Monday, February 24, 2014

Season 1, Episode 5 Probabilities - with blog assistance

MTV is revealing perfect matches for Are You The One? on their blog. This post will keep track of known combinations given the information on the blog.

See the original Episode 5 post if you don't want to be spoiled by the MTV blog.

The contestants are now really close with only 142 combinations remaining after Episode 4.

Blog Reveal

None yet this week.

Truth Booth #1

Dre and Ashleigh had been together in two matchup ceremonies - Episode 2 and less successful Episode 3 (the most successful to-date), so they were a good choice here for one of two truth booths. But they weren't a match - which reduced the number of possible combinations to 56. However, no other combinations were eliminated. This left the following probabilities, with Ashleigh and Dre each now lacking the strong favorite that everyone else has (red = eliminated, yellow = twice as likely as randomly guessing, green = most likely pairing):

AdamChris SChris TDillanDreEthanJoeyJohnRyanWesley
AmberXXXXXMatchXXXX
Ashleigh8.9%26.8%21.4%1.8%XX5.4%10.7%16.1%8.9%
BrittanyX3.6%1.8%7.1%7.1%X55.4%5.4%16.1%3.6%
Coleysia1.8%X1.8%82.1%XXX1.8%1.8%10.7%
Jacy3.6%1.8%X1.8%23.2%X7.1%57.1%5.4%X
Jessica8.9%5.4%16.1%X12.5%X8.9%1.8%19.6%26.8%
Kayla7.1%5.4%10.7%1.8%8.9%X8.9%5.4%14.3%37.5%
Paige5.4%1.8%48.2%3.6%7.1%X14.3%5.4%7.1%7.1%
Shanley62.5%3.6%XX8.9%XX12.5%10.7%1.8%
Simone1.8%51.8%X1.8%32.1%XXX8.9%3.6%

Truth Booth #2

Coleysia and Dillan were the second couple picked for the truth booth. Undoubtedly, the producers chose them to go second for dramatic effect. They had been together on the most number of episodes (3) and the probabilities to this point had suggested that they were the most likely match. And the team finally breaks through with a perfect match! This eliminates only 10 possibilities, but it's good to get someone as 100% certain. Out of the remaining 46 possible combinations, the following are eliminated, including all of the other pairings from episode 3:
  • Jessica - John (paired in episode 3)
  • Kayla - Ryan (paired in episodes 2 and 3)
  • Paige - Chris S (paired in episode 3)
This is especially surprising given how strongly Scali pursues Paige this episode. So her brushing him off ends up being fortunate! The probabilities after the first perfect match:

AdamChris SChris TDillanDreEthanJoeyJohnRyanWesley
AmberXXXXXMatchXXXX
Ashleigh10.9%19.6%19.6%XXX6.5%13.0%19.6%10.9%
BrittanyX4.3%2.2%X8.7%X58.7%4.3%17.4%4.3%
ColeysiaXXXMatchXXXXXX
Jacy2.2%2.2%XX19.6%X4.3%65.2%6.5%X
Jessica8.7%6.5%8.7%X15.2%X10.9%X23.9%26.1%
Kayla8.7%6.5%13.0%X10.9%X10.9%6.5%X43.5%
Paige4.3%X56.5%X8.7%X8.7%4.3%8.7%8.7%
Shanley63.0%4.3%XX10.9%XX6.5%13.0%2.2%
Simone2.2%56.5%XX26.1%XXX10.9%4.3%

Matchup Ceremony

The men go first this time, and many of the guys choose the girls who picked them in episode 2:
  • Ethan - Amber (confirmed match, repeat from episodes 2 and 3)
  • Joey - Jessica
  • Wes - Kayla (repeat from episode 1)
  • John - Jacy (repeat from episode 2)
  • Chris S - Simone (repeat from episode 2)
  • Adam - Shanley (repeat from episode 2)
  • Chris T - Paige (repeat from episode 2)
  • Dre - Brittany
  • Ryan - Ashleigh
The result of 5 of 10 doesn't help much over episode 2's 4 of 10. They were guaranteed at least 4 of 10 correct given information that viewers knew in the past, although this guess was not one of the possible remaining combinations. A bunch of possible pairings are eliminated:
  • Brittany - Chris S
  • Brittany - Chris T
  • Brittany - Dre
  • Brittany - John
  • Jacy - Adam
  • Jacy - Joey (paired in episode 4)
  • Jessica - Joey
  • Kayla - Adam
  • Kayla - John
  • Shanley - Wes
  • Simone - Adam
Only 19 possible combinations left.

AdamChris SChris TDillanDreEthanJoeyJohnRyanWesley
AmberXXXXXMatchXXXX
Ashleigh15.8%10.5%36.8%XXX5.3%10.5%10.5%10.5%
BrittanyXXXXXX68.4%X21.1%10.5%
ColeysiaXXXMatchXXXXXX
JacyX5.3%XX5.3%XX73.7%15.8%X
Jessica10.5%15.8%15.8%X26.3%XXX26.3%5.3%
KaylaX5.3%10.5%X10.5%X15.8%XX57.9%
Paige10.5%X36.8%X15.8%X10.5%10.5%5.3%10.5%
Shanley63.2%5.3%XX10.5%XX5.3%15.8%X
SimoneX57.9%XX31.6%XXX5.3%5.3%

