Here I'll be keeping track of the possible remaining perfect match combinations (with the help of a computer), and looking into the potential strategy of playing this game. The math work here will be independent of the romance and excitement that comes with the pairings. Unless noted otherwise, assume the probabilities of a matchup here being successful are random, ignoring chemistry and all the parts of the show that are actually fun.
Prize and Probability of Winning
All 20 winners will split a 30-year annuity that will pay out $1,000,000. That means if they elect to take the present day "lump sum," they'll end up with around $25,000 each (in addition to a shot at finding their perfect match and getting some weekly face time on MTV).The number of possible permutations in the original game is 10 factorial = 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800. Put simply, a random guess would have a 1 in 3,628,800 chance of winning (0.00002756%).
The show has multiple challenges where additional information is provided, reducing the number of possible combinations. The contestants only have 10 episodes to find the perfect match, so they'll need to reduce it quickly to have a chance.
Live Blog
11:02: And we're off!11:06: The twist this year is that a "blackout" of no matches reduces the payout by $250,000.
11:07: I was going to say no Asians this year, but Kiki is Asian apparently.
11:10: This got super serious super quickly. Rashida apparently thought making out in the first 3 minutes was planting a flag
11:12: Did nobody tell these people what this show is about? Of course people are going to be making out with multiple people. I feel like it would be way more real if one of the guys was mad that nobody was making out with him.
11:18: Devin is my early favorite.
11:19: Not knowing half of their names might be a problem.
11:20: Make Tyler my new favorite.
11:30: "You're my match" is top quality dirty talk.
11:34: Good strategy to puke with the pants off.
11:37: Hunter and Kiki in the truth booth. Wow, people really don't want to go into the truth booth.
Truth Booth
Hunter and Kiki are not a match. As in season 1, this leaves 3,265,920 combinations.
| Alec | Austin | Chuck | Connor | Devin | Hunter | Mike | Nelson | Tyler | Zak | |
|---|---|---|---|---|---|---|---|---|---|---|
| Amanda | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Britni | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Chelsey | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Cheyenne | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Hannah | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Kayla | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Kiki | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% | X | 11.1% | 11.1% | 11.1% | 11.1% |
| Melanie | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Rashida | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
| Stacey | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% |
11:54: Wow, Nelson blowing up Devin's shit!!!
11:56: How can Stacey and Alec fight like that on just the first pick? What?
Matchup Ceremony
- Hannah - Chuck
- Rashida - Tyler
- Amanda - Mike
- Melanie - Devin
- Chelsey - Connor
- Kiki - Austin
- Stacey - Alec
- Britni - Hunter
- Cheyenne - Nelson
- Kayla - Zak
The chance of this matchup ceremony resulting in a blackout is 36.3% (1,186,632 possible blackout combinations). But there were 2 matches - leaving 608,153 combinations.
| Alec | Austin | Chuck | Connor | Devin | Hunter | Mike | Nelson | Tyler | Zak | |
|---|---|---|---|---|---|---|---|---|---|---|
| Amanda | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 9.8% | 19.5% | 8.9% | 8.9% | 8.9% |
| Britni | 8.7% | 8.5% | 8.7% | 8.7% | 8.7% | 22.0% | 8.7% | 8.7% | 8.7% | 8.7% |
| Chelsey | 8.9% | 8.7% | 8.9% | 19.5% | 8.9% | 9.8% | 8.9% | 8.9% | 8.9% | 8.9% |
| Cheyenne | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 9.8% | 8.9% | 19.5% | 8.9% | 8.9% |
| Hannah | 8.9% | 8.7% | 19.5% | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 8.9% | 8.9% |
| Kayla | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 8.9% | 19.5% |
| Kiki | 9.8% | 22.0% | 9.8% | 9.8% | 9.8% | X | 9.8% | 9.8% | 9.8% | 9.8% |
| Melanie | 8.9% | 8.7% | 8.9% | 8.9% | 19.5% | 9.8% | 8.9% | 8.9% | 8.9% | 8.9% |
| Rashida | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 19.5% | 8.9% |
| Stacey | 19.5% | 8.7% | 8.9% | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 8.9% | 8.9% |
Glad you're back!
ReplyDeleteCan you explain the math that brings you down to 608,153 after the matchup?
ReplyDeleteI wrote a computer program that goes through all of the possible combinations of perfect matches and eliminates the ones that don't fit what we know from truth booth / matchup ceremonies.
DeleteWould you be willing to share your code?
DeleteI've been trying to come up with some code of my own, but it's not working out that well...
This is so interesting to read! Please continue to recap. My office mates and I made a pool lol. Biggest loser buys Starbucks for everyone :-)
ReplyDelete