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 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.
Truth Booth
No optimal strategy here. Just pick a couple and go into the Truth Booth, which would be a pretty boring room if you took out the TV and green lasers.Learning that a couple was a match would have eliminated 9 * 9! = 3,265,920 combinations, but learning that Shanley and Chris T weren't a match eliminated 9! = 362,880 possible combinations.
| Adam | Chris S | Chris T | Dillan | Dre | Ethan | Joey | John | Ryan | Wesley | |
|---|---|---|---|---|---|---|---|---|---|---|
| Amber | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Ashleigh | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Brittany | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Coleysia | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Jacy | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Jessica | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Kayla | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Paige | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Shanley | 11.1% | 11.1% | X | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% |
| Simone | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
3,265,920 combinations remain.
Matchup Ceremony
Obviously, the only restriction here is don't put Shanley and Chris T together.- Wesley - Kayla
- Ethan - Shanley
- Adam - Brittany
- Dre - Jacy
- John - Simone
- Chris T - Jessica
- Joey - Paige
- Chris S - Ashleigh
- Ryan - Amber
- Dillan - Coleysia
Out of those possible combinations, we have the following probabilities:
| Adam | Chris S | Chris T | Dillan | Dre | Ethan | Joey | John | Ryan | Wesley | |
|---|---|---|---|---|---|---|---|---|---|---|
| Amber | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 8.7% | 8.9% | 8.9% | 19.5% | 8.9% |
| Ashleigh | 8.9% | 19.5% | 9.8% | 8.9% | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 8.9% |
| Brittany | 19.5% | 8.9% | 9.8% | 8.9% | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 8.9% |
| Coleysia | 8.9% | 8.9% | 9.8% | 19.5% | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 8.9% |
| Jacy | 8.9% | 8.9% | 9.8% | 8.9% | 19.5% | 8.7% | 8.9% | 8.9% | 8.9% | 8.9% |
| Jessica | 8.7% | 8.7% | 22.0% | 8.7% | 8.7% | 8.5% | 8.7% | 8.7% | 8.7% | 8.7% |
| Kayla | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 8.7% | 8.9% | 8.9% | 8.9% | 19.5% |
| Paige | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 8.7% | 19.5% | 8.9% | 8.9% | 8.9% |
| Shanley | 9.8% | 9.8% | X | 9.8% | 9.8% | 22.0% | 9.8% | 9.8% | 9.8% | 9.8% |
| Simone | 8.9% | 8.9% | 9.8% | 8.9% | 8.9% | 8.7% | 8.9% | 19.5% | 8.9% | 8.9% |
Stay tuned for next week when the real strategy begins.
