[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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