The remaining 19 combinations:
  1. Ashleigh - Chris T, Brittany - Joey, Jacy - John, Jessica - Dre, Kayla - Wesley, Paige - Adam, Shanley - Ryan, Simone - Chris S
  2. Ashleigh - Chris T, Brittany - Joey, Jacy - Ryan, Jessica - Dre, Kayla - Wesley, Paige - John, Shanley - Adam, Simone - Chris S
  3. Ashleigh - Chris T, Brittany - Joey, Jacy - John, Jessica - Ryan, Kayla - Wesley, Paige - Adam, Shanley - Dre, Simone - Chris S
  4. Ashleigh - Chris T, Brittany - Joey, Jacy - John, Jessica - Adam, Kayla - Wesley, Paige - Dre, Shanley - Ryan, Simone - Chris S
  5. Ashleigh - Adam, Brittany - Joey, Jacy - John, Jessica - Chris S, Kayla - Wesley, Paige - Chris T, Shanley - Ryan, Simone - Dre
  6. Ashleigh - Chris T, Brittany - Joey, Jacy - John, Jessica - Chris S, Kayla - Wesley, Paige - Dre, Shanley - Adam, Simone - Ryan
  7. Ashleigh - John, Brittany - Joey, Jacy - Ryan, Jessica - Chris S, Kayla - Wesley, Paige - Chris T, Shanley - Adam, Simone - Dre
  8. Ashleigh - Adam, Brittany - Joey, Jacy - John, Jessica - Ryan, Kayla - Wesley, Paige - Chris T, Shanley - Chris S, Simone - Dre
  9. Ashleigh - John, Brittany - Joey, Jacy - Chris S, Jessica - Ryan, Kayla - Wesley, Paige - Chris T, Shanley - Adam, Simone - Dre
  10. Ashleigh - Chris T, Brittany - Joey, Jacy - John, Jessica - Adam, Kayla - Wesley, Paige - Ryan, Shanley - Dre, Simone - Chris S
  11. Ashleigh - Chris T, Brittany - Wesley, Jacy - John, Jessica - Ryan, Kayla - Dre, Paige - Joey, Shanley - Adam, Simone - Chris S
  12. Ashleigh - Adam, Brittany - Joey, Jacy - Ryan, Jessica - Dre, Kayla - Wesley, Paige - Chris T, Shanley - John, Simone - Chris S
  13. Ashleigh - Chris S, Brittany - Wesley, Jacy - John, Jessica - Ryan, Kayla - Joey, Paige - Chris T, Shanley - Adam, Simone - Dre
  14. Ashleigh - Wesley, Brittany - Ryan, Jacy - John, Jessica - Chris T, Kayla - Joey, Paige - Dre, Shanley - Adam, Simone - Chris S
  15. Ashleigh - Wesley, Brittany - Ryan, Jacy - John, Jessica - Dre, Kayla - Chris T, Paige - Joey, Shanley - Adam, Simone - Chris S
  16. Ashleigh - Ryan, Brittany - Joey, Jacy - John, Jessica - Chris T, Kayla - Chris S, Paige - Wesley, Shanley - Adam, Simone - Dre
  17. Ashleigh - Chris S, Brittany - Ryan, Jacy - John, Jessica - Dre, Kayla - Joey, Paige - Chris T, Shanley - Adam, Simone - Wesley
  18. Ashleigh - Joey, Brittany - Ryan, Jacy - John, Jessica - Chris T, Kayla - Dre, Paige - Wesley, Shanley - Adam, Simone - Chris S
  19. Ashleigh - Ryan, Brittany - Joey, Jacy - Dre, Jessica - Wesley, Kayla - Chris T, Paige - John, Shanley - Adam, Simone - Chris S

10 comments:

  1. Hey, I was just wondering how you're keeping track of the remaining possibilities? I'm using integer linear programming, but I can only solve for the solutions, not the number of solutions.

    ReplyDelete
  2. I wrote a computer program that generates all 3M+ permutations, then removes invalid permutations as new truth booth or matchup ceremony results are added.

    ReplyDelete
  3. I agree with your 19 possible solutions (I too wrote a program to identify each of the 3.6M+ possible solutons, then eliminated invalid ones as results came out). But where are you getting the probabilities for each one? Seems to me that each of the 19 are equally as likely. What information do you have that makes one more likely than any of the others? Thanks.

    ReplyDelete
    Replies
    1. Perhaps frequency with which the pair appears in the remaining solutions?

      SPOILER FOLLOWS:
      Are you considering including the gif clue that pretty clearly suggests brittany and joey as a match and/or the episode description spoiler for episode 7 which suggests Paige w/Chris T?

      Delete
    2. You're right, they are equally likely. My apologies, got the results tangled with a formula I was working on for a strategy post. I'll take the probabilities out.

      Delete
  4. Kay.(SPOILER)..No, the 19 solutions identified do not include the information of the Joey-Brittany match or Paige-Chris T. You can take the 19 above yourself and reduce them to 13 with Joey-Brittany as a match. You can then reduce it to just 5 possibilities if you believe Paige-Chris T. is a match.

    ReplyDelete
  5. I don't know why MTV gives away so much in blogs and episode descriptions but one should be cautious before reading too much into such spoilers.

    Keep in mind the first episode began with teaser scenes from Day 26, Day 31, and Day 41.

    The "Day 41 clip" aired in Episode 5, while I'm pretty certain the other 2 clips have yet to air.

    ReplyDelete
  6. And don't forget we just had the Real World episode description tell us the Exes were moving in the first episode, even though that happened at the end of episode 4.

    ReplyDelete
  7. This comment has been removed by the author.

    ReplyDelete
  8. 1. Coleysia- Dillan
    2. Paige - Chris T.
    3. Amber - Ethan
    4. Jacy -Jon
    5. Kayla- Wes
    6. Britt-Joey
    7. Shanley -Adam
    8. Simone -Chris S
    9. Ashleigh-Ryan
    10. Jessica-Dre
    Not sure about the last three but I think its pretty good!!!! We will see!!! What do you guys think???

    ReplyDelete