[HN Gopher] Show HN: Fermi - A Wordle-style game for order-of-ma...
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       Show HN: Fermi - A Wordle-style game for order-of-magnitude
       thinking
        
       I always thought it was cool when someone could make a plausible
       estimate from reasonable guesses. I recently learned that these are
       sometimes named after Enrico Fermi, the famous physicist, and its
       the same technique used to create his famous Fermi paradox.  You
       build a rough logic chain using a few sliders and fixed quantities
       (e.g. weeks per year), and the goal is to get within an order of
       magnitude of the true answer. The math is simple; the thinking is
       the game.  Would love feedback.
        
       Author : andrewrn
       Score  : 47 points
       Date   : 2025-04-09 14:04 UTC (8 hours ago)
        
 (HTM) web link (fermi-game.andrewnoble.me)
 (TXT) w3m dump (fermi-game.andrewnoble.me)
        
       | jy14898 wrote:
       | Some feedback:
       | 
       | 1. Why are factors reorderable? axb = bxa
       | 
       | 2. Why are factors pickable? Is it coincidence that all of todays
       | choices are useful (or did I mess it up)
       | 
       | 3. The ranges/sliders ruin it for me IMO, they pick the order of
       | magnitude for you
        
         | andrewrn wrote:
         | Appreciate all that. You're right about all of these, they're
         | mostly there because I just wanted to get out the door and get
         | feedback.
         | 
         | The reorderability/pickability is a remnant from when there
         | were multiple operations (+-*/), but I figured it still allows
         | the user to build the reasoning. Mathematically it doesn't
         | matter as you said, but there is an intuitive order for the
         | chain of reasoning.
         | 
         | You think the sliders ought to be a wider range?
        
           | jy14898 wrote:
           | > You think the sliders ought to be a wider range?
           | 
           | Perhaps, or just no sliders (or something else). To
           | illustrate, setting all the sliders to the min gets the
           | correct order of magnitude, setting all the sliders to the
           | middle gets the correct answer, and max is only off by 1
           | order.
           | 
           | Maybe the slider just picking the order of magnitude would
           | make it more fun (1e-9 to 1e9 for example, 20 ish steps), not
           | sure. Perhaps the rough range of magnitudes could be a hint
           | provided if the user has no idea?
        
             | andrewrn wrote:
             | These thoughts are all really valuable. I ought to probably
             | pick between general estimation and pure order-of-magnitude
             | stuff. Thanks!
        
           | BoiledCabbage wrote:
           | Some more feedback
           | 
           | > Fermi Game is a brain teaser that challenges your ability
           | to make real-world (if outlandish) estimates using reasonable
           | assumptions and mathematical reasoning.
           | 
           | What assumptions am I making? All the assumptions have all
           | been made for me? What mathematical training am I doing?
           | What's the point of the separate formulas if they are all
           | present and to be used? How is this order of magnitude
           | thinking if all of the orders of magnitude have been already
           | been determined? It kinda feels like "Hey do you like chess?
           | Come play checkers with chess pieces."
           | 
           | > You're right about all of these, they're mostly there
           | because I just wanted to get out the door and get feedback.
           | 
           | I've got no problem if someone has put a bunch of effort in
           | and made a game and wants feedback. But this feels like
           | asking people to come up with your game for you. It feels you
           | kinda you don't see it as a game either yet.
           | 
           | That said, it's always hard to ship things so congrats on
           | shipping something. It's an interesting idea, but spend a bit
           | of time figuring out the game. Good luck with it!
        
             | andrewrn wrote:
             | Hey, I appreciate the thoughts.
             | 
             | Yeah these are things I considered. As a person I have a
             | nasty habit of over-optimizing super hard and never
             | shipping because I am paralyzed by all the considerations.
             | So I forced myself to ship it and face the music. If I end
             | up working on it more, making it a more pure estimation
             | experience is the first thing that I'll do. I also maybe
             | mis-titled calling it "order of magnitude" here. Its more
             | just general estimation.
             | 
             | Thanks again.
        
