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 - 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.