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). If either of the women who are perfect matches with the same man is identified at any point as a perfect match, the other woman is kicked out of the house and wins no prize.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. The added factor of the 11th woman multiplies that probability by 10 for 36,288,000 guesses. Put simply, a random guess would have a 1 in 36,288,000 chance of winning (0.000002756%).
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.
11th Girl Strategy
I guess MTV thought last season was too easy (I disagree - I think the group got very lucky!) and added the 11th girl to make the game potentially 10 times harder. The optimal strategy for the men would to never guess Christina and continue playing the game as if she didn't exist - that would bring the game back down to the 3,628,800 permutations and as simple as last season.My guess is that they will probably alternate between men choosing their partners and women choosing their partners as they did last season, which will force Christina to be involved in half of the episodes, further diluting the chances of the team winning.
Episode Jumps Ahead
One of the first things we see is a preview of Day 34 where Anthony indicates he and Jenni are not a perfect match. For the time being, I'll ignore this look-ahead, but in the future, I'll start calculating using this information.Truth Booth
Here, the optimal strategy is once again not to pick Christina. Layton-Alexandria, Brandon-Jessica, and Pratt-Paris are the couples, so they're safe from this. Just pick a couple and go into the Truth Booth.As an aside, Pratt and Paris conniving to stay in the house is a pretty good strategy for fun. If they are a perfect match, they'll spend the remaining 9 episodes together instead of meeting the other 19 people. Seems like a good idea to me.
Jessica and Brandon were nominated. If they were a match and Christina-Brandon weren't a match, that would have eliminated (9 * 9 * 9!) + (10!) = 33,022,080 combinations. If they were a match and Brandon was Christina's perfect match, that would have eliminated 35,925,120 combinations (leaving 9! = 362,880 combinations). Learning that Jessica and Brandon weren't a match eliminated 10 * 9! = 3,628,800 possible combinations.
| Alex | Anthony | Brandon | Curtis | Dario | Garland | John | Layton | Nathan | Pratt | |
|---|---|---|---|---|---|---|---|---|---|---|
| Alexandria | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Ashley | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Briana | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Ellie | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Jasmine | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Jenni | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Jessica | 11.1% | 11.1% | X | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% | 11.1% |
| Paris | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Shelby | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Tyler | 9.9% | 9.9% | 11.1% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% | 9.9% |
| Christina | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% |
32,659,200 combinations remain.
Matchup Ceremony
Obviously, the only restriction here is don't put Brandon and Jessica together.- Layton + Jenni
- Dario + Ashley
- Pratt + Paris
- Curtis + Briana
- John + Jasmine
- Brandon + Christina
- Garland + Alexandria
- Anthony + Jessica
- Nathan + Shelby
- Alex + Ellie
- Tyler not picked
- 1 out of the 9 standard pairings were correct, Brandon + Christina was correct, and Brandon + Tyler are a match.
- 1 out of the 9 standard pairings were correct, another of the 9 women were not paired with Brandon, and Brandon + Christina was correct, and Brandon + Tyler are not a match.
- 2 of the 9 standard pairings were correct, Brandon + Christina were incorrect, and Brandon + Tyler are a match.
- 2 of the 9 standard pairings were correct, Brandon + Christina were incorrect, and Brandon + Tyler are not a match.
| Alex | Anthony | Brandon | Curtis | Dario | Garland | John | Layton | Nathan | Pratt | |
|---|---|---|---|---|---|---|---|---|---|---|
| Alexandria | 8.7% | 8.5% | 11.1% | 8.7% | 8.7% | 19.7% | 8.7% | 8.7% | 8.7% | 8.7% |
| Ashley | 8.7% | 8.5% | 11.1% | 8.7% | 19.7% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% |
| Briana | 8.7% | 8.5% | 11.1% | 19.7% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% |
| Ellie | 19.7% | 8.5% | 11.1% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% |
| Jasmine | 8.7% | 8.5% | 11.1% | 8.7% | 8.7% | 8.7% | 19.7% | 8.7% | 8.7% | 8.7% |
| Jenni | 8.7% | 8.5% | 11.1% | 8.7% | 8.7% | 8.7% | 8.7% | 19.7% | 8.7% | 8.7% |
| Jessica | 9.7% | 23.5% | X | 9.7% | 9.7% | 9.7% | 9.7% | 9.7% | 9.7% | 9.7% |
| Paris | 8.7% | 8.5% | 11.1% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% | 19.7% |
| Shelby | 8.7% | 8.5% | 11.1% | 8.7% | 8.7% | 8.7% | 8.7% | 8.7% | 19.7% | 8.7% |
| Tyler | 9.8% | 9.6% | 12.1% | 9.8% | 9.8% | 9.8% | 9.8% | 9.8% | 9.8% | 9.8% |
| Christina | 8.9% | 8.9% | 19.8% | 8.9% | 8.9% | 8.9% | 8.9% | 8.9% | 8.9% | 8.9% |
Looks like the best strategy in the next episode would be to send Anthony and Jessica through the truth booth. I'll have the calculator up and running next week.
Hey, I created a calculator for the 1st season and after a lot of thinking I finally figured out the best way to deal with the 11th girl and I have updated my calculator. Let me know if you need any assistance. Good luck.
ReplyDeleteCan you share what you did to create this chart? I am very interested in the math behind it. Ive taken some minor stat classes.
DeleteI'm trying to figure out these probabilities as well. Can you please explain how Jessica & Anthony jumped up to 23.5%, just from the first match up ceremony? Thanks!
ReplyDeleteDid you ever figure out what was going on? This is very interesting to me.
DeleteI am just as curious as to how the odds changed. Can you explain your cell formulas?
ReplyDeleteCan you explain why 10! Are the possible permutations?
ReplyDeleteI believe there are 10*10 possible heterosexual couples. And for each match ceremony there are 100 choose 10 possible groups of 10 couples.