“Are you the one?” is free money
51 comments
·December 12, 2025stevage
This was great, but it skipped over the most interesting bit - how you actually choose which matchups and truth booths. That is, an actual strategy that contestants could use that doesn't require a computer.
karel-3d
A thing to note - the contestants are not allowed to have even pen and paper, as mentioned in the other blogpost. So they need to do these computations in their heads.
rahimnathwani
After he described the rules, my immediate reaction was 'this is like mastermind'. Sure enough, further down the page:
Other than that, in my research I came across a boardgame called Mastermind, which has been around since the 70s. This is a very similar premise - think of it as "Guess Who?" on hard mode.Medea
They have an example that calculates the expected information gained by truth booths and all of the top ones are giving more than one bit. How can this be? It is a yes/no question a max of 1 bit should be possible
tobyjsullivan
The author defines one “bit” as ruling out half the remaining options.
So a yes might rule out 75% of remaining options (for example) which provides 2 bits of information.
hatthew
We have to make a distinction between "expected information gain" vs "maximum information gain". An answer of "yes" generally gains >1 bit, but an answer of "no" generally gains <1 bit, and the average outcome ends up <1. It is impossible for a single yes/no question to have an expected gain of >1; the maximum possible is precisely 1.
tobyjsullivan
The total probabilities add up to 1. But I’m not following how that relates to the average bits.
Despite summing to 1, the exact values of P(true) and P(false) are dependent on the options which have previously been discounted. Then those variables get multiplied by the amount of information gained by either answer.
latortuga
Because when it's true, you also learn about any prior match ups involving those two people.
MarkusQ
That's not how information works. Learning more from one outcome than the other decreases the probability of that outcome occurring, so the expected information (which is the sum of the outcome probability times the outcome information for each of the two possible outcomes) is always less than or equal to one.
If all you can get is a "true" or "false" you expect, at most, one bit of information.
sebastos
Right - but coming back to the original question, if I'm not mistaken, the explanation is that the blogpost is measuring information gained from an actual outcome, as opposed to _expected_ information gain. An example will help:
Say you're trying to guess the number on a 6-sided die that I've rolled. If I wanted to outright tell you the answer, that would be 2.58 bits of information I need to convey. But you're trying to guess it without me telling, so suppose you can ask a yes or no question about the outcome. The maximum of the _expected_ information add is 1 bit. If you ask "was it 4 or greater?", then that is an optimal question, because the expected information gain is min-maxed. That is, the minimum information you can gain is also the maximum: 1 bit. However, suppose you ask "was it a 5?". This is a bad question, because if the answer is no, there are still 5 numbers it could be. Plus, the likelihood of it being 'no' is high: 5/6. However, despite these downsides, it is true that 1/6 times, the answer WILL be yes, and you will gain all 2.58 bits of information in one go. The downside case more than counteracts this and preserves the rules of information theory: the _expected_ information gain is still < 1 bit.
EDIT: D'oh, nevermind. Re-reading the post, it's definitely talking about >1 bit expectations of potential matchings. So I don't know!
kevindamm
It's not a yes/no per contestent, it's per edge between contestants. There are n(n-1)/2 of these.
A true answer for a potential match is actually a state update for all of the (n-1) edges connecting either contestant, that's 2(n-2) edges that can be updated to be false. Some of these may already be known from previous rounds' matchups but that's still more than a single binary.
jncfhnb
I’m not really following. But if you’re told that one of A, B, or C is true; you learn more by being told A is True than if you learn D is True, no?
stevage
You also learn about other pairings now being impossible.
jncfhnb
I saw an episode of this and felt the contestants didn’t seem that interested in winning the money. Just romance. I was curious how suboptimally they tended to play.
codebje
Everything is lined up for sub-optimal play.
For a start, the setting is an emotive one. It's not just a numeric game with arbitrary tokens, it's about "the perfect romantic partner." It would take an unusually self-isolating human to not identify who they feel their perfect match should be and bias towards that, subconsciously or consciously. We (nearly) all seek connection.
Then, it's reality TV. Contestants will be chosen for emotional volatility, and relentlessly manipulated to generate drama. No-one is going to watch a full season of a handful of math nerds take a few minutes to progress a worksheet towards a solution each week coupled with whatever they do to pass the time otherwise.
pants2
I'd watch a game show where you put a variety of math nerds on each team and watch them argue about the optimal strategy. Who's strategy will win? The quant analyst or the bioinformatician? Tune in next week!
bryanhogan
Reminds me a bit of Devils Plan, or other similar reality game shows in Korea / Asia.
bronco21016
We need a ManningCast version of the show. For those unaware, ManningCast is a show following an NFL game with special guests and nontraditional commentary and analysis. Think of it kind of like having the Mannings in the living room while watching an NFL game.
In my hypothetical version of "Are you the one?", the math nerds would be giving commentary and explaining the math behind how they'll solve "Are you the one?" while also hilariously explaining how foolish the contestants' theories are.
nrhrjrjrjtntbt
Need to find out their psycopath screening technique
yaur
Just Ask them to describe Shannon Entropy. If they start talking about information they are out, if they start talking about their crazy cousin they are in.
Yossarrian22
That's because the real game is occurring both before and after the show in modern reality tv competitions. The goal is to be entertaining and get social media followers and potential invites to further reality tv shows.
verteu
Fun post. I'd be interested to know: How many consecutive Truth Booths (or: how many consecutive Match Ups) are needed to narrow down the 10! possibilities to a single one?
Discussing "events" (ie, Truth Booth or Match Up) together muddles the analysis a bit.
I agree with Medea above that a Truth Booth should give at most 1 bit of information.
jncfhnb
If you can only check pairings one at a time I’m not sure it’s possible to do better than greedily solving one person at a time.
gaogao
> Season 8: In this season, they introduced gender fluidity. Whilst an interesting problem on its own, this would have wreaked havoc on my model.
Well I guess free money except for that one. In that one, one of the contestants, Danny, did the math for optimizing their remaining Truth Booths and Match Ups to get it down to a 50/50 shot.
jellevdv
what a nice interactive blogpost, that's amazing all the effort that went into it
wonger_
> I also pitched this idea to The Pudding, and had a great experience with them nerding out about this subject. Though they didn't take my up on my idea, I left with really great and actionable feedback, and I'm looking forward to my next rejection.
Would've been a great Pudding post imo, but oh well, happy to find this nice devblog instead.
ChristopherDrum
I think the part that stings most about this article is when he says, "In my research I came across a boardgame called Mastermind."
My lived childhood is old enough to be someone's "research."
travisjungroth
This brings up an area that’s been on the edge of my curiosity for years: how do you combine the knowledge of the experts (contestants) with logic to do better either than either strategy individually?
It’s mostly about how to elicit the information from the contestants. Once you have the probabilities from them, it seems relatively straightforward.
Yossarrian22
I think you could do some form of Bayesian analysis with the prior being how likely each contestant thought that their available partners were "The One" for each other. Then the truth booth would be used to update your priors.
As a math guy who loves reality tv, I was also drawn to the show and wrote a blog post [0] about how to programmatically calculate the probabilities as the show progresses. It was a lot of fun optimizing it to be performant. You can `pip install ayto` to use it to follow along with the show or try out scenarios.
The linked post is a very thorough treatment of AYTO and a great read. I really like the "guess who" bit on how to maximize the value of guesses. It's a shame the participants aren't allowed to have pen and paper—it makes optimization a lot trickier! I'm impressed they do as well as they do.
[0]: https://danturkel.com/2023/01/25/math-code-are-you-the-one.h...