           | tetha wrote:
           | > You think the sliders ought to be a wider range?
           | 
           | With this presentation, I'd think so.
           | 
           | Like, your presentation says this is an "order of magnitude
           | estimation". However, the slider of "85 - 125 people on a
           | plane" locks me into ~100 people on a plane, ~100k flights,
           | and the hours is a bit weird. However, if I just put that in,
           | I get 200k - 1M people no matter what hours I choose, and
           | about 500k if I choose 1 hour. As an order of magnitude,
           | that's correct and not bad.
           | 
           | Maybe something bigger & coarser could be interesting - high
           | 100s, low 1000s, high 1000s and so on. We use that kind of
           | magnitude estimation at work quite a bit.
           | 
           | It'd also be interesting to see a highlight where you
           | estimated very incorrectly. I'm not certain if I had guessed
           | 100k+ flights / day.
        
             | andrewrn wrote:
             | Awesome, I greatly appreciate the input!!
        
             | jagger27 wrote:
             | Consider this my feedback as well. The slider range feels
             | way too narrow.
        
       | mNovak wrote:
       | It looks very nice visually, but I think the input sliders are
       | way too narrow. Point in fact, in this example they have roughly
       | a 2:1 range, which means virtually any combination of inputs
       | 'wins' the game (is within 1 order of magnitude). That's not
       | particularly fun, is it.
       | 
       | Personally, I approach Fermi estimates as order of magnitude
       | guesses for each factor (e.g. if guessing how many ping pong
       | balls fit in a 747, you might say, "well the width of the jet is
       | closer to 10ft than 100ft", rather than guess 22ft), so having
       | such fine-grained sliders feels like it misses the point.
        
         | andrewrn wrote:
         | This is revealing an important design distinction. The game
         | needs to adapt to different scales. There are huge scale
         | estimations (day 3's question is the volume of air humanity
         | inhales each day, for ex), and smaller ones that are still
         | useful "how many cups of coffee can a barista make in a hour".
         | Both seem like they could still be fun, with the mechanics
         | being more dynamic to the question's scale. Do this seem right?
         | 
         | I ought to make this cleaner in the app. Thanks so much!
        
       | beeftime wrote:
       | Why do I have to pick the factors first? Do I have to use all of
       | them? Why shouldn't I use all of them? If I do, why aren't they
       | already picked?
       | 
       | Why are all of these sliders? Why don't they start at zero? Why
       | do all of them at the default setting result in me winning?
       | 
       | Speaking of, am I winning? Failure and success give me the same
       | feedback. I can play this game over and over until I win? That's
       | not really in the Wordle style.
       | 
       | imo you should be picking from a palette of maybe-relevant
       | factors and increasing/decreasing _their_ order of magnitude and
       | order /operation, then when you submit you're locked into a
       | win/loss state like wordle. This would be much more of a game
       | than what you've got here.
        
         | andrewrn wrote:
         | A better palette of possible factors was something I thought
         | about. It will require rewriting nearly the whole app, but it's
         | likely the direction I'll go when I make v2.
         | 
         | To take it a step further I thought I could use even smaller
         | building blocks via dimensional "toolboxes" like quantity,
         | distance, volume, and conversions and each question files its
         | factors into each tool box (with some dummies like you said).
         | Do you think that'd be more interesting? It's more complex
         | though so mass appeal might go down.
        
           | rappatic wrote:
           | > mass appeal might go down
           | 
           | I don't think Fermi questions have mass appeal anyway. I
           | don't think most people know what "order of magnitude" means,
           | let alone understand dimensional analysis (ie., the
           | conceptual idea of what it means for units to cancel).
           | 
           | I don't think making the game a little more complex would
           | really affect its appeal, because it's already targeted at
           | people with a certain level of scientific understanding.
        
