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.

Season 3, Episode 2 Probabilities - Live Blog

10:05: USA! Except... uh... 51 states?

10:08: Pretty interesting challenge... memorization and running.

10:09: Am I crazy or does Hannah look like Hannah Davis?

10:17: Kiki crazy

10:17: If this were to follow the same formula as previous seasons, Kiki and Devin could go into the truth booth, come out not a match, and then keep hooking up all season.

10:18 "I'm a GIANT mama's boy."

10:19: Kayla and Connor with some early chemistry.

10:21: OK, Mike may actually be the filet mignon of his craft.

10:28: Refreshing to hear Tyler having a personality other than "I'm just here to have sex."

Truth Booth

10:30: Devin and Kiki have a 9.8% chance of being a perfect match.

10:38: They're always surprised when a truth booth results in not a perfect match, but that's the math for you.

548,821 combinations remain.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	8.8%	8.4%	8.8%	8.8%	9.8%	9.8%	18.9%	8.8%	8.8%	8.8%
Britni	8.6%	8.3%	8.6%	8.6%	9.6%	21.6%	8.6%	8.6%	8.6%	8.6%
Chelsey	8.8%	8.4%	8.8%	18.9%	9.8%	9.8%	8.8%	8.8%	8.8%	8.8%
Cheyenne	8.8%	8.4%	8.8%	8.8%	9.8%	9.8%	8.8%	18.9%	8.8%	8.8%
Hannah	8.8%	8.4%	18.9%	8.8%	9.8%	9.8%	8.8%	8.8%	8.8%	8.8%
Kayla	8.8%	8.4%	8.8%	8.8%	9.8%	9.8%	8.8%	8.8%	8.8%	18.9%
Kiki	10.8%	24.3%	10.8%	10.8%	X	X	10.8%	10.8%	10.8%	10.8%
Melanie	8.6%	8.3%	8.6%	8.6%	21.6%	9.6%	8.6%	8.6%	8.6%	8.6%
Rashida	8.8%	8.4%	8.8%	8.8%	9.8%	9.8%	8.8%	8.8%	18.9%	8.8%
Stacey	18.9%	8.4%	8.8%	8.8%	9.8%	9.8%	8.8%	8.8%	8.8%	8.8%

10:40: What a surprise, my prediction of Kiki and Devin staying together was correct!

10:48: Devin is a math genius apparently.

10:55: Devin reciprocates Melanie's pick from episode 1... but she doesn't seem happy about it.

10:57: LOTS of repeats from episode 1. A zero here would get them a lot closer to getting the right answer (it would leave 63,208 combinations), but it would also dock their prize $250,000.

Matchup Ceremony

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

BLACKOUT! The chances of a blackout with this specific combination was 11.5%. They got really unlucky here.

What are the odds of a blackout?

That reduces the total prize to a 30-year annuity that will pay out $750,000 - or $18,750 per person in present value.

	Alec	Austin	Chuck	Connor	Devin	Hunter	Mike	Nelson	Tyler	Zak
Amanda	7.4%	13.9%	13.3%	7.4%	16.2%	8.0%	X	13.3%	13.3%	7.4%
Britni	2.0%	6.9%	6.5%	2.3%	8.1%	54.8%	6.5%	6.5%	6.5%	X
Chelsey	X	7.7%	7.4%	48.6%	9.0%	2.8%	7.4%	7.4%	7.4%	2.4%
Cheyenne	7.4%	13.9%	13.3%	7.4%	16.2%	8.0%	13.3%	X	13.3%	7.4%
Hannah	7.4%	13.9%	X	7.4%	16.2%	8.0%	13.3%	13.3%	13.3%	7.4%
Kayla	2.8%	7.8%	7.5%	X	9.1%	2.4%	7.5%	7.5%	7.5%	48.1%
Kiki	9.6%	X	17.8%	9.6%	X	X	17.8%	17.8%	17.8%	9.6%
Melanie	7.6%	14.3%	13.7%	7.6%	X	8.2%	13.7%	13.7%	13.7%	7.6%
Rashida	7.4%	13.9%	13.3%	7.4%	16.2%	8.0%	13.3%	13.3%	X	7.4%
Stacey	48.6%	7.7%	7.4%	2.4%	9.0%	X	7.4%	7.4%	7.4%	2.8%

63,208 combinations remain. They know for certain that 2 perfect matches are among: Chelsea - Connor, Stacey - Alec, Britni - Hunter, Kayla - Zak.

New this year, see how the competitors match up by season: