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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

#71

Post by owenlacey »

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.

Based on my research, MUs perform better than TBs. For my simulated information theories, the MUs gained ~2 bits of information on average vs ~1.1 for TBs.

So if only MUs, we're talking around 10 events - meaning you could get enough information on MUs alone to win the game! Conversely, it would take about 20 events to do this just for TBs.

It's not super obvious from the graphs, but you can just about notice that the purple dots drop a bit lower than the pink ones!

Hope this helps

Re: “Are you the one?” is free money

#72

Post by owenlacey »

komali2 wrote: post #53

I would love to know how the author went about constructing those lovely charts. Some library, or done by hand?

Hey! It's all vanilla html/js/css - which I'm pretty proud of. I wanted something really minimal, and felt most charting libraries were overkill so wanted to keep my bundle size small. I'm thinking of making the interactive parts open source so people can take a look for themselves if that would be helpful

Re: “Are you the one?” is free money

#73

Post by owenlacey »

ChristopherDrum wrote: post #49

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."

Sorry :')

My wife and I bought the game - it's a great turn based came you can play whilst having trashy reality shows on in the background!

Re: “Are you the one?” is free money

#75

Post by owenlacey »

What are some other gameshows one could nerd out about? I'll start:

An obvious one is the traitors, but I dunno if there's much you can do with this one as the contestants rarely gain much concrete information.

"Deal or no deal" / "let's make a deal" would have interesting game theory approaches - probably has a lot of parallels with Monty Hall?

Countdown (UK) - solving the maths puzzles on here using integer programming would be cool

Re: “Are you the one?” is free money

#78

Post by philipwhiuk »

> This time, one guy has two matches which means that there will be eleven girls, but only ten boys.

One thing the show runners do subtle alterations that makes the logic much harder.

The Traitors has to do lots of these tricks when not playing the Celebrity edition because there's a self-selection for the sort of person who has already played Werewolf/Avalon-type games.

Re: “Are you the one?” is free money

#79

Post by vitus »

owenlacey wrote: post #65
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.

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 sufficient. At the extreme of getting a score of 0, you also need the constraint that you're not repeating known-bad pairs. The same applies for pairs ruled out (or in!) from truth booths.

Further, if your score goes down, you need to use that as a signal that one (or more) of the pairs you swapped out was actually correct, and you need to cycle those back in.

I don't know what a human approximation of the entropy-minimization approach looks like in full. Good luck!

Re: “Are you the one?” is free money

#80

Post by yoan9224 »

Love the approach of using information theory to optimize decisions. The concept of "expected information gained" is fascinating - it's basically what good analytics should do: help you ask the right questions to eliminate uncertainty fastest.

The interactive visualizations on this post are fantastic. More technical content should be presented this way. Makes complex probability much more intuitive.

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