earlier - it's probably closer to 40% 90%. In fact, we'd expect more than one blackout on average per season. Great money-saving move by MTV.

Obviously, once a perfect match has been identified in the truth booth, the chances of a blackout drop to zero, since the couple is automatically paired in the matchup ceremony.

I do have information at the time of the matchup ceremony what the chances of that combination being a blackout are, and I'll post that with each episode going forward.