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.