             | andrewrn wrote:
             | Good call. It easy to forget that the world isn't as nerdy
             | as me lol. This would definitely let me focus the game a
             | lot better anyway.
        
               | tgv wrote:
               | OTOH, not so long ago, a colleague and I tried to guess
               | the number of piano tuners in large cities, e.g. New
               | York. I find your idea nice, but the execution could be
               | more flexible, more puzzle-like. E.g., you could have
               | units (like #passengers, #planes, #flights, time), and
               | the user can create factors out of those.
               | 
               | But I'm afraid that it'll lose its appeal after a while.
               | These problems seem same-y to me, more so than Wordle.
        
       | _diyar wrote:
       | Neat idea, reminds me of this clip[1] from a Twitch streamer
       | guessing the Costco price of sliced cheese.
       | 
       | [1] https://www.youtube.com/watch?v=LKoYrpFn-Ls
        
       | bangaladore wrote:
       | My honest opinion is I have no clue what's going on. To some
       | extent it is because traditionally you wouldn't consider this a
       | game like Worlde, other than the fact you presumably release a
       | new setup for each day.
       | 
       | To some extent, the idea could be improved by always including
       | all factors by default and only allowing sliders to be changed.
       | Or allow me to use less factors.
       | 
       | The biggest issue is I have no clue what happened when I clicked
       | guess. Going back I see the reference estimate, but frankly its
       | unclear what that even means (again average person is
       | uninformed). I want something to clearly tell me how close I got,
       | and maybe what percentile I'm in for users who have played today.
       | It's simply not addicting in the way that the other recent Worlde
       | like games are meant to be.
       | 
       | Other nitpicks:
       | 
       | The example popup does not help me understand anything
       | 
       | Its not apparent why the sliders have an initial value nor what
       | the significance is
        
       | hallh wrote:
       | The idea has potential, but needs polishing. When I read the
       | tutorial, I thought that I had to guess the target number using
       | completely unrelated values. Was a bit disappointed to see the
       | "options" were obvious and not really optional, and the scales
       | too limited. Seemed too easy. It would be more entertaining to
       | guess the number of people currently in flight based on x number
       | of full football stadiums, the avg number of eggs laid by y hens
       | per month, etc.
       | 
       | A visual queue of reaching within the success range would do a
       | lot too. Was a bit confused whether I was right or not after
       | submitting the answer.
        
       | crmi wrote:
       | I like the concept.
       | 
       | However the UI is a little confusing (on mobile anyway).
       | 
       | I might suggest you don't present the pre-set range values, as it
       | makes it a lot easier.
       | 
       | Have you considered - perhaps in a way to gamify it a bit more -
       | giving a first hint, and hiding the next 3 unless the player asks
       | for them? It would add an element of 'getting it in 1 go' etc.
       | I'd imagine one or two-shot winners are also more likely to share
       | their results. More potential for your app to go viral.
        
       | zamadatix wrote:
       | I echo what the others say about the current interface.
       | 
       | I think there is an opportunity for "normal" and "hard mode" like
       | Wordle. In normal you are given the names of the factors but have
       | to enter the expressions for their value (no default values
       | given). In hard you have to come up with your own factor names as
       | well as the values (the name is purely aesthetic for the user to
       | keep track of their ideas). The win condition is the same (be
       | within an order of magnitude of the answer) but maybe there is a
       | special "super" win for being within 10% (log scaled, so lower
       | bound n^0.9 and upper bound n^1.1).
        
       | iterance wrote:
       | I am not sure I entirely understand the game. In typical Fermi
       | questions, the goal is to arrive at the appropriate order of
       | magnitude. In this game, the order of magnitude appears to be
       | provided for you. The extrema are ~220k and ~1.8M for the
       | question regarding passengers in the air, and these extrema are
       | less than an order of magnitude apart. Am I misunderstanding
       | something...?
        
       | mrngm wrote:
       | A few thoughts, I tried this on mobile but got a bit confused by
       | the initial "How to play" dialog (besides that it was too large
       | to fit on screen). The dialog says:                 How to play.
       | String together factors to answer the question.
       | 
       | ... but the dialog doesn't pose a question! It just shows two
       | factors with sliders, and the calculated answer, but no reason
       | why we're sliding these two elements from left to right. I would
       | skip the initial dialog for now, and perhaps make the "How to
       | play" dialog very easy to reach to give a general description of
       | the game, what is asked of the player, and how they could think
       | about answering the question, instead of trying to explain the
       | interface.
       | 
       | For the question I got ("How many people are flying in airplanes
       | right now?"), the influencing four factors were nicely chosen,
       | although I would refrain from guiding the player too much with
       | (too) narrow "x - y" bands. We're looking for orders of
       | magnitude, so you could think about sliders that also suggest
       | thinking in orders of magnitude, say "1, 10, 100, 1000" (e.g.
       | number of passengers on a plane), and "10 minutes, 30 minutes, 1
       | hours, 2 hours, 8 hours" (e.g. flight duration).
       | 
       | (Another angle here could be: how many flights and/or passengers
       | does the nearest airport handle during a year, or how many
       | flights/passengers do the global top 10 airports handle during a
       | year, and how does that account for the total amount of flights
       | in a year?). In other words: I don't think you want your players
       | to do _exact_ guesses using these rather precise sliders and
       | narrow bandwidth, but hint them into _also thinking_ in orders of
       | magnitude.
       | 
       | I would skip the clicking on factors (I saw in another comment
       | that you thought about arbitrarily mixing addition and
       | multiplication, and their order in an earlier version, but that
       | seems too difficult), and just give the player a few sliders and
       | their proposed answer directly. Perhaps you can show the proposed
       | answer directly beneath the question, start with 0, and have all
       | sliders set to 0 (instead of the current random values) as well.
       | 
       | Another idea, perhaps even more intuitive, could be to give the
       | player one (easy), two (intermediate) or three sliders (expert),
       | without giving them hints for individual contributing factors:
       | 
       | - (slider 1) 1, 10, 100, 1000, ... for the rough orders of
       | magnitude (e.g. "100")
       | 
       | - (slider 2) 1-9 multiplier for the chosen order of magnitude to
       | give the player a way to say "it's more in the order of 500 than
       | 100"
       | 
       | - (slider 3) 0-9 multiplier for one order of magnitude lower, to
       | give the player a way to say "it's more 550 than 500"
       | 
       | Then the answer is calulated as (1) * (2) + (3). You can then
       | tell the player if their chosen orders of magnitude were correct
       | ("within the chosen order of magnitude"), slightly off (one order
       | of magnitude too high or low), or too far off. Let the player
       | decide if they want to be rather precise (with three sliders), or
       | not.
       | 
       | Or even combine these ideas! Let the player choose a strategy
       | ("guided" as you've already implemented with a couple of factors
       | already given, or "non-guided", for lack of a better term, for
       | those looking for an extra challenge).
       | 
       | Closing nit: "Share results" contains a non-existing domain.
       | 
       | If you need inspiration for future questions, have a look at this
       | recent discussion [0] and linked website [1].
       | 
       | [0] https://news.ycombinator.com/item?id=43389455
       | 
       | [1] https://taylor.town/napkin-math
        
       | bobdigit wrote:
       | A kid/younger audience version of this would be great!
        
       | whiterook6 wrote:
       | I'm on my phone, trying this. It's a question about how many
       | people are in the air right now.
       | 
       | - when I tap on a factor, I can edit the slider, but it doesn't
       | do anything.
       | 
       | - when I tap another factor, the previous editor stays in place.
       | 
       | - how do I choose my factor?
       | 
       | - where do I actually do the multiplication?
       | 
       | - where do I check my answer?
       | 
       | - why do the factors have "grab icons" (the six dots)? Why would
       | I drag one?
       | 
       | https://imgur.com/a/QSRBbYR
       | 
       | Etc.
        
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