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“Are you the one?” is free money

blog.owenlacey.dev

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Re: “Are you the one?” is free money

#81

Post by vitus »

jncfhnb wrote: post #19
verteu wrote: post #11

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.

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.

So, for 10 pairs, 45 guesses (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) in the worst case, and roughly half that on average?

It's interesting how close 22.5 is to the 21.8 bits of entropy for 10!, and that has me wondering how often you would win if you followed this strategy with 18 truth booths followed by one match up (to maintain the same total number of queries).

Simulation suggests about 24% chance of winning with that strategy, with 100k samples. (I simplified each run to "shuffle [0..n), find index of 0".)

Re: “Are you the one?” is free money

#83

Post by CmdDot »

stevage wrote: post #16

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.

In addition to Mastermind, Wordle also falls into the same category.

Optimal play to reduce the search space in both follow the same general pattern - the next check should satisfy all previous feedback, and included entries should be the most probable ones, both of those previously tested, and those not. If entries are equally probable, include the one which eliminates the largest number of remaining possibilities if it is correct.

For wordle, «most probable» is mostly determined by letter frequency - while in Mastermind, it’s pure probability based on previous guesses. For instance, if you play a Mastermind variant with 8 pegs, and get a 2/8 in the first test - each of your 8 pegs had a 1/4 chance of being correct. So you select 2 at random to include in the next guess.

If you then get a 2/8 from the second - you would include 4 previous entries in the next guess, 2 entries from the first that was not used in the second, as well as 2 entries from the 2nd - because the chance you chose the correct entries twice, is less than the chance the two hits are from the 6 you changed.

Re: “Are you the one?” is free money

#84

Post by pixiemagic »

oneeyedpigeon wrote: post #82

Love this article, OP, especially those interactive demos. One small suggestion: > A truth booth is where a male & female ... The use of "male" and "female" as nouns sounds very unnatural. "A man and a woman" would be a little less jarring, imo.

[flagged]

Re: “Are you the one?” is free money

#85

Post by jncfhnb »

bryanhogan wrote: post #32
pants2 wrote: post #26

Earlier quoted context omitted.

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!

Reminds me a bit of Devils Plan, or other similar reality game shows in Korea / Asia.

I saw a couple devils plan and felt they were trying to imply Mathematical scheming without substance. There was one guy who kept talking about “science” but then his “game theory” for a game of mafia was “social distancing” like Covid…

Re: “Are you the one?” is free money

#86

Post by CmdDot »

vitus wrote: post #79
owenlacey wrote: post #65

Earlier quoted context omitted.

Thank you! This is consistent with feedback I got from the pudding, and is ultimately the reason they didn't go ahead with the post. I tried reverse-engineering the information-theory approach to try see what sort of decisions it made. I noticed that for any match up score of X, the following match up would keep exactly X pairs in common. So if they scored 4/10 one week, they would change 6 couples before the next on…

It should be easier to understand the optimal truth booth strategy. Since this is a yes/no type of question, the maximum entropy is 1 bit, as noted by yourself and others. As such, you want to pick a pair where the odds are as close to 50/50 as possible. > Employing that approach alone performed worse than the contestants did in real life, so didn't think it was worth mentioning! Yeah, this alone should not be suffic…

«As such, you want to pick a pair where the odds are as close to 50/50 as possible.»

This is incorrect, the correct strategy is mostly to check the most probable match (the exception being if the people in that match has less possible pairings remaining than the next most probable match).

The value of confirming a match, and thus eliminate all other pairings involving those two from the search space, is much higher than a 50/50 chance of getting a no match and only excluding that single pairing.

Re: “Are you the one?” is free money

#87

Post by jncfhnb »

hatthew wrote: post #24
jncfhnb wrote: post #14

Earlier quoted context omitted.

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?

Yes, you learn more than 1 bit in that case. However, if you are told A is false, you still don't know whether B or C is true, so you gain less than 1 bit. Assuming A, B and C all have equal probability, your average/expected information gain is If you ask the question "which of A, B, or C is true?" then you're not asking a yes/no question, and it's not surprising that you expect to gain more than 1 bit of informatio…

but that’s all consistent. “Expected” gain is less than 1 for the truth booths and sometimes > 1 for actuals; and is > 1 on expected value of the match ups, which aren’t binary questions.

Re: “Are you the one?” is free money

#88

Post by daturkel »

owenlacey wrote: post #64
daturkel wrote: post #40

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 o…

Let's be friends :') Loved your post, really enjoyed getting into the meat of it. I wanted to position mine to a layman, kept asking myself "can I explain this to my Dad?" I think where the post falls short is the absence of a silver bullet that contestants can use to win the game sooner.

Thanks! Optimization was something I'd played with in previous rounds of coding up AYTO simulations, but not in the most recent version. (See the bottom section of this notebook [0]). There's also a very thorough treatment of the problem in a blog post from 2018 by SAS (the software company) [1]. It's surprising how many people have been drawn in by the allure of AYTO!

[0]: https://github.com/daturkel/pyto/blob/master/AYTO_S8.ipynb [1]: https://blogs.sas.com/content/operations/2018/08/14/are-you-...

Re: “Are you the one?” is free money

#89

Post by daturkel »

vasco wrote: post #54
daturkel wrote: post #40

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 o…

And sometimes they just don't do better as a plot point, staying together an extra week after finding out they are not the one because of the intensity of their love (they met 4 days before)

Giving them more credit than they probably deserve but: when you're solving "by hand" like they are in the show, keeping a known non-match couple together may actually be helpful for interpreting the results of a matchup ceremony because you'll know that that couple didn't contribute to the beams.

Re: “Are you the one?” is free money

#90

Post by edgineer »

pixiemagic wrote: post #84
oneeyedpigeon wrote: post #82

Love this article, OP, especially those interactive demos. One small suggestion: > A truth booth is where a male & female ... The use of "male" and "female" as nouns sounds very unnatural. "A man and a woman" would be a little less jarring, imo.

[flagged]

I hear this commonly about using the words "male" and "female." I think it's unfair. For one thing, the military uses them frequently, and so would veterans. Another reason is that their meanings are age-agnostic which helps to emphasize the intent of the speaker--to differentiate on sex alone, not sex plus age.
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